In the paper "The GARCH OPTION PRICING MODEL", Duan(1995) developed a pricing model for options on an asset whose returns follow GARCH process. Let $X_t$ be the asset price at time t, its process is modeled under physical measure P as GARCH(1,1)-M: $$
ln(\frac{X_t}{X_{t-1}})=r+\lambda \sqrt{h_t} -0.5h_t+\epsilon_t \quad (2.1)\\
\epsilon_t|\phi_{t-1} \sim N(0,h_t) \\
h_t = \alpha_0 +\alpha_1 \epsi…
