LOGNORMAL-MIXTURE DYNAMICS AND CALIBRATION TO MARKET VOLATILITY SMILES

Damiano Brigo and Fabio Mercurio ()
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Fabio Mercurio: Product and Business Development Group, Banca IMI, San Paolo-IMI Group, Corso Matteotti, 6, 20121 Milano, Italy

International Journal of Theoretical and Applied Finance (IJTAF), 2002, vol. 05, issue 04, 427-446

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, deriving explicit dynamics, 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.

Keywords: Local-volatility models; stock-price dynamics; forward measure; mixure of densities; analytical tractability; explicit option pricing; lognormal-mixture dynamics; volatility smaile (search for similar items in EconPapers)
Date: 2002
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DOI: 10.1142/S0219024902001511

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