16.17 Consider the Hull and White (1987) model dSt = SStdt + #YtStdBt dYt = Y Ytdt + YtdWt. The volatility process is Yt. Show

16.17 Consider the Hull and White (1987) model dSt = μSStdt + #YtStdBt dYt = μY Ytdt + ξYtdWt.

The volatility process is √Yt. Show that the volatility process has moments E[

#Yt] = #Y0 e 1

2μY t− 1 8 ξ2t V[

#Yt] = #Y0 2

eμY t

%

1 − e− 1 4 ξ2t

&

and study what happens with these moments when t → ∞ depending on the values of the parameters in the model.