Pricing of Options

Options contracts, as well, must be evaluated to determine their worth. Although like any good or service, supply and demand for, say, options will affect the price; to understand the value underlying the price, we need to look deeper. Just as we would consider such factors as the quantity and quality of earnings, price-earnings ratio, and industry outlook, to determine the value of a firm; so we must use the various performance measures  to analyze options and futures. Their analysis is complicated by their relationship with the underlying instrument. The underlying asset price therefore is a critical ingredient in the valuation or pricing of options.

A key ingredient in the pricing of options thus is the relationship of the option or future to the underlying security on or before expiration determines its value. The price of an option or a futures security will always be a function of the price of the underlying asset. This relationship we have noted is called “intrinsic value” and represents the profit, which can be realized if the option were exercised (used) immediately. An option allowing one to sell a share of ABB at Rs. 1000 per share when the cash market price is Rs. 950 per share would have an intrinsic value of Rs. 50. Thus it can be seen that the price of the underlying asset is critical to the valuation analysis.

Frequently, an option will sell at a price exceeding its intrinsic value. This is known as “time value” and represents the price of continuing interest in the option and its underlying security. Time value is affected by the factors described earlier, in particular time before expiration, the rate of interest, and volatility.

Together these factors are used by analysts to evaluate the performance of an option to establish a fair price. With this insight, the requirements of hedgers and the interests of speculators will be served.

To summarize, the key parameters to the valuation or pricing of options are as under:

  1. Underlying asset price: The higher the asset price for a call option, the higher the intrinsic value if the call is in-the-money and hence the higher the premium or price of the option. If the call is out-of-the money then it will lead to the higher asset price and the greater probability that it will be possible to exercise the call at a profit and hence the higher the time value, or premium, of the option. The reverse will apply with Put Options.
  2. Strike Price: The strike price determines if the option has any intrinsic value. Remember, intrinsic value is the difference between the strike price of the option and the current price of the underlying. The premium typically increases as the option becomes further in-the-money (where the strike price becomes more favorable in relation to the current underlying price). The premium generally decreases as the option becomes more out-of-the-money (when the strike price is less favorable in relation to the underlying).
  3. Time to expiration: The longer an option has to run, the greater probability that it be possible to exercise the option profitably, hence the greater time value of the option. As expiration approaches, the option’s time value decreases. In general, an option loses one-third of its time value during the first half of its life and two-thirds of its value during the second half. The underlying’s volatility is a factor in time value; if the underlying is highly volatile, one could reasonably expect a greater degree of price movement before expiration. The opposite holds true where the underlying typically exhibits low volatility; the time value will be lower if the underlying price is not expected to move much.
  4. Interest rates: The role of interest rates in the determination of option premiums is complex and varies from one type of option to another. A call option can be thought of as the right to buy the underlying asset at the discounted value of the future spot price; the greater the degree of discount, the more valuable is the right and higher the interest rate, the greater the degree of discount. So, other things being equal, option prices should rise with short-term interest rates.
  5. Dividends: Dividends can affect option prices because the underlying stock’s price typically drops by the amount of any cash dividend on the ex-dividend date. As a result, if the underlying’s dividend increases, call prices will decrease and put prices will increase. Conversely, if the underlying’s dividend decreases, call prices will increase and put prices will decrease.
  6. Volatility: Volatility is the degree to which the underlying asset prices are expected to move as time passes. It is a measure of the speed and magnitude of the underlying’s price changes. The greater the expected movement in the underlying asset price, the greater the probability that the option can be exercised at a profit and hence the more valuable the option. Historical volatility refers to the actual price changes that have been observed over a specified time period. Option traders can evaluate historical volatility to determine possible volatility in the future. Implied volatility, on the other hand, is a forecast of future volatility and acts as an indicator of the current market sentiment. While implied volatility is often difficult to quantify, option premiums will generally be higher if the underlying exhibits higher volatility, because it will have higher expected price fluctuations.

The various pricing formulas for options, widely used in computer software, all are based upon the above five parameters to derive a valuation for a call or a put option. Knowing what an option should be worth, comparing it with the market valuation is critical to the successful use of such products. The investor is advised to consider each parameter with regard to its effect upon valuation, and moreover, how they may interact with each other to affect the price of an option.

All option contracts have price limits. This implies that one would pay maximum or a definite minimum price for acquiring an option. The limits can be defined as follows:

  • The maximum price of a call option can be the price of underlying asset. In case of stocks a call option on it can never be larger than its spot price. This is true for both European and American call options.
  • The minimum price for a European call option would always be the difference in the spot price and present value of the strike price.
  • The maximum price for a put option can never be more than the present value of the strike price. This is true for both types of options European and American.
  • The minimum price of the European put option would always be equal to difference between present value of strike price and the spot price of the asset.