The Evaluation of American Compound Option Prices under Stochastic Volatility Using the Sparse Grid Approach
Quantitative Finance Research Centre Research Paper No. 245
19 Pages Posted: 3 Mar 2009
Date Written: February 1, 2009
A compound option (the mother option) gives the holder the right, but not obligation to buy (long) or sell (short) the underlying option (the daughter option). In this paper, we demonstrate a partial differential equation (PDE) approach to pricing American-type compound options where the underlying dynamics follow Heston's stochastic volatility model. This price is formulated as the solution to a two-pass free boundary PDE problem. A modified sparse grid approach is implemented to solve the PDEs, which is shown to be accurate and efficient compared with the results from Monte Carlo simulation combined with the Method of Lines.
Keywords: American compound option, stochastic volatility, free boundary problem, sparse grid, combination technique, Monte Carlo simulation, method of lines
JEL Classification: C61, D11
Suggested Citation: Suggested Citation