STOCHASTIC VOLATILITY

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

International Journal of Theoretical and Applied Finance (IJTAF), 2002, vol. 05, issue 05, 515-530

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.

Keywords: Change of measure; stochastic volatility; Hull and White model; stochastic calculus (search for similar items in EconPapers)
Date: 2002
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DOI: 10.1142/S021902490200150X

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