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Efficient \(L\)-stable method for parabolic problems with application to pricing American options under stochastic volatility. (English) Zbl 1173.91022

The paper proposes an efficient \(L\)-stable numerical method for a semilinear parabolic problem with non-smooth initial data. The method presented here is based on a Padé approximation of the matrix exponential function, which is used to modify the existent exponential time differencing Runge-Kutta schemes for nonlinear parabolic problems. By using splitting techniques, computationally efficient parallel versions of the schemes are constructed. Based on this modified scheme, the author develops and implements an algorithm for solving two problems from financial mathematics: pricing American options under stochastic volatility and the two asset American options pricing problem. The numerical experiments presented here show a good agreement with the results obtained previously in the literature.

MSC:

91B28 Finance etc. (MSC2000)
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