CM1 paper B resources CH11 Q2 - Convexity calculation

Discussion in 'CM1' started by Danny, Mar 19, 2024.

  1. Danny

    Danny Active Member

    Could you please explain why the convexity numerator column is calculated as

    c*t*(t+1)*v^(t+2)

    Thanks
     
  2. Joe Hook

    Joe Hook ActEd Tutor Staff Member

    For the formula itself see page 27 of chapter 11.

    If we differentiate the PV of a cashflow twice:

    PV of cashflow at time t = c * v^t = c * (1+i)^-t
    Differentiate once with respect to i = -c * t * (1+i)^-t-1
    Differentiate again = c * t * (t+1) * (1+i)^-t-2 = c * t * (t+1) * v ^(t+2) as required.

    Joe
     

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