Recall the celebrated Black-Scholes equation
∂ V ∂ t + 1 2 σ 2 S 2 ∂ 2 V ∂ S 2 + ( r − q ) S ∂ V ∂ S − r V = 0. {\displaystyle {\frac {\partial V}{\partial t}}+{\frac {1}{2}}\sigma ^{2}S^{2}{\frac {\partial ^{2}V}{\partial S^{2}}}+(r-q)S{\frac {\partial V}{\partial S}}-rV=0.}
