How risk perception, interest rates affect option premium

Written by Sunil K Parameswaran | Updated: Mar 8 2013, 07:56am hrs
Both call and put options entail the payment of a price known as the option price or the option premium, by the buyer to the writer at the time of acquisition. The option premium is influenced by certain variables. The arguments are presented using options on equity shares as an expositional device. The logic can, however, be extended to options on any underlying asset.

Options on shares are influenced by the share price. The higher the share price, keeping other variables constant, the more attractive the option will be for the holder in the case of call options. In case of put options, the lower the stock price, the more attractive will the option be for the holder. Thus, keeping other factors constant, the higher the stock price, the greater the call premium and the lower the put premium. For a given stock price level, the lower the exercise price, the higher will be the call premium and the lower the put premium.

Dividends that are scheduled to be paid out during the life of the options contract will have implications for the option premium. Most exchange-traded options are not payout protected. That is, the terms of the contract will not be altered if the underlying asset were to pay a dividend during the life of the contract. However, there are exchanges that will amend the contract terms if the dividend were to be perceived as extraordinary, a term which will be defined by the exchange concerned.

For instance, the NSE defines the term extraordinary as 10% or more of the prevailing market price. Dividends will lead to a decline in the asset price when the stock goes ex-dividend. And we know that the lower the stock price, the lower will be the call premium and the higher will be the put premium. Thus, dividends that are scheduled to be paid out during the life of the contract will serve to reduce the premiums of call options and increase the prices of put options.

Conventional finance theory postulates that investors are risk averse. Thus, the greater the perceived risk, the higher will be the return demanded, which implies that market price will be correspondingly lower. However, volatility has positive implications for option premiums. The greater the volatility, the higher is the probability of very high and very low prices.

From a call holders standpoint, while he stands to gain if the stock price were to attain very high values, the loss in the event of it plummeting is always the premium paid at the outset. In other words, options being contingent contracts permit the holders to take advantage of favourable price movements, while protecting them from adverse price movements. The same rationale holds for puts. That is, while the put holder will benefit from declining asset prices, he will never lose more than the premium if the stock were to attain very high values. Thus, the higher the volatility of returns, the greater will be the premiums of both call options as well as put options.

The time to maturity of the contract is yet another factor that has implications for option premiums. Most options are what we term as wasting assets. That is, most options will have a positive time value prior to expiration, which must decline to a value of zero at the time of expiration. The time value at expiration must be zero for all options, for the simple reason that waiting further is not a choice.

Thus, if the exercise price and the asset price are held constant, the option premium will steadily decline over time. This rationale is applicable for all American options and European calls on non-dividend paying stocks.

However, European puts on a non-dividend paying asset may have a negative time value prior to expiration, if they happen to be deep in-the-money, that is the stock price is much lower than the exercise price. The only way the time value will approach a value of zero in such cases, is if it gradually increases over time, which implies that the premium will increase and approach the intrinsic value as we approach expiration. Thus, while options are generally wasting assets, there could be exceptions.

The final variable which has consequences for the option premium is the risk-less rate of interest. Consider an investor who has adequate funds to buy a stock at its prevailing price. An alternative is to buy a call option and invest the balance at the risk-less rate. The higher the interest rate, the more attractive will be the alternative course of action, which would lead to a greater demand for the calls. Thus, the higher the rate of interest the greater will be the call premium.

Now, consider the case of an investor who owns the underlying asset and is contemplating the possibility of its sale. One alternative is to buy a put and lock in a minimum sale price. The higher the interest rate, the more attractive is the possibility of an immediate sale, followed by a reinvestment of the proceeds at the riskless rate. Consequently the higher the interest rate, the lower will be the demand for put options and, consequently, the lower will be the put premium.

The writer is the author of Fundamentals of Financial Instruments, published by Wiley, India