ASYMPTOTIC ANALYSIS FOR FOREIGN EXCHANGE DERIVATIVES WITH STOCHASTIC VOLATILITY

Charles Cuthbertson, Grigorios Pavliotis (), Avraam Rafailidis and Petter Wiberg
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Charles Cuthbertson: Department of Statistics, University of Oxford, OX1 3TG, UK
Grigorios Pavliotis: Department of Mathematics, Imperial College London, SW7 2AZ, UK
Avraam Rafailidis: Department of Mathematics, King's College London, WC2R 2LS, UK
Petter Wiberg: Mathematics Institute, The University of Warwick, Coventry CV4 7AL, UK

International Journal of Theoretical and Applied Finance (IJTAF), 2010, vol. 13, issue 07, 1131-1147

Abstract: We consider models for the valuation of derivative securities that depend on foreign exchange rates. We derive partial differential equations for option prices in an arbitrage-free market with stochastic volatility. By use of standard techniques, and under the assumption of fast mean reversion for the volatility, these equations can be solved asymptotically. The analysis goes further to consider specific examples for a number of options, and to a considerable degree of complexity.

Keywords: Derivatives pricing; FX options; stochastic volatility; multiscale analysis; singular perturbation theory (search for similar items in EconPapers)
Date: 2010
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DOI: 10.1142/S0219024910006145

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