Campus Only Senior Thesis
Bachelor of Arts
© 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  stochastic volatility PDE derived from indifference pricing. In , 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.
Roth, Jacob M., "The Explicit Finite Difference Method: Option Pricing Under Stochastic Volatility" (2013). CMC Senior Theses. 545.
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