Journal
INTERNATIONAL JOURNAL OF THEORETICAL AND APPLIED FINANCE
Volume 10, Issue 2, Pages 331-361Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0219024907004202
Keywords
American option pricing; stochastic volatility model; linear complementarity problem; componentwise splitting method; Strang symmetrization
Categories
Funding
- Academy of Finland [207089]
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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.
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