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A Numerical Analysis Of The Extended Black–Scholes Model

Author

Listed:
  • SERGIO ALBEVERIO

    (Institut für Angewandte Mathematik, Universität Bonn, Wegelerstr 6, 53115 Bonn, Germany)

  • ALEX POPOVICI

    (Institut für Angewandte Mathematik, Universität Bonn, Wegelerstr 6, 53115 Bonn, Germany)

  • VICTORIA STEBLOVSKAYA

    (Department of Mathematical Sciences, Bentley College, 175 Forest Street, Waltham, MA 02452, USA)

Abstract

In this article some numerical results regarding the multidimensional extension of the Black–Scholes model introduced by Albeverio and Steblovskaya [1] (a multidimensional model with stochastic volatilities and correlations) are presented. The focus lies on aspects concerning the use of this model for the practice of financial derivatives. Two parameter estimation methods for the model using historical data from the market and an analysis of the corresponding numerical results are given. Practical advantages of pricing derivatives using this model compared to the original multidimensional Black–Scholes model are pointed out. In particular the prices of vanilla options and of implied volatility surfaces computed in the model are close to those observed on the market.

Suggested Citation

  • Sergio Albeverio & Alex Popovici & Victoria Steblovskaya, 2006. "A Numerical Analysis Of The Extended Black–Scholes Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 9(01), pages 69-89.
    • Handle: RePEc:wsi:ijtafx:v:09:y:2006:i:01:n:s0219024906003469
    DOI: 10.1142/S0219024906003469
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