Pricing Equity Derivatives under Stochastic Volatility - A PDE Approach.pdf
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Pricing Equity Derivatives under Stochastic Volatility :

A Partial Differential Equation Approach
Roelof Sheppard
March 23, 2007

1 Introduction 1

2 The PDE for Stochastic Volatility Models 5
3 One Dimensional Finite Difference Methods 13
4 Alternative Approaches for the One Dimensional FDM 35
5 Two Dimensional Finite Difference Methods 53
6 Alternative Approaches for the Two Dimensional FDM 86
7 Extensions on the Finite Difference Method 102
8 Numerical solution of stochastic volatility PDEs: Heston, Hull & White, and SABR 117
9 Numerical Results 122