The evaluation of American compound option prices under stochastic volatility and stochastic interest rates

Carl Chiarella, Boda Kang

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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 consider the problem of pricing American-type compound options when the underlying dynamics follow Heston’s stochastic volatility and with stochastic interest rate driven by Cox-Ingersoll-Ross (CIR) processes. We use a partial differential equation (PDE) approach to obtain a numerical solution. The problem is formulated as the solution to a two-pass free boundary PDE problem which is solved via a sparse grid approach and is found to be accurate and efficient compared with the results from a benchmark solution based on a least-squares Monte Carlo simulation combined with the PSOR.
Original languageEnglish
Pages (from-to)71-92
Number of pages22
JournalJournal of Computational Finance
Issue number1
Publication statusPublished - 30 Sept 2013

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