Calibrating the HW - Model to Price a Put_ACiD, A00 Q4

Can someone explain to me how the prices of the put Options 0.01 and 0.43 were calculated, I can somewhat follow the Calibration of the Hull-White Model but I’m lost when it comes to these values.

 

Acted tutors - any help on this will be appreciated! Thanks.

 

I approached it like this (could be waaaay off but its an attempt)

Using blacks model:
D1 = (ln(F/K) + .5*vol)/(root(vol))

Fut price at the end of 3 months, given current term structure = 6*exp(-.06*.5) + 106*exp(-.11) - these rates are taken from the r(t) equation for 6 and 12 months respectively (after the 3 month period).

Volatility is now the sum of future price volatility and the stochastic interest volatility (for zero coupon rates) - which will be (sig1^2*t + sig2^2*t^2). Where sig1 = price volatility and sig2 = interest rate volatility.

Since sig1 is not given, sig2 using H&W model is s^2*(1-exp(-2*alpha*t))/(2*alpha) = (.06916)^2 for 3 month period

Using this in the put equation for Garman-Kohlhagen, we get
100*psi(-.525) - 100.66*psi(-.5517) = 2.37.

No where close to the solution of .44!

Edit:
Oh wait, there needs to be another integral for r(t) to compute the zero coupon volatility!)

 

This is explained in Page 706-707 of Hull.

 

I still don't understand what is going on in the ER!I think I agree with Oxy that we need input from Acted tutors.

 

Hoooooray.....the part of the work being examined is on page 695 of Hull. An example of how to go about is on Technical note 15.