CM1 paper B resources CH11 Q2 - Convexity calculation

[Danny]

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

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

Thanks

 

[Joe Hook]

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