From characteristic functions to implied volatility expansions

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Title: From characteristic functions to implied volatility expansions
Authors: Jacquier, A
Lorig, M
Item Type: Journal Article
Abstract: For any strictly positive martingale S with an analytically tractable characteristic function, we provide an expansion for the implied volatility. This expansion is explicit in the sense that it involves no integrals, but only polynomials in log(K/S0). We illustrate the versatility of our expansion by computing the approximate implied volatility smile in three well-known martingale models: one finite activity exponential Levy model (Merton), one infinite activity exponential Levy model (Variance Gamma), and one stochastic volatility model (Heston). We show how this technique can be extended to compute approximate forward implied volatilities and we implement this extension in the Heston setting. Finally, we illustrate how our expansion can be used to perform a model-free calibration of the empirically observed implied volatility surface.
Date of Acceptance: 30-Jul-2014
ISSN: 1475-6064
Journal / Book Title: Advances in Applied Probability
Copyright Statement: Accepted manuscript will be available when article is published.
Publication Status: Accepted
Embargo Date: publication subject to indefinite embargo
Appears in Collections:Financial Mathematics
Faculty of Natural Sciences

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