Chapter 16, Problem 17PS

Summary Introduction

Adequate information:

A put option with the following details-

Time to expiration (t) = 6 months = 0.5 years

Standard deviation per annum (s) = 50% = 0.5

Exercise price (X) = $50

Current stock price (S) = $50

Interest rate per annum ('r) = 3%

Dividend = $0

To Compute:

Value of the put option as per Black Scholes model.

Introduction:

As per Black scholes model, value of put option (P) is given by:

  $P=X{e}^{-rt}\times \left[1-N\left(d_2\right)\right]–S\times \left[1-N\left(d_1\right)\right]$

Where

'd₁ = $\begin{array}{l}\frac{\ln \frac{S}{X}+(r+\frac{{\sigma }^2}{2})\times t}{\sqrt{{\sigma }^2\times t}}\\ \end{array}$

_'d₂ = $\begin{array}{l}\frac{\ln \frac{S}{X}+(r-\frac{{\sigma }^2}{2})\times t}{\sqrt{{\sigma }^2\times t}}\\ \end{array}$