{ min ( ∂ V ∂ t ( t , S ) + r S ∂ V ∂ S ( t , S ) + 1 2 σ 2 S 2 ∂ 2 V ∂ S 2 ( t , S ) − r V ( t , S ) , V ( t , S ) − Φ ( S ) ) = 0 , S ∈ [ 0 , + ∞ ) , t ∈ [ 0 , T ] V ( T , S ) = Φ ( S ) {\displaystyle \left\{{\begin{aligned}&\min \left({\frac {\partial V}{\partial t}}(t,S)+rS{\frac {\partial V}{\partial S}}(t,S)+{\frac {1}{2}}{{\sigma }^{2}}{{S}^{2}}{\frac {{{\partial }^{2}}V}{\partial {{S}^{2}}}}(t,S)-rV(t,S),V(t,S)-\Phi (S)\right)=0,S\in \left[0,+\infty \right),t\in \left[0,T\right]\\&V(T,S)=\Phi (S)\\\end{aligned}}\right.}

Mô phỏng Monte Carlo

Lược đồ θ {\displaystyle \theta }