Page 88 - DCOM510_FINANCIAL_DERIVATIVES

Unit 6: Valuation and Pricing of Options

6.2 Option Pricing Notes

Modern option pricing techniques are often considered among the most mathematically complex
of all applied areas of finance. Financial analysts have reached the point where they are able to
calculate, with alarming accuracy, the value of a stock option. Most of the models and techniques
employed by today’s analysts are rooted in a model developed by Fischer Black and Myron
Scholes in 1973.
The price of an option contract is that amount which is paid by the option buyer to the option
seller. This is otherwise, known as option premium. Like, other price mechanism the premium
(option price) on a particular option contract is computed by the demand and supply of the
underlying asset (option). There are two types of option price i.e., intrinsic value and time value.
The intrinsic value of a call option is that amount by which stock price exceeds the strike price,
whenever the option is in-the-money. This intrinsic value will be zero when the stock price is
less than the option strike price. On the other hand, the intrinsic value of put option is that
amount by which strike price exceeds the stock price, whenever the option is in-the-money. This
intrinsic value of put option will be zero when the strike price is less than the stock price.

Did u know? Time value of an option is the excess of option price over the intrinsic value.

6.2.1 Primary Option Pricing Factors

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 – Xt, 0) therefore, more the spot price, more is the
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

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