Determining option prices — Part 2

We covered three factors that determine option premium in our last column.

These were moneyness (whether the position is in profit or not), type of option (European or American) and time to expire. Other factors that affect the premium are:

Volatility: Volatility of an underlying reflects uncertainty about future price movement. Contract with volatile underlying tend to record large gains or losses.

The difficulty of predicting the behaviour of a volatile stock results in the contract commanding higher price for the option.

The option writer also demands higher premium since such contracts deviate widely from the strike price.

Effects of interest rates: The risk free interest rate also affects the option premium. So what is risk free interest rate?

It is an interest rate that you can get on an investment in a treasury bill issued by Government of India.

At first glance it is little hard to imagine why interest rate will affect option premium. However, it cannot be presumed the option writer will tie up his capital without any return prospect.

Call option

Now let’s have a look at call options. In case of call options the option writer (seller) is obligated to sell the underlying security at exercise price.

This mean the option writer is supposed to earn some risk free interest rate for the value of the contract.

Thus the premium of the call option includes the risk free interest rate, and therefore, higher the risk free interest rate, higher the call premium. One important point is to be noted here is risk free interest rate is fully priced in for deep in-the-money call option whereas it is not at all included in far out-the-money call option.

Put option

For put option the story is quite different. Option holder is presumed to be holding the underlying stock and has the right to sell the underlying to the option writer.

So it is the put option holder who is compensated for loss of interest income on cash before putting to the option writer.

Therefore, in this case, the risk free rate of interest is not added to the option premium.

Option premium for call is greater than the premium for put option for the same strike price despite all the other factors being same, this differential can be attributed to the risk free rate of interest. Hence, all things being equal, higher the interest rates cheaper the option prices.

Effects of dividends: Normally there is a drop in price once the day the stock becomes ex-dividend.

Since holder of a call options gains by increase in price and the put option holder gains by fall in price. So the price movements due to dividend announcement are beneficial for put option holders.

Due to this effect, premium for the call option is less than the premium for the put option for a stock that has declared dividend.

One important point to be noted here is that the premium for far out-the-money option for both call and put is not at all affected by dividends.

Readers who are interested in technical explanations for option pricing can refer to models such as Black-Scholes model.

> shaurya.mishra@thehindu.co.in

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