# Determinants of Option Pricing

The price at which the stock under option may be put or called is the contract price.

Sometimes, it is referred to as the striking price. During the life of the contract, the contract price remains fixed, except that market practice is for the contract price to be reduced by the amount of any dividend paid or by the value of any stock right which becomes effective during the life of the contract.

In purchasing an option the amount the buyer pays for the option privilege is called the premium, or sometimes the option money.

In most option transactions, the contract price is the stock market price prevailing at the time the option is written, and the premium becomes the variable over which buyer and seller bargain.

Option prices are calculated using mathematical models. Options are affected by the variables that drive option prices.

The ongoing valuation of the option depends on the following seven variables:

1. Spot Price: It is the current price of the underlying stock. In the case of a call, as the stock price rises the value of the call increases.

In the case of a put, as the stock price falls the value, of the put increases, assuming everything else is equal.

2. Strike Price: It is the exercise price of the option. It can be expressed as either an absolute level or a percentage of the spot price.

Market participants commonly use the latter. A higher strike price means a lower call value, and a lower strike price means a higher call value.

A higher strike price means a higher put value, and a lower strike price means a lower put value.

3. Time to Expiration: It is the time period remaining to expiration. It is calculated as the difference, commonly in days, between the expiration date and the current date.

Generally, the longer the time until expiration, the greater the value of an option.

In other words, the longer the time until expiration, the higher the probability that the option will expire with a larger positive value.

Note that sometimes changes in time to expiration have an ambiguous effect on European options due to the potential adverse effect of dividend payments during the life of the option.

4. Implied Volatility: It is the expected volatility of the underlying during the life of the option. It is an estimation of the amplitude in the movement of the underlying stock price.

Because the option pay-off is asymmetric (i.e., the maximum pay-off is larger than the premium paid), the higher the volatility, the more likely it is that a large movement of the stock price will translate into a larger pay-off.

Therefore, the higher the implied volatility, the more expensive the option. The implied volatility is an annualized statistic expressed in percentage terms.

5. Expected Dividends: The expected dividends to be distributed to the underlying shares.

If the company of the underlying stock decides to increase the dividends to be paid during the life of the option, this will cause a larger than expected drop in the stock price once it goes ex-dividend.

Higher dividends lower the forward price, thus reducing the price of the call and increasing the price of the put.

6. Interest Rate: Purchasing a call is comparable to buying a portion of the underlying stock.

In a perfect market and in absence of dividends, the stock is expected to appreciate identically to an investment in a riskless interest rate instrument.

As a result, an increase in interest rates implies that the underlying stock will rise higher.

A call price will increase as the interest rate increases. Similarly, a put price will decrease as the interest rate increases.

7. Repo Rate: It is the borrowing fee paid by a stock borrower of the underlying shares. The higher the repo rate, the lower the forward price.

As a result, the higher the repo rate, the lower the price of the call and the higher the value of a put.

The impact of each of these factors depends on whether,

1. The option is a put or a call
2. The option is an American option or a European option.

The following table summarises the impact on the value of a call and a put on a specific stock of an increase in the specified variable, assuming everything else is equal.

It can be observed that changes in time to expiration and volatility have similar effects on the call and put values, while changes to the other factors affect call and put values in an opposite way.

Example: A 2-month call option on Infosys with a strike price of Rs. 2,100 is selling for Rs. 140 when the share is trading at Rs. 2,200. Find out the following:

1. What is the intrinsic worth of the call option?
2. Why should one buy the call for a price in excess of intrinsic worth?
3. Under what circumstances the option holder would exercise his call?
4. At what price of the asset the call option holder would break even?

Solution:

1. The intrinsic worth of the option is (S – X) = 2,200 – 2,100 = Rs. 100.

2. The price of the option is Rs. 140, i.e., Rs. 40 more than the intrinsic worth.

This is the time value of the option and is paid because there are chances that in the next two months the price of Infosys may rise further and the holder stands to gain a greater amount than Rs. 100, the present intrinsic worth.

3. The option holder would exercise his call if the price of the asset, S > X, the exercise price, i.e., when s > 2,100.

4. Call option holder would break even when pay-off of the call S – X – c = 0, which happens at S = Rs. 2,240.