India's growth rate falls to 6.1% in Q1

The country managed a reasonable economic growth of 6.1 per cent during the first quarter of the current fiscal despite the global financial crisis impacting manufacturing and certain services like hotels.

The gross domestic product growth rate during April-June 2009 at 6.1 per cent was higher than 5.8 per cent in the previous quarter, though it witnessed a decline when compared to 7.8 per cent economic expansion recorded during the corresponding period of the last fiscal.

The government have been maintaining that the Indian economy will grow by six per cent growth with upward bias. If agriculture growth does not crash and this trend continues, growth this fiscal would be in line with the expectations of the authorities.

Mining and electricity among industrial sector, and financing among services sector posted higher growth of 7.9, 6.2 and 8.1 per cent, respectively, in the first quarter of this fiscal, against 4.6, 2.7 and 6.9 per cent a year ago.

Construction and community services also managed good growth of 7.1 and 6.8 per cent against 8.4 and 8.2 per cent, respectively.

However, agriculture and manufacturing expanded at a slower rate of 2.4 and 3.4 per cent against three and 5.5 per cent, respectively.

Growth in services like hotels, trade, transport and communication was significantly lower at 8.1 per cent against 13 per cent.

Investing in an IPO !! Steps how to analyse

Here is a simplified idea of how to analyse initial public offerings (IPOs) using technical and fundamental analysis.
There have been raging discussions during the past three years, both, when the Indian IPO market was booming and when it was crashing.
Should we invest in IPOs or rather buy the stock when it comes to the secondary market? The debate over this a long-drawn one with varying answers during boom and bust.
This article will try to give some tools and ratios, which help us decide whether to invest in an IPO or not at any time!
Analysis based on market value (market cap)
Market value in the case of an IPO can be defined as the number of shares available for subscription multiplied by the price per share plus the price per share multiplied by outstanding shares if any.
In the case of analysis, when there is a price band available, it's advisable to do the analysis based on the lowest price.


check 1: Price to Sales (P/S) ratio
This number is derived by dividing the market value by the value of annualised sales. It can also be derived by dividing the price of a share by the sales per share. It is basically an indication of the amount the company is trying to garner from the market vis-a-vis its current business.
A rule of thumb for the P/S ratio when deciding on IPO investment is that lower the P/S ratio the better it is as an investment.
A word of caution is that it should not be the only parameter before deciding.

Check 2: Price to Earnings (or Loss) P/E ratio
This number is derived by dividing the market value by the annualised profits (loss) for the company. It is an indicator of the number of multiples that the market is ready to pay for the stock over its current profit levels.
If the profit is Rs 2,500 crore (Rs 25 billion) and number of equity shares is 1,000, then the P/E is 2.5. Meaning, the market is ready to pay 2.5 times the profit per share to buy the stock.
Thumb Rule for P/E with respect to IPOs
The lower the P/E, the better it is for the investor. In simple terms, a lower P/E means, you are getting to buy something that has the ability to reap high benefits at a very cheap price.
The irony is that during boom times uninformed investors get carried away by high P/E multiples.


check 3: Price to Book value (P/B) ratio
The book value is defined as the difference between total assets and liabilities. In a more crude way, it is also defined as the amount that will be left back after paying all liabilities in case of a closure.
The P/B of an IPO is calculated as market value divided by the book value. It gives an idea on what value the market places on the stock based on its books.
Thumb rule: Lower the P/B the better. It would be advisable for a potential IPO investor to look for IPOs with low P/B. Some of these stocks are called value stocks.
Long-term investors buy such companies and hold on to them till they slowly but steadily grow their business till a day when the share prices might shoot up phenomenally and then exit with huge profits.

Check 4: Price to Tangible Book Value (PTBV) ratio
This number is derived by dividing the market value by the tangible book value. The Tangible Book Value (TBV) is equal to the book value of the company minus the intangible assets.
Intangible assets are those that cannot be seen or felt. Examples include IP rights, goodwill patents, etc. Similar to P/B, it can also be crudely seen as the amount an investor would get if the company ceases to exist and all its assets have to be sold.
The reason it is seen separately is that most intangible assets would be very difficult to sell in case of closure.
Thumb rule: Lower the PBTV the better. A PBTV of 0-1.0 (zero to one) means the company is trading at or below the worth of its own tangible assets. Once the mark crosses one, the risk for the investor too is proportionally higher.
In case of certain companies the PBTV could be negative too.


check 5: Gross margin percentage
The gross margin percentage is derived by dividing the gross margin of the company (the margin before accounting for taxes, depreciation, expenses, etc) by the total value of sales. This gives an idea of what is the percentage of margins for any value of sales.
Thumb rule: Higher the gross margin the better. This in simple terms indicates that the company's product of service has a good margin of income. The higher the gross margin, the better would be the actual profit. For certain industries where costs are very high the gross margin percentage would be low.
In such cases, we need to analyse if it's higher than for other competitors in the same domain of business.

Check 6: Profit margin percentage
This number is derived by dividing the profits by total value of sales. Again, as in the case of gross margin percentage, higher the profit margin percentage, the better it would be to invest in the IPO of that company.
A word of caution, though. The gross profit margin percentage and the profit margin percentage should be analysed for at least 3-4 years to check for consistency.
Some companies might show higher margins due to one off reasons which might not hold true after the IPO.
All the above calculations need to be taken into consideration along with the analysis of the company's management, its business model, the sustainability of its product/service and other such fundamental parameters while deciding to invest in an IPO or not.

Brush up ur DERIVATIVES FUNDAS !!

What are forward contracts?

Derivatives as a term conjures up visions of complex numeric calculations, speculative dealings and comes across as an instrument which is the prerogative of a few ‘smart finance professionals’. In reality it is not so. In fact, a derivative transaction helps cover risk, which would arise on the trading of securities on which the derivative is based and a small investor, can benefit immensely.
A derivative security can be defined as a security whose value depends on the values of other underlying variables. Very often, the variables underlying the derivative securities are the prices of traded securities.
Let us take an example of a simple derivative contract:

• Ram buys a futures contract.
• He will make a profit of Rs 1000 if the price of Infosys rises by Rs 1000.
• If the price is unchanged Ram will receive nothing.
• If the stock price of Infosys falls by Rs 800 he will lose Rs 800.

As we can see, the above contract depends upon the price of the Infosys scrip, which is the underlying security. Similarly, futures trading has already started in Sensex futures and Nifty futures. The underlying security in this case is the BSE Sensex and NSE Nifty.
Derivatives and futures are basically of 3 types:

• Forwards and Futures
• Options
• Swaps

Forward contract
A forward contract is the simplest mode of a derivative transaction. It is an agreement to buy or sell an asset (of a specified quantity) at a certain future time for a certain price. No cash is exchanged when the contract is entered into.
Illustration 1:
Shyam wants to buy a TV, which costs Rs 10,000 but he has no cash to buy it outright. He can only buy it 3 months hence. He, however, fears that prices of televisions will rise 3 months from now. So in order to protect himself from the rise in prices Shyam enters into a contract with the TV dealer that 3 months from now he will buy the TV for Rs 10,000. What Shyam is doing is that he is locking the current price of a TV for a forward contract. The forward contract is settled at maturity. The dealer will deliver the asset to Shyam at the end of three months and Shyam in turn will pay cash equivalent to the TV price on delivery.
Illustration 2:
Ram is an importer who has to make a payment for his consignment in six months time. In order to meet his payment obligation he has to buy dollars six months from today. However, he is not sure what the Re/$ rate will be then. In order to be sure of his expenditure he will enter into a contract with a bank to buy dollars six months from now at a decided rate. As he is entering into a contract on a future date it is a forward contract and the underlying security is the foreign currency.
The difference between a share and derivative is that shares/securities is an asset while derivative instrument is a contract.

What is an Index?

To understand the use and functioning of the index derivatives markets, it is necessary to understand the underlying index. A stock index represents the change in value of a set of stocks, which constitute the index. A market index is very important for the market players as it acts as a barometer for market behavior and as an underlying in derivative instruments such as index futures.
The Sensex and Nifty
In India the most popular indices have been the BSE Sensex and S&P CNX Nifty. The BSE Sensex has 30 stocks comprising the index which are selected based on market capitalization, industry representation, trading frequency etc. It represents 30 large well-established and financially sound companies. The Sensex represents a broad spectrum of companies in a variety of industries. It represents 14 major industry groups. Then there is a BSE national index and BSE 200. However, trading in index futures has only commenced on the BSE Sensex.
While the BSE Sensex was the first stock market index in the country, Nifty was launched by the National Stock Exchange in April 1996 taking the base of November 3, 1995. The Nifty index consists of shares of 50 companies with each having a market capitalization of more than Rs 500 crore.
Futures and stock indices
For understanding of stock index futures a thorough knowledge of the composition of indexes is essential. Choosing the right index is important in choosing the right contract for speculation or hedging. Since for speculation, the volatility of the index is important whereas for hedging the choice of index depends upon the relationship between the stocks being hedged and the characteristics of the index.
Choosing and understanding the right index is important as the movement of stock index futures is quite similar to that of the underlying stock index. Volatility of the futures indexes is generally greater than spot stock indexes.
Everytime an investor takes a long or short position on a stock, he also has an hidden exposure to the Nifty or Sensex. As most often stock values fall in tune with the entire market sentiment and rise when the market as a whole is rising.
Retail investors will find the index derivatives useful due to the high correlation of the index with their portfolio/stock and low cost associated with using index futures for hedging.

Understanding index futures

A futures contract is an agreement between two parties to buy or sell an asset at a certain time in the future at a certain price. Index futures are all futures contracts where the underlying is the stock index (Nifty or Sensex) and helps a trader to take a view on the market as a whole.
Index futures permits speculation and if a trader anticipates a major rally in the market he can simply buy a futures contract and hope for a price rise on the futures contract when the rally occurs. We shall learn in subsequent lessons how one can leverage ones position by taking position in the futures market.
In India we have index futures contracts based on S&P CNX Nifty and the BSE Sensex and near 3 months duration contracts are available at all times. Each contract expires on the last Thursday of the expiry month and simultaneously a new contract is introduced for trading after expiry of a contract.
Example:
Futures contracts in Nifty in July 2001

Contract month	Expiry/settlement
July 2001	July 26
August 2001	August 30
September 2001	September 27

                                On July 27

Contract month	Expiry/settlement
August 2001	August 30
September 2001	September 27
October 2001	October 25

The permitted lot size is 200 or multiples thereof for the Nifty. That is you buy one Nifty contract the total deal value will be 200*1100 (Nifty value)= Rs 2,20,000.
In the case of BSE Sensex the market lot is 50. That is you buy one Sensex futures the total value will be 50*4000 (Sensex value)= Rs 2,00,000.
The index futures symbols are represented as follows:

BSE	NSE
BSXJUN2001 (June contract)	FUTDXNIFTY28-JUN2001
BSXJUL2001 (July contract)	FUTDXNIFTY28-JUL2001
BSXAUG2001 (Aug contract)	FUTDXNIFTY28-AUG2001

In subsequent lessons we will learn about the pricing of index futures.
Options
Stock markets by their very nature are fickle. While fortunes can be made in a jiffy more often than not the scenario is the reverse. Investing in stocks has two sides to it –a) Unlimited profit potential from any upside (remember Infosys, HFCL etc) or b) a downside which could make you a pauper.
Derivative products are structured precisely for this reason -- to curtail the risk exposure of an investor. Index futures and stock options are instruments that enable you to hedge your portfolio or open positions in the market. Option contracts allow you to run your profits while restricting your downside risk.
Apart from risk containment, options can be used for speculation and investors can create a wide range of potential profit scenarios.
We have seen in the Derivatives School how index futures can be used to protect oneself from volatility or market risk. Here we will try and understand some basic concepts of options.
What are options?
Some people remain puzzled by options. The truth is that most people have been using options for some time, because options are built into everything from mortgages to insurance.
An option is a contract, which gives the buyer the right, but not the obligation to buy or sell shares of the underlying security at a specific price on or before a specific date.
‘Option’, as the word suggests, is a choice given to the investor to either honour the contract; or if he chooses not to walk away from the contract.
To begin, there are two kinds of options: Call Options and Put Options.
A Call Option is an option to buy a stock at a specific price on or before a certain date. In this way, Call options are like security deposits. If, for example, you wanted to rent a certain property, and left a security deposit for it, the money would be used to insure that you could, in fact, rent that property at the price agreed upon when you returned. If you never returned, you would give up your security deposit, but you would have no other liability. Call options usually increase in value as the value of the underlying instrument rises.
When you buy a Call option, the price you pay for it, called the option premium, secures your right to buy that certain stock at a specified price called the strike price. If you decide not to use the option to buy the stock, and you are not obligated to, your only cost is the option premium.
Put Options are options to sell a stock at a specific price on or before a certain date. In this way, Put options are like insurance policies
If you buy a new car, and then buy auto insurance on the car, you pay a premium and are, hence, protected if the asset is damaged in an accident. If this happens, you can use your policy to regain the insured value of the car. In this way, the put option gains in value as the value of the underlying instrument decreases. If all goes well and the insurance is not needed, the insurance company keeps your premium in return for taking on the risk.
With a Put Option, you can "insure" a stock by fixing a selling price. If something happens which causes the stock price to fall, and thus, "damages" your asset, you can exercise your option and sell it at its "insured" price level. If the price of your stock goes up, and there is no "damage," then you do not need to use the insurance, and, once again, your only cost is the premium. This is the primary function of listed options, to allow investors ways to manage risk.
Technically, an option is a contract between two parties. The buyer receives a privilege for which he pays a premium. The seller accepts an obligation for which he receives a fee.
We will dwelve further into the mechanics of call/put options in subsequent lessons.

Call option

An option is a contract between two parties giving the taker (buyer) the right, but not the obligation, to buy or sell a parcel of shares at a predetermined price possibly on, or before a predetermined date. To acquire this right the taker pays a premium to the writer (seller) of the contract.
There are two types of options:

• Call Options
• Put Options

Call options
Call options give the taker the right, but not the obligation, to buy the underlying shares at a predetermined price, on or before a predetermined date.
Illustration 1:
Raj purchases 1 Satyam Computer (SATCOM) AUG 150 Call --Premium 8
This contract allows Raj to buy 100 shares of SATCOM at Rs 150 per share at any time between the current date and the end of next August. For this privilege, Raj pays a fee of Rs 800 (Rs eight a share for 100 shares).
The buyer of a call has purchased the right to buy and for that he pays a premium.
Now let us see how one can profit from buying an option.
Sam purchases a December call option at Rs 40 for a premium of Rs 15. That is he has purchased the right to buy that share for Rs 40 in December. If the stock rises above Rs 55 (40+15) he will break even and he will start making a profit. Suppose the stock does not rise and instead falls he will choose not to exercise the option and forego the premium of Rs 15 and thus limiting his loss to Rs 15.

Let us take another example of a call option on the Nifty to understand the concept better.
Nifty is at 1310. The following are Nifty options traded at following quotes.

Option contract	Strike price	Call premium
Dec Nifty	1325	Rs 6,000
	1345	Rs 2,000
Jan Nifty	1325	Rs 4,500
	1345	Rs 5000

A trader is of the view that the index will go up to 1400 in Jan 2002 but does not want to take the risk of prices going down. Therefore, he buys 10 options of Jan contracts at 1345. He pays a premium for buying calls (the right to buy the contract) for 500*10= Rs 5,000/-.
In Jan 2002 the Nifty index goes up to 1365. He sells the options or exercises the option and takes the difference in spot index price which is (1365-1345) * 200 (market lot) = 4000 per contract. Total profit = 40,000/- (4,000*10).
He had paid Rs 5,000/- premium for buying the call option. So he earns by buying call option is Rs 35,000/- (40,000-5000).
If the index falls below 1345 the trader will not exercise his right and will opt to forego his premium of Rs 5,000. So, in the event the index falls further his loss is limited to the premium he paid upfront, but the profit potential is unlimited.

Call Options-Long & Short Positions

When you expect prices to rise, then you take a long position by buying calls. You are bullish.
When you expect prices to fall, then you take a short position by selling calls. You are bearish.

Put Options

A Put Option gives the holder of the right to sell a specific number of shares of an agreed security at a fixed price for a period of time.
eg: Sam purchases 1 INFTEC (Infosys Technologies) AUG 3500 Put --Premium 200
This contract allows Sam to sell 100 shares INFTEC at Rs 3500 per share at any time between the current date and the end of August. To have this privilege, Sam pays a premium of Rs 20,000 (Rs 200 a share for 100 shares).
The buyer of a put has purchased a right to sell. The owner of a put option has the right to sell.
Illustration 2: Raj is of the view that the a stock is overpriced and will fall in future, but he does not want to take the risk in the event of price rising so purchases a put option at Rs 70 on ‘X’. By purchasing the put option Raj has the right to sell the stock at Rs 70 but he has to pay a fee of Rs 15 (premium).
So he will breakeven only after the stock falls below Rs 55 (70-15) and will start making profit if the stock falls below Rs 55.

Illustration 3:

An investor on Dec 15 is of the view that Wipro is overpriced and will fall in future but does not want to take the risk in the event the prices rise. So he purchases a Put option on Wipro.
Quotes are as under:
Spot   Rs 1040
Jan Put at 1050 Rs 10
Jan Put at 1070 Rs 30

He purchases 1000 Wipro Put at strike price 1070 at Put price of Rs 30/-. He pays Rs 30,000/- as Put premium.

His position in following price position is discussed below.

1. Jan Spot price of Wipro = 1020
2. Jan Spot price of Wipro = 1080

In the first situation the investor is having the right to sell 1000 Wipro shares at Rs 1,070/- the price of which is Rs 1020/-. By exercising the option he earns Rs (1070-1020) = Rs 50 per Put, which totals Rs 50,000/-. His net income is Rs (50000-30000) = Rs 20,000.
In the second price situation, the price is more in the spot market, so the investor will not sell at a lower price by exercising the Put. He will have to allow the Put option to expire unexercised. He looses the premium paid Rs 30,000.

Put Options-Long & Short Positions

When you expect prices to fall, then you take a long position by buying Puts. You are bearish.
When you expect prices to rise, then you take a short position by selling Puts. You are bullish.

	CALL OPTIONS	PUT OPTIONS
If you expect a fall in price(Bearish)	Short	Long
If you expect a rise in price (Bullish)	Long	Short

SUMMARY:

CALL OPTION BUYER	CALL OPTION WRITER (Seller)
Pays premium Right to exercise and buy the shares Profits from rising prices Limited losses, Potentially unlimited gain	Receives premium Obligation to sell shares if exercised Profits from falling prices or remaining neutral Potentially unlimited losses, limited gain
PUT OPTION BUYER	PUT OPTION WRITER (Seller)
Pays premium Right to exercise and sell shares Profits from falling prices Limited losses, Potentially unlimited gain	Receives premium Obligation to buy shares if exercised Profits from rising prices or remaining neutral Potentially unlimited losses, limited gain

Hedging

We have seen how one can take a view on the market with the help of index futures. The other benefit of trading in index futures is to hedge your portfolio against the risk of trading. In order to understand how one can protect his portfolio from value erosion let us take an example.
Illustration:
Ram enters into a contract with Shyam that six months from now he will sell to Shyam 10 dresses for Rs 4000. The cost of manufacturing for Ram is only Rs 1000 and he will make a profit of Rs 3000 if the sale is completed.

Cost (Rs)	Selling price	Profit
1000	4000	3000

However, Ram fears that Shyam may not honour his contract six months from now. So he inserts a new clause in the contract that if Shyam fails to honour the contract he will have to pay a penalty of Rs 1000. And if Shyam honours the contract Ram will offer a discount of Rs 1000 as incentive.

Shyam defaults	Shyam honours
1000 (Initial Investment)	3000 (Initial profit)
1000 (penalty from Shyam)	(-1000) discount given to Shyam
- (No gain/loss)	2000 (Net gain)

As we see above if Shyam defaults Ram will get a penalty of Rs 1000 but he will recover his initial investment. If Shyam honours the contract, Ram will still make a profit of Rs 2000. Thus, Ram has hedged his risk against default and protected his initial investment.
The above example explains the concept of hedging. Let us try understanding how one can use hedging in a real life scenario.
Stocks carry two types of risk – company specific and market risk. While company risk can be minimized by diversifying your portfolio market risk cannot be diversified but has to be hedged. So how does one measure the market risk? Market risk can be known from Beta.
Beta measures the relationship between movement of the index to the movement of the stock. The beta measures the percentage impact on the stock prices for 1% change in the index. Therefore, for a portfolio whose value goes down by 11% when the index goes down by 10%, the beta would be 1.1. When the index increases by 10%, the value of the portfolio increases 11%. The idea is to make beta of your portfolio zero to nullify your losses.
Hedging involves protecting an existing asset position from future adverse price movements. In order to hedge a position, a market player needs to take an equal and opposite position in the futures market to the one held in the cash market. Every portfolio has a hidden exposure to the index, which is denoted by the beta. Assuming you have a portfolio of Rs 1 million, which has a beta of 1.2, you can factor a complete hedge by selling Rs 1.2 mn of S&P CNX Nifty futures.
Steps:

1. Determine the beta of the portfolio. If the beta of any stock is not known, it is safe to assume that it is 1.

2.      Short sell the index in such a quantum that the gain on a unit decrease in the index would offset the losses on the rest of his portfolio. This is achieved by multiplying the relative volatility of the portfolio by the market value of his holdings.

Therefore in the above scenario we have to shortsell 1.2 * 1 million = 1.2 million worth of Nifty.
Now let us study the impact on the overall gain/loss that accrues:

	Index up 10%	Index down 10%
Gain/(Loss) in Portfolio	Rs 120,000	(Rs 120,000)
Gain/(Loss) in Futures	(Rs 120,000)	Rs 120,000
Net Effect	Nil	Nil

As we see, that portfolio is completely insulated from any losses arising out of a fall in market sentiment. But as a cost, one has to forego any gains that arise out of improvement in the overall sentiment. Then why does one invest in equities if all the gains will be offset by losses in futures market. The idea is that everyone expects his portfolio to outperform the market. Irrespective of whether the market goes up or not, his portfolio value would increase.
The same methodology can be applied to a single stock by deriving the beta of the scrip and taking a reverse position in the futures market.
Thus, we have seen how one can use hedging in the futures market to offset losses in the cash market.

Speculation

Speculators are those who do not have any position on which they enter in futures and options market. They only have a particular view on the market, stock, commodity etc. In short, speculators put their money at risk in the hope of profiting from an anticipated price change. They consider various factors such as demand supply, market positions, open interests, economic fundamentals and other data to take their positions.
Illustration:
Ram is a trader but has no time to track and analyze stocks. However, he fancies his chances in predicting the market trend. So instead of buying different stocks he buys Sensex Futures.
On May 1, 2001, he buys 100 Sensex futures @ 3600 on expectations that the index will rise in future. On June 1, 2001, the Sensex rises to 4000 and at that time he sells an equal number of contracts to close out his position.
Selling Price : 4000*100            = Rs 4,00,000
Less: Purchase Cost: 3600*100 = Rs 3,60,000
Net gain                                              Rs 40,000
Ram has made a profit of Rs 40,000 by taking a call on the future value of the Sensex. However, if the Sensex had fallen he would have made a loss. Similarly, if would have been bearish he could have sold Sensex futures and made a profit from a falling profit. In index futures players can have a long-term view of the market up to atleast 3 months.

Arbitrage

An arbitrageur is basically risk averse. He enters into those contracts were he can earn riskless profits. When markets are imperfect, buying in one market and simultaneously selling in other market gives riskless profit. Arbitrageurs are always in the look out for such imperfections.
In the futures market one can take advantages of arbitrage opportunities by buying from lower priced market and selling at the higher priced market. In index futures arbitrage is possible between the spot market and the futures market (NSE has provided a special software for buying all 50 Nifty stocks in the spot market.

• Take the case of the NSE Nifty.

·         Assume that Nifty is at 1200 and 3 month’s Nifty futures is at 1300.

·         The futures price of Nifty futures can be worked out by taking the interest cost of 3 months into account.

• If there is a difference then arbitrage opportunity exists.

Let us take the example of single stock to understand the concept better. If Wipro is quoted at Rs 1000 per share and the 3 months futures of Wipro is Rs 1070 then one can purchase ITC at Rs 1000 in spot by borrowing @ 12% annum for 3 months and sell Wipro futures for 3 months at Rs 1070.
Sale                = 1070
Cost= 1000+30 = 1030
Arbitrage profit =    40
These kind of imperfections continue to exist in the markets but one has to be alert to the opportunities as they tend to get exhausted very fast.

Bull Market Strategies

Calls in a Bullish Strategy	Puts in a Bullish Strategy
Bullish Call Spread Strategies	Bullish Put Spread Strategies

Calls in a Bullish Strategy

An investor with a bullish market outlook should buy call options. If you expect the market price of the underlying asset to rise, then you would rather have the right to purchase at a specified price and sell later at a higher price than have the obligation to deliver later at a higher price.

The investor's profit potential buying a call option is unlimited. The investor's profit is the the market price less the exercise price less the premium. The greater the increase in price of the underlying, the greater the investor's profit.
The investor's potential loss is limited. Even if the market takes a drastic decline in price levels, the holder of a call is under no obligation to exercise the option. He may let the option expire worthless.
The investor breaks even when the market price equals the exercise price plus the premium.
An increase in volatility will increase the value of your call and increase your return. Because of the increased likelihood that the option will become in- the-money, an increase in the underlying volatility (before expiration), will increase the value of a long options position. As an option holder, your return will also increase.
A simple example will illustrate the above:
Suppose there is a call option with a strike price of Rs 2000 and the option premium is Rs 100. The option will be exercised only if the value of the underlying is greater than Rs 2000 (the strike price). If the buyer exercises the call at Rs 2200 then his gain will be Rs 200. However, this would not be his actual gain for that he will have to deduct the Rs 200 (premium) he has paid.
The profit can be derived as follows
Profit = Market price - Exercise price - Premium
Profit = Market price – Strike price – Premium.
                 2200 – 2000 – 100 = Rs 100

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Puts in a Bullish Strategy

An investor with a bullish market outlook can also go short on a Put option. Basically, an investor anticipating a bull market could write Put options. If the market price increases and puts become out-of-the-money, investors with long put positions will let their options expire worthless.
By writing Puts, profit potential is limited. A Put writer profits when the price of the underlying asset increases and the option expires worthless. The maximum profit is limited to the premium received.
However, the potential loss is unlimited. Because a short put position holder has an obligation to purchase if exercised. He will be exposed to potentially large losses if the market moves against his position and declines.
The break-even point occurs when the market price equals the exercise price: minus the premium. At any price less than the exercise price minus the premium, the investor loses money on the transaction. At higher prices, his option is profitable.
An increase in volatility will increase the value of your put and decrease your return. As an option writer, the higher price you will be forced to pay in order to buy back the option at a later date , lower is the return.

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Bullish Call Spread Strategies

A vertical call spread is the simultaneous purchase and sale of identical call options but with different exercise prices.
To "buy a call spread" is to purchase a call with a lower exercise price and to write a call with a higher exercise price. The trader pays a net premium for the position.
To "sell a call spread" is the opposite, here the trader buys a call with a higher exercise price and writes a call with a lower exercise price, receiving a net premium for the position.
An investor with a bullish market outlook should buy a call spread. The "Bull Call Spread" allows the investor to participate to a limited extent in a bull market, while at the same time limiting risk exposure.

To put on a bull spread, the trader needs to buy the lower strike call and sell the higher strike call. The combination of these two options will result in a bought spread. The cost of Putting on this position will be the difference between the premium paid for the low strike call and the premium received for the high strike call.
The investor's profit potential is limited. When both calls are in-the-money, both will be exercised and the maximum profit will be realised. The investor delivers on his short call and receives a higher price than he is paid for receiving delivery on his long call.

The investors's potential loss is limited. At the most, the investor can lose is the net premium. He pays a higher premium for the lower exercise price call than he receives for writing the higher exercise price call.
The investor breaks even when the market price equals the lower exercise price plus the net premium. At the most, an investor can lose is the net premium paid. To recover the premium, the market price must be as great as the lower exercise price plus the net premium.
An example of a Bullish call spread:
Let's assume that the cash price of a scrip is Rs 100 and you buy a November call option with a strike price of Rs 90 and pay a premium of Rs 14. At the same time you sell another November call option on a scrip with a strike price of Rs 110 and receive a premium of Rs 4. Here you are buying a lower strike price option and selling a higher strike price option. This would result in a net outflow of Rs 10 at the time of establishing the spread.
Now let us look at the fundamental reason for this position. Since this is a bullish strategy, the first position established in the spread is the long lower strike price call option with unlimited profit potential. At the same time to reduce the cost of puchase of the long position a short position at a higher call strike price is established. While this not only reduces the outflow in terms of premium but his profit potential as well as risk is limited. Based on the above figures the maximum profit, maximum loss and breakeven point of this spread would be as follows:
Maximum profit = Higher strike price - Lower strike price - Net premium                                    paid
                              = 110 - 90 - 10 = 10
Maximum Loss = Lower strike premium - Higher strike premium
                             = 14 - 4 = 10
Breakeven Price = Lower strike price + Net premium paid
                               = 90 + 10 = 100

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Bullish Put Spread Strategies

A vertical Put spread is the simultaneous purchase and sale of identical Put options but with different exercise prices.
To "buy a put spread" is to purchase a Put with a higher exercise price and to write a Put with a lower exercise price. The trader pays a net premium for the position.
To "sell a put spread" is the opposite: the trader buys a Put with a lower exercise price and writes a put with a higher exercise price, receiving a net premium for the position.
An investor with a bullish market outlook should sell a Put spread. The "vertical bull put spread" allows the investor to participate to a limited extent in a bull market, while at the same time limiting risk exposure.

To put on a bull spread, a trader sells the higher strike put and buys the lower strike put.
The bull spread can be created by buying the lower strike and selling the higher strike of either calls or put. The difference between the premiums paid and received makes up one leg of the spread.
The investor's profit potential is limited. When the market price reaches or exceeds the higher exercise price, both options will be out-of-the-money and will expire worthless. The trader will realize his maximum profit, the net premium

The investor's potential loss is also limited. If the market falls, the options will be in-the-money. The puts will offset one another, but at different exercise prices.
The investor breaks-even when the market price equals the lower exercise price less the net premium. The investor achieves maximum profit i.e the premium received, when the market price moves up beyond the higher exercise price (both puts are then worthless).
An example of a bullish put spread.
Lets us assume that the cash price of the scrip is Rs 100. You now buy a November put option on a scrip with a strike price of Rs 90 at a premium of Rs 5 and sell a put option with a strike price of Rs 110 at a premium of Rs 15.
The first position is a short put at a higher strike price. This has resulted in some inflow in terms of premium. But here the trader is worried about risk and so caps his risk by buying another put option at the lower strike price. As such, a part of the premium received goes off and the ultimate position has limited risk and limited profit potential. Based on the above figures the maximum profit, maximum loss and breakeven point of this spread would be as follows:
Maximum profit = Net option premium income or net credit
                             = 15 - 5 = 10
Maximum loss = Higher strike price - Lower strike price - Net premium received
                          = 110 - 90 - 10 = 10
Breakeven Price = Higher Strike price - Net premium income
                               = 110 - 10 = 100

Bear Market Strategies

Puts in a Bearish Strategy	Calls in a Bearish Strategy
Bearish Put Spread Strategies	Bearish Call Spread Strategies

Puts in a Bearish Strategy

When you purchase a put you are long and want the market to fall. A put option is a bearish position. It will increase in value if the market falls. An investor with a bearish market outlook shall buy put options. By purchasing put options, the trader has the right to choose whether to sell the underlying asset at the exercise price. In a falling market, this choice is preferable to being obligated to buy the underlying at a price higher.

An investor's profit potential is practically unlimited. The higher the fall in price of the underlying asset, higher the profits.
The investor's potential loss is limited. If the price of the underlying asset rises instead of falling as the investor has anticipated, he may let the option expire worthless. At the most, he may lose the premium for the option.
The trader's breakeven point is the exercise price minus the premium. To profit, the market price must be below the exercise price. Since the trader has paid a premium he must recover the premium he paid for the option.
An increase in volatility will increase the value of your put and increase your return. An increase in volatility will make it more likely that the price of the underlying instrument will move. This increases the value of the option.

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Calls in a Bearish Strategy
Another option for a bearish investor is to go short on a call with the intent to purchase it back in the future. By selling a call, you have a net short position and needs to be bought back before expiration and cancel out your position.
For this an investor needs to write a call option. If the market price falls, long call holders will let their out-of-the-money options expire worthless, because they could purchase the underlying asset at the lower market price.

The investor's profit potential is limited because the trader's maximum profit is limited to the premium received for writing the option.
Here the loss potential is unlimited because a short call position holder has an obligation to sell if exercised, he will be exposed to potentially large losses if the market rises against his position.
The investor breaks even when the market price equals the exercise price: plus the premium. At any price greater than the exercise price plus the premium, the trader is losing money. When the market price equals the exercise price plus the premium, the trader breaks even.
An increase in volatility will increase the value of your call and decrease your return.
When the option writer has to buy back the option in order to cancel out his position, he will be forced to pay a higher price due to the increased value of the calls.

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Bearish Put Spread Strategies
A vertical put spread is the simultaneous purchase and sale of identical put options but with different exercise prices.
To "buy a put spread" is to purchase a put with a higher exercise price and to write a put with a lower exercise price. The trader pays a net premium for the position.
To "sell a put spread" is the opposite. The trader buys a put with a lower exercise price and writes a put with a higher exercise price, receiving a net premium for the position.
To put on a bear put spread you buy the higher strike put and sell the lower strike put.
You sell the lower strike and buy the higher strike of either calls or puts to set up a bear spread.
An investor with a bearish market outlook should: buy a put spread. The "Bear Put Spread" allows the investor to participate to a limited extent in a bear market, while at the same time limiting risk exposure.

The investor's profit potential is limited. When the market price falls to or below the lower exercise price, both options will be in-the-money and the trader will realize his maximum profit when he recovers the net premium paid for the options.
The investor's potential loss is limited. The trader has offsetting positions at different exercise prices. If the market rises rather than falls, the options will be out-of-the-money and expire worthless. Since the trader has paid a net premium
The investor breaks even when the market price equals the higher exercise price less the net premium. For the strategy to be profitable, the market price must fall. When the market price falls to the high exercise price less the net premium, the trader breaks even. When the market falls beyond this point, the trader profits.
An example of a bearish put spread.
Lets assume that the cash price of the scrip is Rs 100. You buy a November put option on a scrip with a strike price of Rs 110 at a premium of Rs 15 and sell a put option with a strike price of Rs 90 at a premium of Rs 5.
In this bearish position the put is taken as long on a higher strike price put with the outgo of some premium. This position has huge profit potential on downside. If the trader may recover a part of the premium paid by him by writing a lower strike price put option. The resulting position is a mildly bearish position with limited risk and limited profit profile. Though the trader has reduced the cost of taking a bearish position, he has also capped the profit portential as well. The maximum profit, maximum loss and breakeven point of this spread would be as follows:
Maximum profit = Higher strike price option - Lower strike price option                                   - Net premium paid
                          = 110 - 90 - 10 = 10
Maximum loss = Net premium paid
                          = 15 - 5 = 10
Breakeven Price = Higher strike price - Net premium paid
                         = 110 - 10 = 100

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Bearish Call Spread Strategies
A vertical call spread is the simultaneous purchase and sale of identical call options but with different exercise prices.
To "buy a call spread" is to purchase a call with a lower exercise price and to write a call with a higher exercise price. The trader pays a net premium for the position.
To "sell a call spread" is the opposite: the trader buys a call with a higher exercise price and writes a call with a lower exercise price, receiving a net premium for the position.
To put on a bear call spread you sell the lower strike call and buy the higher strike call. An investor sells the lower strike and buys the higher strike of either calls or puts to put on a bear spread.
An investor with a bearish market outlook should: sell a call spread. The "Bear Call Spread" allows the investor to participate to a limited extent in a bear market, while at the same time limiting risk exposure.

The investor's profit potential is limited. When the market price falls to the lower exercise price, both out-of-the-money options will expire worthless. The maximum profit that the trader can realize is the net premium: The premium he receives for the call at the higher exercise price.
Here the investor's potential loss is limited. If the market rises, the options will offset one another. At any price greater than the high exercise price, the maximum loss will equal high exercise price minus low exercise price minus net premium.
The investor breaks even when the market price equals the lower exercise price plus the net premium. The strategy becomes profitable as the market price declines. Since the trader is receiving a net premium, the market price does not have to fall as low as the lower exercise price to breakeven.

An example of a bearish call spread.
Let us assume that the cash price of the scrip is Rs 100. You now buy a November call option on a scrip with a strike price of Rs 110 at a premium of Rs 5 and sell a call option with a strike price of Rs 90 at a premium of Rs 15.
In this spread you have to buy a higher strike price call option and sell a lower strike price option. As the low strike price option is more expensive than the higher strike price option, it is a net credit startegy. The final position is left with limited risk and limited profit. The maximum profit, maximum loss and breakeven point of this spread would be as follows:
Maximum profit = Net premium received
                               = 15 - 5 = 10
Maximum loss = Higher strike price option - Lower strike price option -                                  Net premium received
                          = 110 - 90 - 10 = 10
Breakeven Price = Lower strike price + Net premium paid
                               = 90 + 10 = 100

Stable Market Strategies

Straddles in a Stable Market Outlook

Volatile market trading strategies are appropriate when the trader believes the market will move but does not have an opinion on the direction of movement of the market. As long as there is significant movement upwards or downwards, these strategies offer profit opportunities. A trader need not be bullish or bearish. He must simply be of the opinion that the market is volatile. This market outlook is also referred to as "neutral volatility."

·         A straddle is the simultaneous purchase (or sale) of two identical options, one a call and the other a put.

·         To "buy a straddle" is to purchase a call and a put with the same exercise price and expiration date.

·         To "sell a straddle" is the opposite: the trader sells a call and a put with the same exercise price and expiration date.

A trader, viewing a market as stable, should: write option straddles. A "straddle sale" allows the trader to profit from writing calls and puts in a stable market environment.

The investor's profit potential is limited. If the market remains stable, traders long out-of-the-money calls or puts will let their options expire worthless. Writers of these options will not have be called to deliver and will profit from the sum of the premiums received.
The investor's potential loss is unlimited. Should the price of the underlying rise or fall, the writer of a call or put would have to deliver, exposing himself to unlimited loss if he has to deliver on the call and practically unlimited loss if on the put.
The breakeven points occur when the market price at expiration equals the exercise price
plus the premium and minus the premium. The trader is short two positions and thus, two breakeven points; One for the call (common exercise price plus the premiums paid), and one for the put (common exercise price minus the premiums paid).
Strangles in a Stable Market Outlook
A strangle is similar to a straddle, except that the call and the put have different exercise prices. Usually, both the call and the put are out-of-the-money.
To "buy a strangle" is to purchase a call and a put with the same expiration date, but different exercise prices. Usually the call strike price is higher than the put strike price.
To "sell a strangle" is to write a call and a put with the same expiration date, but different exercise prices.
A trader, viewing a market as stable, should: write strangles.
A "strangle sale" allows the trader to profit from a stable market.
The investor's profit potential is: unlimited.
If the market remains stable, investors having out-of-the-money long put or long call positions will let their options expire worthless.
The investor's potential loss is: unlimited.
If the price of the underlying interest rises or falls instead of remaining stable as the trader anticipated, he will have to deliver on the call or the put.
The breakeven points occur when market price at expiration equals...the high exercise price plus the premium and the low exercise price minus the premium.
The trader is short two positions and thus, two breakeven points. One for the call (high exercise price plus the premiums paid), and one for the put (low exercise price minus the premiums paid).

Why would a trader choose to sell a strangle rather than a straddle?
The risk is lower with a strangle. Although the seller gives up a substantial amount of potential profit by selling a strangle rather than a straddle, he also holds less risk. Notice that the strangle requires more of a price move in both directions before it begins to lose money.
Long Butterfly Call Spread Strategy The long butterfly call spread is a combination of a bull spread and a bear spread, utilizing calls and three different exercise prices.
A long butterfly call spread involves:

·         Buying a call with a low exercise price,

·         Writing two calls with a mid-range exercise price,

·         Buying a call with a high exercise price.

To put on the September 40-45-50 long butterfly, you: buy the 40 and 50 strike and sell two 45 strikes.
This spread is put on by purchasing one each of the outside strikes and selling two of the inside strike. To put on a short butterfly, you do just the opposite.
The investor's profit potential is limited.
Maximum profit is attained when the market price of the underlying interest equals the mid-range exercise price (if the exercise prices are symmetrical).

The investor's potential loss is: limited.
The maximum loss is limited to the net premium paid and is realized when the market price of the underlying asset is higher than the high exercise price or lower than the low exercise price.
The breakeven points occur when the market price at expiration equals ... the high exercise price minus the premium and the low exercise price plus the premium. The strategy is profitable when the market price is between the low exercise price plus the net premium and the high exercise price minus the net premium.

Pricing of options

Options are used as risk management tools and the valuation or pricing of the instruments is a careful balance of market factors.
There are four major factors affecting the Option premium:

• Price of Underlying
• Time to Expiry
• Exercise Price Time to Maturity
• Volatility of the Underlying

And two less important factors:

• Short-Term Interest Rates
• Dividends

Review of Options Pricing Factors

The Intrinsic Value of an Option
The intrinsic value of an option is defined as the amount by which an option is in-the-money, or the immediate exercise value of the option when the underlying position is marked-to-market.
For a call option: Intrinsic Value = Spot Price - Strike Price
For a put option: Intrinsic Value = Strike Price - Spot Price
The intrinsic value of an option must be positive or zero. It cannot be negative. For a call option, the strike price must be less than the price of the underlying asset for the call to have an intrinsic value greater than 0. For a put option, the strike price must be greater than the underlying asset price for it to have intrinsic value.
Price of underlying
The premium is affected by the price movements in the underlying
instrument. For Call options – the right to buy the underlying at a fixed strike
price – as the underlying price rises so does its premium. As the underlying price falls so does the cost of the option premium. For Put options – the right to sell the underlying at a fixed strike
price – as the underlying price rises, the premium falls; as the underlying price falls the premium cost rises.
The following chart summarises the above for Calls and Puts.

Option	Underlying price	Premium cost
Call
Put

The Time Value of an Option
Generally, the longer the time remaining until an option’s expiration, the higher its premium will be. This is because the longer an option’s lifetime, greater is the possibility that the underlying share price might move so as to make the option in-the-money. All other factors affecting an option’s price remaining the same, the time value portion of an option’s premium will decrease (or decay) with the passage of time.
Note: This time decay increases rapidly in the last several weeks of an option’s life. When an option expires in-the-money, it is generally worth only its intrinsic value.

Option	Time to expiry	Premium cost
Call
Put

Volatility
Volatility is the tendency of the underlying security’s market price to fluctuate either up or down. It reflects a price change’s magnitude; it does not imply a bias toward price movement in one direction or the other. Thus, it is a major factor in determining an option’s premium. The higher the volatility of the underlying stock, the higher the premium because there is a greater possibility that the option will move in-the-money. Generally, as the volatility of an under-lying stock increases, the premiums of both calls and puts overlying that stock increase, and vice versa.
Higher volatility=Higher premium
Lower volatility = Lower premium

Option	Volatility	Premium cost
Call
Put

Interest rates
In general interest rates have the least influence on options and equate approximately to the cost of carry of a futures contract. If the size of the options contract is very large, then this factor may take on
some importance. All other factors being equal as interest rates rise, premium costs fall and vice versa. The relationship can be thought of as an opportunity cost. In order to buy an option, the buyer must either borrow funds or use funds on deposit. Either way the buyer incurs an interest rate cost. If interest rates are rising, then the opportunity cost of buying options increases and to compensate the buyer premium costs fall. Why should the buyer be compensated? Because the option writer receiving the premium can place the funds on deposit and receive more interest than was previously anticipated. The situation is reversed when interest rates fall – premiums rise. This time it is the writer who needs to be compensated.

Option	Interest rates	Premium cost
Call
Put

 How do we measure the impact of change in each of these pricing determinants on option premium we shall learn in the next module.

Greeks

The options premium is determined by the three factors mentioned earlier – intrinsic value, time value and volatility. But there are more sophisticated tools used to measure the potential variations of options premiums. They are as follows:

• Delta
• Gamma
• Vega
• Rho

Delta
Delta is the measure of an option’s sensitivity to changes in the price of the underlying asset. Therefore, its is the degree to which an option price will move given a change in the underlying stock or index price, all else being equal.

               Change in option premium
Delta = --------------------------------
               Change in underlying price

For example, an option with a delta of 0.5 will move Rs 5 for every change of Rs 10 in the underlying stock or index.
Illustration:
A trader is considering buying a Call option on a futures contract, which has a price of Rs 19. The premium for the Call option with a strike price of Rs 19 is 0.80. The delta for this option is +0.5. This means that if the price of the underlying futures contract rises to Rs 20 – a rise of Re 1 – then the premium will increase by 0.5 x 1.00 = 0.50. The new option premium will be 0.80 + 0.50 = Rs 1.30.
Far out-of-the-money calls will have a delta very close to zero, as the change in underlying price is not likely to make them valuable or cheap. An at-the-money call would have a delta of 0.5 and a deeply in-the-money call would have a delta close to 1.
While Call deltas are positive, Put deltas are negative, reflecting the fact that the put option price and the underlying stock price are inversely related. This is because if you buy a put your view is bearish and expect the stock price to go down. However, if the stock price moves up it is contrary to your view therefore, the value of the option decreases. The put delta equals the call delta minus 1.
It may be noted that if delta of your position is positive, you desire the underlying asset to rise in price. On the contrary, if delta is negative, you want the underlying asset’s price to fall.
Uses: The knowledge of delta is of vital importance for option traders because this parameter is heavily used in margining and risk management strategies. The delta is often called the hedge ratio. e.g. if you have a portfolio of ‘n’ shares of a stock then ‘n’ divided by the delta gives you the number of calls you would need to be short (i.e. need to write) to create a riskless hedge – i.e. a portfolio which would be worth the same whether the stock price rose by a very small amount or fell by a very small amount.
In such a "delta neutral" portfolio any gain in the value of the shares held due to a rise in the share price would be exactly offset by a loss on the value of the calls written, and vice versa.
Note that as the delta changes with the stock price and time to expiration the number of shares would need to be continually adjusted to maintain the hedge. How quickly the delta changes with the stock price is given by gamma, which we shall learn subsequently.

Gamma

This is the rate at which the delta value of an option increases or decreases as a result of a move in the price of the underlying instrument.

                  Change in an option delta
Gamma = -------------------------------------
                  Change in underlying price

For example, if a Call option has a delta of 0.50 and a gamma of 0.05, then a rise of ±1 in the underlying means the delta will move to 0.55 for a price rise and 0.45 for a price fall. Gamma is rather like the rate of change in the speed of a car – its acceleration – in moving from a standstill, up to its cruising speed, and braking back to a standstill. Gamma is greatest for an ATM (at-the-money) option (cruising) and falls to zero as an option moves deeply ITM (in-the-money ) and OTM (out-of-the-money) (standstill).
If you are hedging a portfolio using the delta-hedge technique described under "Delta", then you will want to keep gamma as small as possible as the smaller it is the less often you will have to adjust the hedge to maintain a delta neutral position. If gamma is too large a small change in stock price could wreck your hedge. Adjusting gamma, however, can be tricky and is generally done using options -- unlike delta, it can't be done by buying or selling the underlying asset as the gamma of the underlying asset is, by definition, always zero so more or less of it won't affect the gamma of the total portfolio.
Theta
It is a measure of an option’s sensitivity to time decay. Theta is the change in option price given a one-day decrease in time to expiration. It is a measure of time decay (or time shrunk). Theta is generally used to gain an idea of how time decay is affecting your portfolio.

                  Change in an option premium
Theta = --------------------------------------
                  Change in time to expiry

Theta is usually negative for an option as with a decrease in time, the option value decreases. This is due to the fact that the uncertainty element in the price decreases.
Assume an option has a premium of 3 and a theta of 0.06. After one day it will decline to 2.94, the second day to 2.88 and so on. Naturally other factors, such as changes in value of the underlying stock will alter the premium. Theta is only concerned with the time value. Unfortunately, we cannot predict with accuracy the change’s in stock market’s value, but we can measure exactly the time remaining until expiration.

Vega

This is a measure of the sensitivity of an option price to changes in market volatility. It is the change of an option premium for a given change – typically 1% – in the underlying volatility.

                  Change in an option premium
Vega = -----------------------------------------
                      Change in volatility

If for example, XYZ stock has a volatility factor of 30% and the current premium is 3, a vega of .08 would indicate that the premium would increase to 3.08 if the volatility factor increased by 1% to 31%. As the stock becomes more volatile the changes in premium will increase in the same proportion. Vega measures the sensitivity of the premium to these changes in volatility.
What practical use is the vega to a trader? If a trader maintains a delta neutral position, then it is possible to trade options purely in terms of volatility – the trader is not exposed to changes in underlying prices.

Rho

The change in option price given a one percentage point change in the risk-free interest rate. Rho measures the change in an option’s price per unit increase –typically 1% – in the cost of funding the underlying.

                      Change in an option premium
Rho = ---------------------------------------------------
                  Change in cost of funding underlying

Example:
Assume the value of Rho is 14.10. If the risk free interest rates go up by 1% the price of the option will move by Rs 0.14109. To put this in another way: if the risk-free interest rate changes by a small amount, then the option value should change by 14.10 times that amount. For example, if the risk-free interest rate increased by 0.01 (from 10% to 11%), the option value would change by 14.10*0.01 = 0.14. For a put option the relationship is inverse. If the interest rate goes up the option value decreases and therefore, Rho for a put option is negative. In general Rho tends to be small except for long-dated options.

Options Pricing Models

There are various option pricing models which traders use to arrive at the right value of the option. Some of the most popular models have been enumerated below.
The Binomial Pricing Model
The binomial model is an options pricing model which was developed by William Sharpe in 1978. Today, one finds a large variety of pricing models which differ according to their hypotheses or the underlying instruments upon which they are based (stock options, currency options, options on interest rates).
The Black & Scholes Model
The Black & Scholes model was published in 1973 by Fisher Black and Myron Scholes. It is one of the most popular options pricing models. It is noted for its relative simplicity and its fast mode of calculation: unlike the binomial model, it does not rely on calculation by iteration.
The intention of this section is to introduce you to the basic premises upon which this pricing model rests. A complete coverage of this topic is material for an advanced course
The Black-Scholes model is used to calculate a theoretical call price (ignoring dividends paid during the life of the option) using the five key determinants of an option's price: stock price, strike price, volatility, time to expiration, and short-term (risk free) interest rate.
The original formula for calculating the theoretical option price (OP) is as follows:

Where:


The variables are:
S = stock price
X = strike price
t = time remaining until expiration, expressed as a percent of a year
r = current continuously compounded risk-free interest rate
v = annual volatility of stock price (the standard deviation of the short-term returns over one year).
ln = natural logarithm
N(x) = standard normal cumulative distribution function
e = the exponential function
Lognormal distribution: The model is based on a lognormal distribution of stock prices, as opposed to a normal, or bell-shaped, distribution. The lognormal distribution allows for a stock price distribution of between zero and infinity (ie no negative prices) and has an upward bias (representing the fact that a stock price can only drop 100 per cent but can rise by more than 100 per cent).
Risk-neutral valuation: The expected rate of return of the stock (ie the expected rate of growth of the underlying asset which equals the risk free rate plus a risk premium) is not one of the variables in the Black-Scholes model (or any other model for option valuation). The important implication is that the price of an option is completely independent of the expected growth of the underlying asset. Thus, while any two investors may strongly disagree on the rate of return they expect on a stock they will, given agreement to the assumptions of volatility and the risk free rate, always agree on the fair price of the option on that underlying asset.
The key concept underlying the valuation of all derivatives -- the fact that price of an option is independent of the risk preferences of investors -- is called risk-neutral valuation. It means that all derivatives can be valued by assuming that the return from their underlying assets is the risk free rate.
Limitation: Dividends are ignored in the basic Black-Scholes formula, but there are a number of widely used adaptations to the original formula, which I use in my models, which enable it to handle both discrete and continuous dividends accurately.
However, despite these adaptations the Black-Scholes model has one major limitation: it cannot be used to accurately price options with an American-style exercise as it only calculates the option price at one point in time -- at expiration. It does not consider the steps along the way where there could be the possibility of early exercise of an American option.
As all exchange traded equity options have American-style exercise (ie they can be exercised at any time as opposed to European options which can only be exercised at expiration) this is a significant limitation.
The exception to this is an American call on a non-dividend paying asset. In this case the call is always worth the same as its European equivalent as there is never any advantage in exercising early.
Advantage: The main advantage of the Black-Scholes model is speed -- it lets you calculate a very large number of option prices in a very short time. Since, high accuracy is not critical for American option pricing (eg when animating a chart to show the effects of time decay) using Black-Scholes is a good option. But, the option of using the binomial model is also advisable for the relatively few pricing and profitability numbers where accuracy may be important and speed is irrelevant. You can experiment with the Black-Scholes model using on-line options pricing calculator.
The Binomial Model
The binomial model breaks down the time to expiration into potentially a very large number of time intervals, or steps. A tree of stock prices is initially produced working forward from the present to expiration. At each step it is assumed that the stock price will move up or down by an amount calculated using volatility and time to expiration. This produces a binomial distribution, or recombining tree, of underlying stock prices. The tree represents all the possible paths that the stock price could take during the life of the option.
At the end of the tree -- ie at expiration of the option -- all the terminal option prices for each of the final possible stock prices are known as they simply equal their intrinsic values.
Next the option prices at each step of the tree are calculated working back from expiration to the present. The option prices at each step are used to derive the option prices at the next step of the tree using risk neutral valuation based on the probabilities of the stock prices moving up or down, the risk free rate and the time interval of each step. Any adjustments to stock prices (at an ex-dividend date) or option prices (as a result of early exercise of American options) are worked into the calculations at the required point in time. At the top of the tree you are left with one option price.
Advantage: The big advantage the binomial model has over the Black-Scholes model is that it can be used to accurately price American options. This is because, with the binomial model it's possible to check at every point in an option's life (ie at every step of the binomial tree) for the possibility of early exercise (eg where, due to eg a dividend, or a put being deeply in the money the option price at that point is less than the its intrinsic value).
Where an early exercise point is found it is assumed that the option holder would elect to exercise and the option price can be adjusted to equal the intrinsic value at that point. This then flows into the calculations higher up the tree and so on.
Limitation: As mentioned before the main disadvantage of the binomial model is its relatively slow speed. It's great for half a dozen calculations at a time but even with today's fastest PCs it's not a practical solution for the calculation of thousands of prices in a few seconds which is what's required for the production of the animated charts in my strategy evaluation model