THE PRICING OF EXOTIC OPTIONS BY MONTE–CARLO SIMULATIONS IN A LÉVY MARKET WITH STOCHASTIC VOLATILITY

Wim Schoutens () and Stijn Symens ()
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Wim Schoutens: K. U. Leuven, W. De Croylaan 54, B-3001 Leuven, Belgium
Stijn Symens: University of Antwerp, Middelheimlaan 1, B-2020 Antwerpen, Belgium

International Journal of Theoretical and Applied Finance (IJTAF), 2003, vol. 06, issue 08, 839-864

Abstract: Recently, stock price models based on Lévy processes with stochastic volatility were introduced. The resulting vanilla option prices can be calibrated almost perfectly to empirical prices. Under this model, we will price exotic options, like barrier, lookback and cliquet options, by Monte–Carlo simulation. The sampling of paths is based on a compound Poisson approximation of the Lévy process involved. The precise choice of the terms in the approximation is crucial and investigated in detail. In order to reduce the standard error of the Monte–Carlo simulation, we make use of the technique of control variates. It turns out that there are significant differences with the classical Black–Scholes prices.

Keywords: Exotic options; model risk; Monte–Carlo simulations; Lévy processes; stochastic volatility (search for similar items in EconPapers)
Date: 2003
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Citations: View citations in EconPapers (8)

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DOI: 10.1142/S0219024903002249

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