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

See all articles by Carl Chiarella

Carl Chiarella

University of Technology, Sydney - UTS Business School, Finance Discipline Group

Boda Kang

AMP

Date Written: February 1, 2009

Abstract

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

Chiarella, Carl and Kang, Boda, The Evaluation of American Compound Option Prices under Stochastic Volatility Using the Sparse Grid Approach (February 1, 2009). Quantitative Finance Research Centre Research Paper No. 245, Available at SSRN: https://ssrn.com/abstract=1352150 or http://dx.doi.org/10.2139/ssrn.1352150

Carl Chiarella (Contact Author)

University of Technology, Sydney - UTS Business School, Finance Discipline Group ( email )

PO Box 123
Broadway, NSW 2007
Australia
+61 2 9514 7719 (Phone)
+61 2 9514 7711 (Fax)

HOME PAGE: http://www.business.uts.edu.au/finance/

Boda Kang

AMP ( email )

Sydney, NSW
Australia
0430976988 (Phone)
2154 (Fax)

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