Which measure should I use in the estimation of GARCH model for option pricing, the phsical one or the neutral one?

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: $ln(\frac{X_t}{X_{t-1}})=r+\lambda \sqrt{h_t} -0.5h_t+\epsilon_t \quad (2.1)\\ \epsilon_t|\phi_{t-1} \sim N(0,h_t) \\ h_t = \alpha_0 +\alpha_1 \epsilon_{t-1}^2+ \beta_1 h_{t-1} \quad (2.2)$ For option pricing, Duan then introduce the concept of locally risk-neutral valuation relationship. Under the neutral measure Q , the process changes into $$ ln(\frac{X_t}{X_{t-1}})=r -0.5h_t+\xi_t \quad (2.3)\ \xi_t|\phi_{t-1} \sim N(0,h_t) \ h_t = \alpha_0 +\alpha_1 (\xi_{t-1}-\lambda \sqrt{h_{t-1}})^2+ \beta_1 h_{t-1}