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X3 Assignment QX3.2 (ii)

G

GrahamMac

Member
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?
 
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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.
 
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