Chapter 16, Problem 4PS

Summary Introduction

Call option:

It is an agreement where the buyer is entitled the right to buy a stock at a pre-specified price within a pre-specified period. The stock on which the call option is provided is called the underlying asset.

Put option:

It is an agreement where the buyer is entitled the right to sell a stock at a pre-specified price within a pre-specified period. The stock on which the put option is provided is called the underlying asset.

Put-call parity: The put call parity provides a relationship among the stock price, strike price, call price and the put price. According to this theory, the difference between the price of a call option and put option on the same asset underlined with the same strike price and expiry date equals to the difference between the stock price and the present value of the strike price.

  $\begin{array}{l}\mathrm{Pr}iceofcall-\mathrm{Pr}iceofput=Stockprice-PVofStrikeprice\\ \mathrm{Pr}iceofcall-\mathrm{Pr}iceofput=Stockprice-Strikeprice\times \left(e^{-riskfreerate\times timeto\exp ire}\right)\end{array}$

To determine:

The impact of volatility on the option values and to provide a numerical example using put call parity relationship to support it.