Page 110 - DMGT513_DERIVATIVES_AND_RISK_MANAGEMENT

Unit 8: Option Pricing

8.1 Primary Option Pricing Factors Notes

Various factors affect the price of options on stocks. We shall look at the impact of changes in
each of these factors on option prices one at a time, assuming that all other factors remain the
same. For a given type and style of option contract, there are six primary factors affecting its
price. They are:
1. Current Stock Price: The option price changes as per changing stock price. In case of a call
option the payoff for the buyer is Max (S – X, 0) therefore, more the spot price, more is the
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payoff and it is favourable for the buyer.

Example: For a call option the option price rises as the stock price increases and vice-
versa. As the current stock price goes up, the higher is the probability that the call will be in the
money. As a result, the call price will increase. The effect will be in the opposite direction for a
put. As the stock price goes up, there is a lower probability that the put will be in the money. So
the put price will decrease.

2. Exercise Price: In the case of a call, as the exercise price increases, the stock price has to
make a larger upward move for the option to go in-the-money. Therefore, for a call
option, as the exercise price increases, options become less valuable and as the strike price
decreases they become more valuable. The higher the exercise price, the lower the
probability that the call will be in the money. So for call options that have the same
maturity, the call with the price that is closest (and greater than) the current price will have
the highest value. The call prices will decrease as the exercise prices increase. For the put,
the effect runs in the opposite direction. A higher exercise price means that there is higher
probability that the put will be in the money. So the put price increases as the exercise
price increases.
3. Volatility: The volatility of a stock price represents the uncertainty attached to its future
movement. This measures the degree to which the price of the underlying instruments
tends to fluctuate over time. Both the call and put option will increase in price as the
underlying asset becomes more volatile. As volatility increases, the likelihood that the
stock will do very well or very poorly increases. The value of both calls and puts therefore
increase as volatility increases. The buyer of the option receives full benefit of favourable
outcomes but avoids the unfavourable ones (option price value has zero value).
4. Risk free Interest Rates: The risk-free interest rate is the interest rate that may be obtained
in the marketplace with virtually no risk. The affect of the risk-free interest rate is less
clear-cut. It is found that put option prices decline as the risk-free rate increases whereas
the prices of calls always increase as the risk-free interest rate increases. The higher the
interest rate, the lower the present value of the exercise price. As a result, the value of the
call will increase. The opposite is true for puts. The decrease in the present value of the
exercise price will adversely affect the price of the put option. All other factors remaining
constant, the higher the interest rate the greater the cost of buying the underlying asset
and carrying it to the expiration date of the call option. Hence, the higher the short risk
free interest rate, the greater the price of a call option.

5. Cash Dividends: Dividends have the effect of reducing the stock price on the ex-dividend
date. This has a negative effect on the value of call options and a positive effect on the
value of put options. When dividends are announced then the stock prices on ex-dividend
are reduced. This is favourable for the put option and unfavourable for the call option. On
ex-dividend dates, the stock price will fall by the amount of the dividend. So the higher
the dividends, the lower the value of a call relative to the stock. This effect will work in the

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