The Evaluation of American Compound Option Prices Under Stochastic Volatility Using the Sparse Grid Approach

Carl Chiarella and Boda Kang

No 245, Research Paper Series from Quantitative Finance Research Centre, University of Technology, Sydney

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 (search for similar items in EconPapers)
JEL-codes: C61 D11 (search for similar items in EconPapers)
Pages: 24 pages
Date: 2009-02-01
New Economics Papers: this item is included in nep-cmp and nep-ore
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (12)

Published as: Chiarella, C. and Kang, B., 2013, "The Evaluation of American Compound Option Prices Under Stochastic Volatility and Stochastic Interest Rates", Journal of Computational Finance, 11(1), 71-92.

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