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

A compound option (the mother option) gives the holder the right, but not the 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 sto...

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Bibliographic Details
Published in:The journal of computational finance 2013-10, Vol.17 (1), p.71-92
Main Authors: Chiarella, Carl, Kang, Boda
Format: Article
Language:English
Subjects:
Interest rates
Monte Carlo simulation
Partial differential equations
Securities prices
Stochastic models
Studies
Volatility
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Summary:A compound option (the mother option) gives the holder the right, but not the 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 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 projected successive over-relaxation method. [PUBLICATION ABSTRACT]
ISSN:1460-1559
1755-2850
DOI:10.21314/JCF.2013.264