X3 Assignment QX3.2 (ii)

This question is bugging me. I just cant get my head around how to use the value given for Gamma in calculating the change in the option price. The value in the question is 0.008p^-1. Does this not mean that for every penny change in the underlying share, delta increases by 0.008? In the solution they take 0.5 x the change in the share price squared x gamma as one of the contributions to the new option price - Can anyone explain the thinking behind this?

 

Let's suppose (just so there's less things to type here) that we just have changes in share price and time to worry about. Taylor/Ito tells us that, for small changes in the variable values, we can estimate the change in derivative value f as:

df(t,S)=Theta.dt + Delta.dS + 0.5 Gamma(dS)^2

[For other parameter changes we'd add more "Greek.d(param)" terms]

This is the formula we use in this solution, which is why we need the 0.5 and the (dS)^2.

What you say about the value of gamma is correct. It can also be thought of as the second-order sensitivity of the derivative value to changes in the share price and therefore this gamma effect needs to be captured in the estimation of df.

 

this is clearer now. thanks