Symmetric martingales and symmetric smiles

Michael R. Tehranchi

Stochastic Processes and their Applications, 2009, vol. 119, issue 10, 3785-3797

Abstract: A local martingale X is called arithmetically symmetric if the conditional distribution of XT-Xt is symmetric given , for all 0 T- t) for all 0 =0. The notion of a geometrically symmetric martingale is also defined and characterized as the Doléans-Dade exponential of an arithmetically symmetric local martingale. As an application of these results, we show that a market model of the implied volatility surface that is initially flat and that remains symmetric for all future times must be the Black-Scholes model.

Keywords: Ocone; martingales; Symmetric; increments; Implied; volatility (search for similar items in EconPapers)
Date: 2009
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Citations: View citations in EconPapers (13)

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