COMPONENTWISE SPLITTING METHODS FOR PRICING AMERICAN OPTIONS UNDER STOCHASTIC VOLATILITY

Samuli Ikonen () and Jari Toivanen ()
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Samuli Ikonen: Nordea Markets, FIN-00020 Nordea, Finland
Jari Toivanen: Department of Mathematical Information Technology, University of Jyväskylä, Agora FIN-40014, Finland

International Journal of Theoretical and Applied Finance (IJTAF), 2007, vol. 10, issue 02, 331-361

Abstract: Efficient numerical methods for pricing American options using Heston's stochastic volatility model are proposed. Based on this model the price of a European option can be obtained by solving a two-dimensional parabolic partial differential equation. For an American option the early exercise possibility leads to a lower bound for the price of the option. This price can be computed by solving a linear complementarity problem. The idea of operator splitting methods is to divide each time step into fractional time steps with simpler operators. This paper proposes componentwise splitting methods for solving the linear complementarity problem. The basic componentwise splitting decomposes the discretized problem into three linear complementarity problems with tridiagonal matrices. These problems can be efficiently solved using the Brennan and Schwartz algorithm, which was originally introduced for American options under the Black and Scholes model. The accuracy of the componentwise splitting method is increased by applying the Strang symmetrization. The good accuracy and the computational efficiency of the proposed symmetrized splitting method are demonstrated by numerical experiments.

Keywords: American option pricing; stochastic volatility model; linear complementarity problem; componentwise splitting method; Strang symmetrization (search for similar items in EconPapers)
Date: 2007
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Citations: View citations in EconPapers (9)

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DOI: 10.1142/S0219024907004202

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