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Stochastic Volatility

Author

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  • SOTIRIOS SABANIS

    (Department of Mathematics and Statistics, The University of Edinburgh, Edinburgh EH9 3JZ, UK)

Abstract

Hull and White [1] have priced a European call option for the case in which the volatility of the underlying asset is a lognormally distributed random variable. They have obtained their formula under the assumption of uncorrelated innovations in security price and volatility. Although the option pricing formula has a power series representation, the question of convergence has been left unanswered. This paper presents an iterative method for calculating all the higher order moments of volatility necessary for the process of proving convergence theoretically. Moreover, simulation results are given that show the practical convergence of the series. These results have been obtained by using a displaced geometric Brownian motion as a volatility process.

Suggested Citation

  • Sotirios Sabanis, 2002. "Stochastic Volatility," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 5(05), pages 515-530.
    • Handle: RePEc:wsi:ijtafx:v:05:y:2002:i:05:n:s021902490200150x
    DOI: 10.1142/S021902490200150X
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    Cited by:

    1. Lu, Xiaoping & Putri, Endah R.M., 2020. "A semi-analytic valuation of American options under a two-state regime-switching economy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 538(C).
    2. Sotirios Sabanis & Ying Zhang, 2020. "A fully data-driven approach to minimizing CVaR for portfolio of assets via SGLD with discontinuous updating," Papers 2007.01672, arXiv.org.

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