- 1 -
Options
Business Valuation Management
Options are contracts which provide the holder the right to sell or buy a specified quantity of an underlying asset at a fixed price on or before the expiration of the option date.The writer gets a price forgranting this option. The person who acquires the right is known as option holder or option buyer and the person who grants this right is known as option seller or option writer. The price payable for this right depends upon the underlying assets/securities.
Types of Options. As the options provide a right to buy or not to buy or a right to sell or not to sell, Options can be classified in different groups as follows:
(i)Call Options and Put Options. Depending upon whether an option is for a right to buy or for a right to sell, the option can be classified into Call option and Put option.
A call option provides to the holder a right to buy specified assets at specified price on or before a specified date. In case of call option, he has a right to call from the market (option writer) the specified asset.
A put option provides to the holder a right to sell specified assets at specified price on or before a specified date. In case of put option, he has a right to put the specified asset in the market (option writer).
For example, an investor, A, enters into a contract with B whereby A has the right to buy 100 shares of XYZ Ltd @ Rs. 95 each on or before a specified date. This is a call option. In the same case, if A has the right to sell instead of buying, it is called put option. Further, A may or may not exercise his right. If he does not exercise his right, it will lapse after the specified date. In order to acquire this right, A has to pay a price to B.
(ii)American Options and European Options. In the American option, the option holder can exercise the right to buy or sell, at anytime before the expiration or on the expiration date. However, in the European option, the right can be exercised only on the expiry date and not before. The possibility of early exercise of right makes the American option to be more valuable than the European option to the option holder. In India, the stock options i.e., options in individual shares, are American options, while the index options, i.e., NIFTY options and Sensex options are European options. The American options have greater profit potentiality than European options.
For example, the price of PQR Ltd. share is Rs. 80 and one month put option is available at Rs. 76. Midway during the month, the rate comes down to Rs. 74 and on the last date the rate is Rs. 77. In case of American option, the investor can exercise his right and can gain Rs. 2 per share. But in case of European option, he will have to wait till the end, and he will incur a loss of Re. 1 per share.
Working of an Option. The working of the options can be explained as follows: Suppose, the price of a share of ABC Ltd. is Rs. 50 at present. An investor expects the price to rise to Rs. 60 per share within one month. If the options are not available, he can buy 100 shares by paying Rs. 5,000 (100 x 50) today. If the price after one month is Rs. 60 (or any thing more than Rs. 50) he will make a profit by selling the shares at that time. However, he may also suffer losses which may be the difference between Rs. 50 and the actual price if the latter falls in future. In the extreme case, the loss may be even Rs. 5,000, if there is no price quotation of the share after one month due to slump in the capital market. So, if the expectations go wrong, the investor may even loose the total capital funds invested.
However, if the options are available and purchased by investor, he can limit his expected loss. This can be substantiated as follows: The investor buys today, the call option for one month of 100 shares by paying a premium of, say, Rs. 3 per share (strike price Rs. 52 per share). He will have to pay a total premium of Rs. 300 (100× 3) only. Now, after one month if the actual price is more than Rs. 52 per share (say, Rs. 59), the investor can exercise his option and will make a profit of Rs. 400, i.e., [(59 - 52) × 100] - Rs. 300. However, if the actual price turns out to be less than Rs. 52, then he may allow the option to lapse and his loss will be restricted to Rs. 300 only (i.e.,the premium already paid).
Options contracts are created by the option holders and the option writers. The option holders and option writers have opposite expectations about the performance of the market or the underlying assets and, therefore, they enterinto an options contract. The call option seller (writer) expects the price of the underlying asset to remain roughly steady or to move down. The call option buyer (holder) expects the price of the asset to move upward during the option period. The put option writer (seller) expects the asset price probably to move up. The put option holder (buyer) expects the price of the asset to move down.
In case, the expectations of the option holder are realised, the option is exercised. If the expectations are belied, the option is allowed to lapse. However, options can be sold by the parties in the secondary transactions. In this case, the options of the existing party will be squarred (set off), but a new party would emerge.
Terminology of Options
Option Premium. In options, the buyer of the option has to buy the right from the seller by paying an option premium. The premium payable by the buyer (also called the option holder) to the seller (also called the option writer) is a one-time non-refundable amount for availing the right. In case, the right is not exercised later, then the premium is not refunded by the option writer.
Expiration Date. The expiration date is the last date when theoption can be exercised. In case of American option, it can be exercised even before this date. However, an European option canbe exercised only on this date. In India, all options are available fora period of one month, two months or three months. All these options end on the lastThursday of a calendar month. For example, an option taken during the month of Januaryfor one, two and three months shall expire on the last Thursday of January, February andMarch respectively.
Strike Price. The specified price at which the option can be exercised is known as the strike price. The relationship between the strike price (SP), actual price (AP) of the asset on the specified date and the profit potentiality has been explained in the following Table
Table : Strike Price, Actual Price and Profit Potentiality
Relationship / Call Option / Put OptionAP>SP / In the Money / Out of Money
AP = SP / At the Money / At the Money
AP<SP / Out of Money / In the Money
'In the money' means that the option holder can make profit by exercising the right. 'Out of money' means that the option need not be exercised and let it lapse. 'At the money' means that there is no chance of making profit or loss.
Options Positions.In any options contract, there are two parties, the option writer and the option holder. These two parties will be there in the call option as well as the put option. An investor can buy a call or put option and thereby become an option holder. Similarly, an investor can sell call or put option and thereby become an option writer. An option holder pays the option premium upfront but has potential gain later on. An option writer receives the option premium upfront but has the potential liabilities later. There are four types of options positions as follows:
1. Buying a Call (also known as a Long position in Call),
2. Buying a Put (also known as a Long position in Put),
3. Selling a Call (also known as Short position in Call),
4. Selling a Put (also known as a Short position in Put).
Expectation about Market Price and Option Strategy
Expectation of Market Price / Option Strategy1. Sharp increase in Price / Buy a Call Option
2. Sharp decrease in Price / Buy a Put Option
3. Moderate increase in Price / Sell a Put Option
4. Moderate decrease in price / Sell a Call Option
Pricing and Valuation of Options;
The valuation .of an option depends upon six factors relating to the underlying asset and the financial market. These factors are:
(i) Current Value of the Underlying Asset.
(ii) Expected Volatility in the Value of the Underlying Asset.
(iii) Strike Price of the Option.
(iv) Expiration Time of Option
(v) Rate of Interest.
(vi)Income from Underlying Asset.
Table:Effect of Different Factors on the Valuation of Options
Factor / Call Option Value / Put Option Value1. Increase in value of Underlying Asset / Increases / Decreases
2. Extent of Volatility in Value of Asset / Increases / Increases
3. Increase in Strike Price / Decreases / Increases
4. Longer Expiration Time / Increases / Increases
5. Increase in Rate of Interest / Increases / Decreases
6. Increase in Income from Asset / Decreases / Increases
Value of an Option. An option is an instrument with limited liability, i.e., the premium. A holder will exercise the option only when it is beneficial to him. An option cannot have a negative value because the option holder cannot be compelled to exercise it. This is applicable to both call and put options. The option price is consisting of two components: the intrinsic value and the time value.
Intrinsic Value of an Option. It is also known as minimum value of an option. It denotes the economic value of the option if it is exercised immediately. The intrinsic value of an option is non-negative. The value of the option which the option holder has (i.e., value of the choice to exercise the option or not) very much depend upon the interplay of the strike price and the market value of the underlying asset. This can be further substantiated as follows:
In case of a Call Option, the option value is equal to the excess of market price over the strike price. The call is said to be in the money and the difference is called the intrinsic value of the option. For example, the market price of a share is Rs. 280 and one month call option is available at a strike price of Rs. 273.
The Intrinsic Value is:
Intrinsic Value = MP - Strike Price= 280 - 273 = Rs. 7
However, if the market price of the asset is less than the strike price, the difference between the two is negative and the call is said to be out of money. In this case, the intrinsic value of the call is zero, and the option value, if any, may be based on the speculative motive only. An option cannothave a negative value. An out of money option has no positive intrinsic value. An option for which the strike price is equal to the current price, is said to be at the money.
In case of Put Option, the situation is reverse. The put option is said to be in the money when the market value is less than the strike price. The difference between the two is negative and is called the intrinsic value of the put option. In the other case, when the market value of the asset is more than the strike price, the put option is said to be out of money and the intrinsic value of the option is zero. As the put options allow the holder to sell the asset at the strike price, in the money put option exist where strike price is more than the market price of the asset. Out of money put options have market price above the strike price.
It may be noted that the value of an option usually does not fall below the intrinsic value. This in fact is ensured by the presence of arbitrageurs. Option price will generally be higher than the intrinsic value.
For example, the current market price of a share is Rs. 250 and the strike price is Rs. 220 for a call option, the intrinsic value of the call option is Rs. 30. In this case, the option holder would exercise the option and sell the share immediately in the market for Rs. 250 and thereby making a profit of Rs. 30. Similarly, the strike price for a put option is Rs. 265. The value of the put option is Rs. 15. The put option holder will buy one share from the market for Rs. 250 and exercise the option to sell it at Rs. 265 and thereby make a profit of Rs. 15.
Time Value of Option. The time value or the time premium of an option is the amount by which the option price exceeds the intrinsic value. It is also known as speculative value. The option holder hopes that change in market price of the underlying asset will increase the value of the option (right) before the expiration date. For this expectation, the option buyer is ready to pay a premium above the intrinsic value. Total premium of an option contract is consisting of two elements: Intrinsic value and Time Value, or
Option Premium = Intrinsic Value + Time Value
On the expiration date, the time value of option is zero and the premium is entirely represented by the intrinsic value. If there is at the money position, it means there is no intrinsic value and the entire premium is represented by the time value.
Time Value of Option = Option Price - Intrinsic Value.
The relationship between intrinsic value, time value, strike price and market price can be explained as follows:
Call Intrinsic value = Market Price - Strike Price
Call Time Value= Call Premium - (Market Price - Strike Price)
Put Intrinsic Value = Strike Price - Market Price
Put Time Value = Put Premium - (Strike Price - Market Price)
Black & Scholes Model (BSM)
Regarded as an important breakthrough in the theory of finance, the BSM computes the fair value of a call option on a share as a complex but exact function of the five variables:
(i) Current value of the share,
(ii) The Strike price,
(iii) Time to expiry,
(iv) The Interest rate, and
(v) Volatility of the price of the underlying asset.
The model provides a perfectly hedged investment strategy by accumulating riskless profits by exploiting the options mispricing. Though the BSM basically deals with the valuation of call options yet it may also be used to value the warrants (which is also a call option). The model is based on the following assumptions:
(i) The call option is the European option i.e., it cannot be exercised before the specified date.
(ii) The underlying shares do not pay any dividend during the option period.
(iii) There are no taxes and transaction costs.
(iv) Share prices move randomly in continuous time.
(v) The short-term risk free rate is known and is constant during option period.
(vi)The short selling in shares is permitted without penalty.
Equations1 through 3 reveal, that the value of call option in BSM is a function of 5 variables i.e., S, K, t, r and σ. The BSM as given in the Equation1 seems to be acomplicated formula, however, 4 parameters used by the BSM are easily observable. These are S, K, r and t.
Example of BSM:
The share of FM Ltd. is currently sold for Rs. 60. There is a call option available at strike price Rs. 56 for a period of 6 months. Find out the value of the call option given that the rate of interest of the investor is 14% and the standard deviation of the return of the share is 30%. Use Black and Scholes Model.