Question

1. Answer the following questions about option valuation.

1. Construct a table to list the six factors affecting option value (including call and put option) and their relation (positive or negative) with option value. (10%)
2. Explain why the six factors positively or negatively affect option value (Hint: Address the difference between the intrinsic value and the time value of the option). (15%)

Answer 1

Factor	Call option price	Put option price
Stock price	+	-
execution price	-	+
Time to maturity	+	+
Volatility	+	+
Dividends	-	+
Interest rates	+	-

a) Effect of the value of the underlying:

    The call option can be viewed as buying the underlying and the put option can be viewed as selling the underlying. So, the value of call option increases with an increase in the value of the underlying and the value of put option decreases with an increase in the value of the underlying.

Effect of the exercise price:

   The lower is the exercise price, the higher will be the value of the call option because we would be able to buy the underlying at a lower price. The opposite is true for the put option i.e. the higher is the exercise price; the higher will be the value of the put option as we would be able to sell the underlying at a higher price. Hence, the value of a European call option is inversely proportional to the exercise price and the value of a European put option is directly proportional to the exercise price.

Effect of time to expiration:

   The more is the time to expiration, the greater is the value of the option. The logic is that the underlying has more potential for movement and thus the option will have a higher value. With the same logic, even the put option will increase with an increase in the time to expiration .

But there is some exception to the European put options. If the risk-free rate is high, the volatility is lower, and the European put option is deep-in-the-money, then the value of put option can decrease with increase in the time to expiration.

Effect of the risk-free rate of interest:

   The value of call option increases in the value with an increase in the risk-free rate and the value of put option decreases with an increase in the risk-free rate.

Effect of volatility:

    Both call options and put options increase in value with an increase in volatility. The call option increases in value because the underlying price can increase to a higher price because of high volatility. Similarly, the put option increases in value because the underlying price can fall to a lower price due to higher volatility.

The volatility factor and time to expiration factor are combined to get the time value of an option. The volatility can have more impact if the time to expiration is longer. The option prices generally decrease as the options approach expiration date and this is referred to as time value decay.

Effect of dividends:

    The call option is equivalent to the long position in the underlying and the put option is equivalent to the short position in the underlying. The value of the underlying decreases with dividends. So, the value of European call option is inversely proportional to the dividends. The opposite is true for the European put option i.e. the value of European put option increases with dividends.