A Finite Difference Method for Multi-asset Option Pricing

In general, solving high dimensional partial differntial equation (PDE) via textbook Crank-Nicolson scheme has intimidating computational cost. However, we reduced this cost for a group of PDEs with special form.

My contribution:

• Proposed a new finite difference scheme, which exploited the structure of option-pricing model and employed the operator-splitting technique to decouple iteration matrix into a sequence of tridiagonal matrices.
• Mitigated the curse of dimensionality by reducing the computational cost while maintaining same accuracy — from $\mathcal{O}(n^4)$ to $\mathcal{O}(n^2)$ for two-asset case.
• Implementated in MATLAB, which showed concise and efficient code compared with old scheme.