• We are pleased to announce that the winner of our Feedback Prize Draw for the Winter 2024-25 session and winning £150 of gift vouchers is Zhao Liang Tay. Congratulations to Zhao Liang. If you fancy winning £150 worth of gift vouchers (from a major UK store) for the Summer 2025 exam sitting for just a few minutes of your time throughout the session, please see our website at https://www.acted.co.uk/further-info.html?pat=feedback#feedback-prize for more information on how you can make sure your name is included in the draw at the end of the session.
  • Please be advised that the SP1, SP5 and SP7 X1 deadline is the 14th July and not the 17th June as first stated. Please accept out apologies for any confusion caused.

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?
 
Last edited by a moderator:
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.
 
You must log in or register to reply here.
Back
Top