The Explicit Finite Difference Method: Option Pricing Under Stochastic Volatility

Author

Jacob M. Roth, Claremont McKenna CollegeFollow

Graduation Year

Spring 2013

Document Type

Campus Only Senior Thesis

Degree Name

Bachelor of Arts

Department

Mathematics

Second Department

Economics

Reader 1

Henry Schellhorn

Rights Information

© 2013 Jacob M. Roth

Abstract

This paper provides an overview of the finite difference method and its application to approximating financial partial differential equations (PDEs) in incomplete markets. In particular, we study German’s [6] stochastic volatility PDE derived from indifference pricing. In [6], it is shown that the first order- correction to derivatives valued by indifference pricing can be computed as a function involving the stochastic volatility PDE itself. In this paper, we present three explicit finite difference models to approximate the stochastic volatility PDE and compare the resulting valuations to those generated by an Euler- Maruyama Monte Carlo pricing algorithm. We also discuss the significance of boundary condition choice for explicit finite difference models.

Recommended Citation

Roth, Jacob M., "The Explicit Finite Difference Method: Option Pricing Under Stochastic Volatility" (2013). CMC Senior Theses. 545.
https://scholarship.claremont.edu/cmc_theses/545