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.
Tao Luo
Tao Luo
CS PhD Student

My interests lie in performance and security aspects in distributed systems/networking.