OPTION PRICING UNDER ORNSTEIN-UHLENBECK STOCHASTIC VOLATILITY: A LINEAR MODEL

Giacomo Bormetti (), Valentina Cazzola () and Danilo Delpini ()
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Giacomo Bormetti: Centro Studi Rischio e Sicurezza, Istituto Universitario di Studi Superiori, V.le Lungo Ticino Sforza 56, Pavia, 27100, Italy;
Valentina Cazzola: Centro Studi Rischio e Sicurezza, Istituto Universitario di Studi Superiori, V.le Lungo Ticino Sforza 56, Pavia, 27100, Italy;
Danilo Delpini: Dipartimento di Fisica Nucleare e Teorica, Università degli Studi di Pavia, via Bassi 6, Pavia, 27100, Italy;

International Journal of Theoretical and Applied Finance (IJTAF), 2010, vol. 13, issue 07, 1047-1063

Abstract: We consider the problem of option pricing under stochastic volatility models, focusing on the linear approximation of the two processes known as exponential Ornstein-Uhlenbeck and Stein-Stein. Indeed, we show they admit the same limit dynamics in the regime of low fluctuations of the volatility process, under which we derive the exact expression of the characteristic function associated to the risk neutral probability density. This expression allows us to compute option prices exploiting a formula derived by Lewis and Lipton. We analyze in detail the case of Plain Vanilla calls, being liquid instruments for which reliable implied volatility surfaces are available. We also compute the analytical expressions of the first four cumulants, that are crucial to implement a simple two steps calibration procedure. It has been tested against a data set of options traded on the Milan Stock Exchange. The data analysis that we present reveals a good fit with the market implied surfaces and corroborates the accuracy of the linear approximation.

Keywords: Econophysics; stochastic volatility; Monte Carlo simulation; option pricing; model calibration (search for similar items in EconPapers)
Date: 2010
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Citations: View citations in EconPapers (1)

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DOI: 10.1142/S0219024910006108

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