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High-order compact finite difference scheme for option pricing in stochastic volatility models. (English) Zbl 1244.91100
Summary: We derive a new high-order compact finite difference scheme for option pricing in stochastic volatility models. The scheme is fourth order accurate in space and second order accurate in time. Under some restrictions, theoretical results like unconditional stability in the sense of von Neumann are presented. Where the analysis becomes too involved we validate our findings by a numerical study. Numerical experiments for the European option pricing problem are presented. We observe fourth order convergence for non-smooth payoff.

91G60Numerical methods in mathematical finance
65M06Finite difference methods (IVP of PDE)
65M12Stability and convergence of numerical methods (IVP of PDE)
91G20Derivative securities
Full Text: DOI arXiv
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