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2010-08-24
請問先進:

In the book John Hull Option Futures And Other Derivatives 7th,
Chapter 21 Estimating Volatilities and correlations,
Questions and Problem 21.14.
(Hint: The variables u_(n-1) is the return on the asset price in time △t, It can be assumed to be normally distributed with mean zero and standard deviation σ_(n-1). It follows that the mean of u_(n-1)^2 and u_(n-1)^4 are σ_(n-1)^2 and 〖3σ〗_(n-1)^3 respectively.)
I could derive that V(u_(n-1)) = E(u_(n-1)^2)-〖(E(u_(n-1)))〗^2
→ σ_(n-1)^2 = E(u_(n-1)^2)- 0
→ E(u_(n-1)^2) = σ_(n-1)^2 → the mean of u_(n-1)^2 is σ_(n-1)^2

But I couldn’t derive the mean of u_(n-1)^4 is 〖3σ〗_(n-1)^3.
E(u_(n-1)^4) =  〖3σ〗_(n-1)^3???


Thanks for your help!
CKyeh
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