CALIBRATING THE SMILE WITH MULTIVARIATE TIME-CHANGED BROWNIAN MOTION AND THE ESSCHER TRANSFORM

Gian Luca Tassinari () and Michele Leonardo Bianchi ()
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Gian Luca Tassinari: Department of Mathematics, Alma Mater Studiorum, University of Bologna, Piazza di Porta San Donato, 5, 40126, Bologna, Italy
Michele Leonardo Bianchi: Regulation and Macroprudential Analysis Department, Bank of Italy, Via Milano 53, 00184, Rome, Italy

International Journal of Theoretical and Applied Finance (IJTAF), 2014, vol. 17, issue 04, 1-34

Abstract: In this study, we investigate two multivariate time-changed Brownian motion option pricing models in which the connection between the historical measure P and the risk-neutral measure Q is given by the Esscher transform. The models incorporate skewness, kurtosis and more complex dependence structures among stocks log-returns than the simple correlation matrix. The two models can be seen as a multivariate extension of the normal inverse Gaussian (NIG) model and the variance gamma (VG) model, respectively. We discuss two possible approaches to estimate historical asset returns and calibrate univariate option implied volatilities. While the first approach considers only time series of log-returns, the second approach makes use of both time series of log-returns and univariate observed volatility surfaces. To calibrate the models, there is no need of liquid multivariate derivative quotes.

Keywords: Volatility smile; asset price dynamics; time-changed Brownian motion; multivariate non-Gaussian processes; multivariate Esscher transform (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (8)

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DOI: 10.1142/S021902491450023X

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