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2005 April Q5

Darragh Kelly

Ton up Member
Hi,

For Part (a) of the question, I'm able to derieve all parts of the SDE except for the df/d(T-t) term. When doing this I let T-t = tau so I have f(x,tau) = exp(-tau*x + sigma^3*tau^3/6). When I differenciate wrt to tau I get -x+sigma^2*tau*f(x,tau) = -rt+sigma^2*(T-t)*B(t,T). In examiners report I think they have rt-igma^2*(T-t)*B(t,T) when they differenicate, so my signs are opposite to the solution. The rest of my SDE lines up with report.

Many thanks,

Darragh
 
As you've switched to using tau, your Taylor's expansion will need to have a term that looks like @f/@tau*d(tau). Notice that d(tau) = - dt, which is maybe where the confusion has arisen. It's difficult to say without your full working.
Hope that helps.
 
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