Game of Vols

43 Pages Posted: 22 Oct 2019

See all articles by Peter Carr

Peter Carr

New York University (NYU) - Finance and Risk Engineering Department

Gregory Pelts

Scotia Bank

Date Written: May 12, 2015

Abstract

The absolute values of the spot and strike derivatives of the vanilla option price are probabilities of finishing in the money under different numeraires. At each fixed term, one of these probabilities can be related to the other using a convex distortion function. Using results from convex duality, we show that arbitrageā€free coterminal option prices can always be generated by specifying a convex distortion function. We also propose a parametrization of this convex distortion function and an interpolation method in the time dimension. The option prices generated by this method are free of any arbitrage - the calendar arbitrage, the strike spread arbitrage, and the butterfly spread arbitrage.

Keywords: volatility, surface, arbitrage-free, options

Suggested Citation

Carr, Peter and Pelts, Gregory, Game of Vols (May 12, 2015). Available at SSRN: https://ssrn.com/abstract=3422540

Peter Carr

New York University (NYU) - Finance and Risk Engineering Department ( email )

6 Metrotech Center
New York, NY 11201
United States

Gregory Pelts (Contact Author)

Scotia Bank ( email )

Word Financial Center
New York City, NY 10278
United States

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