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The Black-Scholes differential equation is a second-order PDE in two dimensions and reads as \begin{align*} \frac{\partial f}{\partial t} + rx\frac{\partial f}{\partial x} + \frac{1}{2}\sigma^2 x^2 \frac{\partial^2 f}{\partial x^2}-rf&=0, \\ \Theta+rx\Delta+ \frac{1}{2}\sigma^2 x^2 \Gamma-rf&= 0, \end{align*} assuming that $f\in \mathcal{C}^{1,2}([...


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