# European Call Option Modelling under 2 factor Hull White interest rates

I have modelled the yield curve through the two factor Hull White Model. Now I want to implement in Matlab the price development of a ATM-Call-Option (European). Has someone an idea how to combine them and which variables do I need in order to implement the Call Option price development.

• It is not clear. What is the dynamics of the two-factor Hull White model? What is the payoff of your option (e.g., underlying, maturity)? – Gordon Jun 10 '18 at 17:35
• The dynamics is given by $r(t) = x(t) + y(t) + \varphi(t), r(0) = r_0 \\ dx(t) = -a x(t) dt + \sigma dW_1(t), x(0) = 0 \\ dy(t) = -by(t) dt + \eta dW_2(t), y(0) = 0 \\$ From that we can derive the bond prices and calculate the yields. Underlying price is 8000 and maturity is 20 years from today. – SinusK Jun 10 '18 at 18:17
• Thanks for clarification. Is $W_1$ and $W_2$ correlated? For the option, I meant whether it is a zero-coupon bond option? How long is the difference between the option maturity and the bond maturity? – Gordon Jun 10 '18 at 18:26
• thank you for your answer and help. Yes they are correlated: $dW_1(t)dW_2(t) = \rho dt$. It is a zero-coupon bond option with one year option maturity. The bond maturity is 20 years. – SinusK Jun 10 '18 at 18:53