Implied Volatility Smirk in Lévy Markets

19 Pages Posted: 1 Jan 2015  

Federico De Olivera

Universidad de la Republica

José Fajardo

Getulio Vargas Foundation

Ernesto Mordecki

Universidad de la Republica - Centro de Matematica

Date Written: December 30, 2014

Abstract

We introduce skewed Lévy models, that have a symmetric jump measure multiplied by dumping exponential factor, in order to study the implied volatility smirk in Lévy markets. The dumping factor depends on a parameter beta, this results in a measure of the skewness of the model. We show that variation of this parameter produces the typical smirk observed in implied volatility curves. Our main result shows a particular monotonicity behavior of the implied volatility of skewed models around the symmetry point beta = -1/2. These results, which apply to many models in the literature, hold independent of any finite maturity.

Keywords: Skewness, Lévy Processes, Implied Volatility Smirk.

JEL Classification: G10, G12

Suggested Citation

De Olivera, Federico and Fajardo, José and Mordecki, Ernesto, Implied Volatility Smirk in Lévy Markets (December 30, 2014). Available at SSRN: https://ssrn.com/abstract=2544108 or http://dx.doi.org/10.2139/ssrn.2544108

Federico De Olivera

Universidad de la Republica ( email )

Gonzalo Ramirez 1926
Montevideo, 11200
Uruguay

José Fajardo (Contact Author)

Getulio Vargas Foundation ( email )

Brazil
55213799 5781 (Phone)

HOME PAGE: http://www.josefajardo.com

Ernesto Mordecki

Universidad de la Republica - Centro de Matematica ( email )

Igua 4225
Facultad de Ciencias
CP 11400 Montevideo
Uruguay
598 2 525 25 22 (Phone)
598 2 522 56 03 (Fax)

HOME PAGE: http://www.cmat.edu.uy/~mordecki

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