OPTIONS AND THEIR VALUATION CHAPTER 7. LEARNING OBJECTIVES Explain the meaning of the term option Describe the types of options Discuss the implications.

OPTIONS AND THEIR VALUATIONCHAPTER 7

LEARNING OBJECTIVES

Explain the meaning of the term option Describe the types of options Discuss the implications of combinations of

options Highlight the factors that have an influence on the

valuation of options Develop a simple model of valuing options Show how the Black-Scholes model of option

valuation works

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Options

An option is a contract that gives the holder a right, without any obligation, to buy or sell an asset at an agreed price on or before a specified period of time.

The option to buy an asset is known as a call option.

The option to sell an asset is called a put option.

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Options

The price at which option can be exercised is called an exercise price or a strike price.

The asset on which the put or call option is created is referred to as the underlying asset.

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When an Option can be Exercised European option When an option is allowed to be

exercised only on the maturity date, it is called a European option.

American option When the option can be exercised any time before its maturity, it is called an American option.

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Possibilities of option holder exercising his rightThere are three possibilities: In-the-money: A put or a call option is said to in- the- money

when it is advantageous for the investor to exercise it. Out-of-the-money: A put or a call option is out-of-the-money

if it is not advantageous for the investor to exercise it. At-the-money: When the holder of a put or a call option does

not lose or gain whether or not he exercises his option, the option is said to be at-the- money.

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Call Option

Buy a call option You should exercise call option when:

• Share price at expiration > Exercise price. Do not exercise call option when:

• Share price at expiration < Exercise price. The value of the call option at expiration is:

• Value of call option at expiration = Maximum [Share price – Exercise price, 0].

The expression above indicates that the value of a call option at expiration is the maximum of the share price minus the exercise price or zero.

The call buyer’s gain is call seller’s loss.

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Pay-off of a call option buyer

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Pay-off of a call option writer

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Call Premium

The buyer of a call option must, pay an up-front price, called call premium, to the call seller to buy the option.

The call premium is a cost to the option buyer and a gain to the call seller.

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Example: Call Option Pay-off The share of Telco is selling for Rs 104. Radhey

Acharya buys a 3 months call option at a premium of Rs 5. The exercise price is Rs 105. What is Radhey’s pay-off if the share price is Rs 100, or Rs 105, or Rs 110, or Rs 115, or Rs 120 at the time the option is exercised?

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Example : Pay-off of the call option buyer

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The Call Option Holder's Pay-off atExpiration

Pay-off of the call option buyer

Example: Pay-off of the call option seller

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The Call Option Seller's Pay-off atExpiration

Pay-off of the call option seller

Put Option

Buy a put option Exercise the put option when:

• Exercise price > Share price at expiration. Do not exercise the put option when:

• Exercise price < Share price at expiration. The value or payoff of a put option at expiration will be:

• Value of put option at expiration = Maximum [Exercise price – Share price at expiration, 0].

The put option buyer’s gain is the seller’s loss.

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Example : Put Option Pay off An investor hopes that the price of BHEL’s share will fall

after three months. Therefore, he purchases a put option on BHEL’s share with a maturity of three months at a premium of Rs 5. The exercise price is Rs 30. The current market price of BHEL’s share is Rs 28. How much is profit or loss of the put buyer and the put seller if the price of the share at the time of the maturity of the option turns out to be Rs 18, or Rs 25, or Rs 28, or Rs 30, or Rs 40?

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ExampleThe Put Option Holder's Pay-off at

ExpirationPay-off for a put option buyer

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The Put Option Seller's Pay-off at Expiration

Pay-off for the put option seller

Options Trading in India

The Security Exchange Board of India (SEBI) has announced a list of 31 shares for the stock-based option trading from July 2002. SEBI selected these shares for option trading on the basis of the following criteria:

Shares must be among the top 200 in terms of market capitalisation and trading volume.

Shares must be traded in at least 90 per cent of the trading days.

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Options Trading in India

The non-promoter holding should be at least 30 per cent and the market capitalisation of free-float shares should be Rs 750 crore.

The six-month average trading volume in the share in the underlying cash market should be a minimum of Rs 5 crore.

The ratio of daily volatility of the share vis-à-vis the daily volatility of the index should not be more than four times at any time during the previous six months.

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Options Trading in India

The minimum size of the contract is Rs 2 lakh. For the first six months, there would be cash settlement in options contracts and afterwards, there would be physical settlement. The option sellers will have to pay the margin, but the buyers will have to only pay the premium in advance. The stock exchanges can set limits on exercise price.

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Index Options

Index options are call or put options on the stock market indices.

In India, there are options on the Bombay Stock Exchange (BSE)—Sensex and the National Stock Exchange (NSE)—Nifty.

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Index Options

The Sensex options are European-type options and expire on the last Thursday of the contract month. The put and call index option contracts with 1-month, 2-month and 3-month maturity are available. The settlement is done in cash on a T + 1 basis and the prices are based on expiration price as may be decided by the Exchange. Option contracts will have a multiplier of 100.

The multiplier for the NSE Nifty Options is 200 with a minimum price change of Rs 10 (200 0.05).

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Combinations of Put, Call and Share A share, a put and a call can be combined together

to create several pay-off opportunities. Some of these combinations have significant implications. They are: Long Position: A long position involves buying and

holding shares (or any other assets) to benefit from capital gains and dividend. An investor may create a long position in the shares of a firm. A long position investment strategy is risky. The investor will incur loss if the share price declines.

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Example Suppose the current share price and the exercise

price to be Rs 100, and possible share prices at expiration Rs 90 or Rs 110. The pay-off (value) of a portfolio of a share (long) and a put (long) at expiration isValue of share

Current shareprice

Share price

Protective Put

Put option at-the-money is called a protective put .The combination of a long position in the share and a protective put helps to avoid the investor’s risk when the share price falls.

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Value of share and put

Current shareprice

Share priceExercise price

Protective Put vs. Call

The value of your portfolio of a share and a put at expiration will always be greater than the value of a call at expiration by the exercise price.

At expiration, the position will be as follows:Share price at expiration + Value of put at expiration = Value

of call at expiration + Exercise price

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Protective Put vs. Call

Put-call Parity

Suppose you buy a share (long position), buy a put (long position) and sell a call (short). The current share price is Rs 100 and the exercise price of put and call options is the same, that is, Rs 100. Both put and call options are European type options and they will expire after three months. Let us further assume that there are two possible share prices after three months: Rs 110 or Rs 90. What is the value of your portfolio?

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Value of a Portfolio of a Share and a Put Option

Covered Call

Naked option is a position where the option writer does not hold a share in her portfolio that has a counterbalancing effect.

A covered call position is an investment in a share plus the

sale of a call on that share. The position is covered because the investor holds a share against a possible obligation to deliver the share. The total value or pay-off of a covered call at expiration is the share price minus the value (pay-off) of the call.

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Pay off of a covered call30

Combinations of Put, Call and Share Straddle: Combining Call and Put at Same

Exercise Price Strips and Straps Strangle: Combining Call and Put at Different

Exercise Prices Spread: Combining Put and Call at Different

Exercise Prices Spread: Combining the Long and Short Options Collars

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Pay offs : Straddle32

Straddle Buyer Straddle Seller

Pay offs: Strips and Straps

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Strips Straps

Strangle: Combining Call and Put at Different Exercise Prices A strangle is a portfolio of a put and a call with the

same expiration date but with different exercise prices. The investor will combine an out-of-the-money call with an out-of-the-money put.

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Example

Suppose the Telco share is currently selling for Rs 110. The exercise prices for the Telco put and call are, respectively, Rs 100 and Rs 105. What will be your pay-off if the price of Telco’s share increases to Rs 120 in three months? You will forgo put option, but you will exercise call option.

So your pay-off will be the excess of the share price over the call exercise price: Rs 120 – Rs 105 = Rs 15.

If Telco’s share price falls to Rs 95, you will exercise put option and pay-off will be the excess of exercise price over the share price: Rs 100 – Rs 95 = Rs 5.

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Payoff from Strangle36