Communications in Mathematical Finance

Option pricing within Hestonís stochastic and stochastic-jump models

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  • Abstract


           The quest to have a model that will be better at approximating market prices and produce fit better than Hestonís Stochastic model motivated us to combine jump components to Hestonís Stochastic model which we called Hestonís Stochastic-Jump model (HSJ).  Complete derivation of the Hestonís Stochastic-Jump model was presented. Simulation studies were conducted. Pricing performances of Hestonís Stochastic and Hestonís Stochastic-Jump models were empirically analysed using the NASDAQ index call option price quotations.  Results show that Hestonís Stochastic-Jump model performed better than Hestonís Stochastic model by about 18% reduction in error.  

    Keywords: Hestonís Stochastic Model, Hestonís Stochastic-Jump Model, Calibration, Fast   Fourier Transform, Mean-Squared Error