Lognormal-Mixture Dynamics and Calibration to Volatility Smiles and Skews

21 Pages Posted: 11 Jul 2001

See all articles by Damiano Brigo

Damiano Brigo

Imperial College London - Department of Mathematics

Gianvittorio Mauri

Banca IMI

Fabio Mercurio

Bloomberg L.P.

Abstract

We introduce a general class of analytically tractable models for the dynamics of an asset price based on the assumption that the asset-price density is given by the mixture of known basic densities. We consider the lognormal-mixture model as a fundamental example, and for the first time we derive the related explicit dynamics and show that it leads to a stochastic differential equation admitting a unique strong solution. We also provide closed form formulas for option prices and analytical approximations for the implied volatility function. We then introduce the asset-price model that is obtained by shifting the previous lognormal-mixture dynamics and investigate its analytical tractability. We finally consider a specific example of calibration to real market option data.

Suggested Citation

Brigo, Damiano and Mauri, Gianvittorio and Mercurio, Fabio, Lognormal-Mixture Dynamics and Calibration to Volatility Smiles and Skews. EFA 2001 Barcelona Meetings. Available at SSRN: https://ssrn.com/abstract=276204 or http://dx.doi.org/10.2139/ssrn.276204

Damiano Brigo

Imperial College London - Department of Mathematics ( email )

South Kensington Campus
London SW7 2AZ, SW7 2AZ
United Kingdom

HOME PAGE: http://www.imperial.ac.uk/people/damiano.brigo

Gianvittorio Mauri (Contact Author)

Banca IMI ( email )

Corso Matteotti 6
20121 Milano, 20100
Italy

Fabio Mercurio

Bloomberg L.P. ( email )

731 Lexington Avenue
New York, NY 10022
United States

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