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Proceedings Paper

Pricing of options on assets with level dependent stochastic volatility
Author(s): Alexander Skabelin
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Paper Abstract

Many asset classes, such as interest rates, exchange rates, commodities, and equities, often exhibit a strong relationship between asset prices and asset volatilities. This paper examines an analytical model that takes into account this level dependence of volatility. We demonstrate how prices of European options under stochastic volatility can be calculated analytically via inverse Laplace transformations. We also examine a Hull-White stochastic volatility expansion. While a success of this expansion in approximate computation of option prices has already been established empirically, the question of convergence has been left unanswered. We demonstrate, in this paper, that this expansion diverges essentially for all possible stochastic volatility processes. In contrast to a majority of volatility expansion models reported in the literature, we construct expansions that explicitly show the contribution of all of the variance moments. Such complete expansions are very useful in analyzing properties of option prices, as we demonstrate by examining why empirical volatility surfaces plotted as a function of the rescaled strike can sometimes exhibit striking time invariance.

Paper Details

Date Published: 23 May 2005
PDF: 15 pages
Proc. SPIE 5848, Noise and Fluctuations in Econophysics and Finance, (23 May 2005); doi: 10.1117/12.616198
Show Author Affiliations
Alexander Skabelin, EBF & Associates (United States)

Published in SPIE Proceedings Vol. 5848:
Noise and Fluctuations in Econophysics and Finance
Derek Abbott; Jean-Philippe Bouchaud; Xavier Gabaix; Joseph L. McCauley, Editor(s)

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