| Popis: |
A non-uniform generation of the points for discretization of the spatial variables in pricing stochastic volatility jump models, such as the model of Bates, is given. The distribution attempts to concentrate on the hotzone at which the price of the option should be given with high precision. The approach is quadratically convergent in space and for the jump term, as well as with quartic rate of convergence in time. We show that the numerical procedure has conditional stability and is fast in pricing both American and European vanilla options under such models. In fact, enough criteria for global convergence of the discrete equations are discussed. Computational results for various options show the superiority and efficiency of our approach. |
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