Pricing of options on assets with level dependent stochastic volatility

Alexander Skabelin

doi:10.1117/12.616198

23 May 2005 Pricing of options on assets with level dependent stochastic volatility

Alexander Skabelin

Proceedings Volume 5848, Noise and Fluctuations in Econophysics and Finance; (2005) https://doi.org/10.1117/12.616198
Event: SPIE Third International Symposium on Fluctuations and Noise, 2005, Austin, Texas, United States

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.

Citation Download Citation

Alexander Skabelin "Pricing of options on assets with level dependent stochastic volatility", Proc. SPIE 5848, Noise and Fluctuations in Econophysics and Finance, (23 May 2005); https://doi.org/10.1117/12.616198

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