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2. ADI schemes with Ikonen-Toivanen splitting for pricing American put options in the Heston model

Author

Tinne Haentjens, Karel in’t Hout, Kim Volders, Theodore E. Simos, George Psihoyios, and Ch. Tsitouras

Subjects
Stochastic partial differential equation, Computer. Automation, Alternating direction implicit method, Partial differential equation, Stochastic volatility, Stochastic process, Numerical analysis, Mathematical economics, Mathematics, Valuation (finance), Heston model
Abstract

The numerical valuation of American put options under the Heston stochastic volatility model is considered. We investigate in this paper the potential of combining the recent splitting approach of Ikonen & Toivanen (2004, 2009) with Alternating Direction Implicit schemes to obtain more efficient numerical methods

Published
2010

3. Stability of central finite difference schemes on non-uniform grids for 1D partial differential equations with variable coefficients

Author

Kim Volders, Theodore E. Simos, George Psihoyios, and Ch. Tsitouras

Subjects
Stochastic partial differential equation, Partial differential equation, Differential equation, Mathematical analysis, Finite difference method, First-order partial differential equation, Finite difference, Mathematics, Numerical stability, Numerical partial differential equations
Abstract

This paper deals with stability in the numerical solution of general one-dimensional partial differential equations with variable coefficients. We will generalize stability results for central finite difference schemes on non-uniform grids that were obtained by In't Hout & Volders (2009) for the Black-Scholes equation. Subsequently we will apply our stability results to the CEV model.

Published
2010

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