# PRICING OF OPTIONS

As has already been explained options are used as risk management tools and the valuation or pricing of these instruments is a careful balance of market factors. There are four major factors affecting the options premium; namely, the price of the underlying, time of expiry, exercise price time to maturity and volatility of the underlying. While there are two lesser important factors; namely, the short term interest rate and dividends.

## Reviewing the Options pricing factors:

While reviewing these options pricing factors; it would come to light that the intrinsic value of an option is the amount by which an option is in-the-money or the immediate exercise value of the option when the underlying position is marked-to-market.

For a Call option, the intrinsic value would be the spot price less the strike price; while for a Put option, its intrinsic value would be the strike price less the spot price. So, the intrinsic value of an option must be either positive or zero and cannot be negative. By extension, for a Call option the strike price must be less than the price of the underlying asset for the Call option to have an intrinsic value greater than zero. Similarly for a Put option, the strike price must be greater than the price of the underlying asset for it to have intrinsic value.

## Pricing of the underlying asset:

The Options premium is affected by the price movement in the underlying instrument. For a Call option (that is, the right to buy the underlying at a fixed strike price) as the price of the underlying rises so does its premium; and as the price of the underlying falls so does its premium. Similarly, for a Put option (that is, the right to sell the underlying at a fixed price) as the price of the underlying rises its premium falls; and as the price of the underlying falls its premium cost rises.

## The time value of an Option:

Generally, the longer the time remaining until option expiration the higher would be its premium. This is because the longer an option's lifetime, the greater is the possibility that the underlying asset or stock price might move so as to make the option in-the-money, while keeping all other factors affecting an option's price constant. Then the time value portion of an Option premium would decrease (or decay) with the passage of time; and the rate of this time decay would increase rapidly in the last few remaining days or weeks of an Option's life. When an Option expires in-the-money, it is generally worth only its intrinsic value.

## Volatility:

Volatility is the tendency of the underlying asset's price to fluctuate upwards or downwards; and would reflect the magnitude of the price change. This does not imply a bias towards price movement in one direction or the other. Thus, it would be a major factor in determining an Option's premium.

The higher the volatility of the underlying asset, the higher the premium, as there would be a greater possibility that the Option would move in-the-money. Usually, as the volatility of an underlying asset increases, the premium of both the Call and Put options overlying that asset would increase, and vice versa.

So, when the volatility of the price of an underlying is high, its overlying Option premium would also be high for both the Calls and the Puts. Conversely, when the volatility of the price of the underlying is low, its overlying Option (both Calls and Puts) premium would also be low.

## Interest Rates:

Generally, the interest rates would have the least influence on Options and would approximate the cost of carry of a Futures contract. However, if the size of the Options is very large, then this factor may take on some importance. So, while keeping all other factors at a constant, an interest cost rise would cause the premium cost to fall and vice versa.

The relationship maybe thought of as an opportunity cost. For instance, in order to buy an Option, the buyer must either borrow funds or use funds on deposit; in either case the buyer incurs an interest rate cost. Now, if the interest rates are rising, then the opportunity cost of buying an Option increases as well; and to compensate the buyer, the premium cost would fall.

Why should the buyer of Options be compensated? This would be because the Option writer receiving the premium can place the funds on deposit and earn (or receive) more interest than was anticipated earlier. This situation would be reversed when interest rates fall and Options premium rise; as on such occasions it is the Option writer who needs to be compensated.

We would strongly recommend that the investor first study these investment instruments; conduct dry runs with pen and paper; understand the nuances of the dynamics of the underlying security and the connectivity between the various risks that he or she would be taking on during the pendency of a futures or options position held by him.