Abstract
We present a novel method for calibrating pricing models to incorporate the effects of the volatility Smile and its dynamics. This is made possible by simultaneously calibrating to the Smile surface of European options as well as to prices of Barrier options which encapsulate information on the Smile dynamics. An arbitrary combination of European and simple exotics may be calibrated to without over-fitting or resorting to non-stationary model parameters. This technique has a natural analogy with classical statistical mechanics, and also allows analytic derivation of hedge ratios. Numerical implementation of the calibration method utilises Monte Carlo and PDE approaches and we present results to illustrate its practical use and effectiveness.
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