Chapter 10, Problem 13Q

Summary Introduction

To discuss: The factors influencing the value of an option.

Explanation of Solution

According to person B’s model the following five factors influencing the price of an option:

• Underlying asset’s spot price
• The strike price on the option
• The exercise date of option
• Underlying asset’s price volatility
• The risk free rate of interest

The profit and loss of an option is associated with the spot price and strike price of an underlying asset. The difference between the spot price and strike price of an option is called the intrinsic value of an option. While considering a call option the intrinsic value is:

$\begin{array}{l}\hfill \\ \text{Stock price - Exercise price If Stock price > Strike price}\hfill \\ \left(\text{option is in the money}\right)\hfill \\ \hfill \\ \text{Zero If Stock price}\le S\text{trike price}\hfill \\ \left(\text{option is out of or at the money}\right)\hfill \\ \hfill \\ \text{For a put option, the intrinsic value is:}\hfill \\ \text{Exercise price - Stock price If Stock price < Strike price}\hfill \\ \left(\text{option is in the money}\right)\hfill \\ \hfill \\ \text{Zero If Stock price } \ge \text{Strike price}\hfill \\ \left(\text{option is out of or at the money}\right)\hfill \end{array}$

At the time of expiry of a contract the value of an option is equivalent to the intrinsic value. The time value of option is a related with the underlying assets price volatility and time until the expiration date of the option.

If the volatility of price increases the probability of stock price will go up or down in value rises. Therefore, over any given period of time, the bigger the underlying asset’s price volatility, the larger the chance the price of stock will upsurge and the superior the option time value.

The risk free rate of interest influence the option value in a less than pure cut manner. All other stable, as the risk-free rate rises, the growth rate of the stock price rises. Though, the current value of any upcoming cash flows received by the option holder declines. For a call option, the first result have a tendency to upsurge the option price, whereas the second result have a tendency to reduction the price.

It can be exposed that the first result all the time governs the second effect. That is, the call option’s price at all times upsurges as the risk-free rate upsurges. The two effects both tend to decline the put option value. Therefore, the price of a put option drops as the risk-free rate rises.