2005 April Q5

Discussion in 'CM2' started by Darragh Kelly, Aug 8, 2022.

  1. Darragh Kelly

    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
     
  2. Steve Hales

    Steve Hales ActEd Tutor Staff Member

    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.
     
  3. Darragh Kelly

    Darragh Kelly Ton up Member

    Thanks I see what you mean, all sorted now.
    Cheers for your help.
    Darragh
     

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