Chapter 16, Problem 28PS

To comment:

on the hedge ratio of a put option as stock price becomes very less.

Summary Introduction

From Black Scholes formula value of d₁ is :

  $d_1= \frac{\text{ln(S0/X) + (r }－\delta \text{+ }{\sigma }^{\text{2}}\text{/2)T}}{\sigma \sqrt{T}}$

And the hedge ratio N(d1) can be calculated from the abovementioned formula.

Now if the put option exercise price is very small then the hedge ratio N(d1) approaches the value of 0.

So as X increases the probability of exercise approaches to 0.

As X increases, the probability of exercise approaches to 0.