Graduation Year

Spring 2013

Document Type

Campus Only Senior Thesis

Degree Name

Bachelor of Arts



Second Department


Reader 1

Henry Schellhorn

Rights Information

© 2013 Jacob M. Roth


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.

This thesis is restricted to the Claremont Colleges current faculty, students, and staff.