Communications in Mathematical Finance

Option pricing within Heston’s 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 Heston’s Stochastic model motivated us to combine jump components to Heston’s Stochastic model which we called Heston’s Stochastic-Jump model (HSJ).  Complete derivation of the Heston’s Stochastic-Jump model was presented. Simulation studies were conducted. Pricing performances of Heston’s Stochastic and Heston’s Stochastic-Jump models were empirically analysed using the NASDAQ index call option price quotations.  Results show that Heston’s Stochastic-Jump model performed better than Heston’s Stochastic model by about 18% reduction in error.  

  Keywords: Heston’s Stochastic Model, Heston’s Stochastic-Jump Model, Calibration, Fast   Fourier Transform, Mean-Squared Error