The forward smile in local–stochastic volatility models

Andrea Pascucci and Andrea Mazzon

Journal of Computational Finance

Abstract: ABSTRACT We introduce an approximation of forward-start options in a multi-factor local-stochastic volatility model. We derive explicit expansion formulas for the so-called;forward implied volatility, which can be useful to price complex path-dependent;options as cliquets. The expansion involves only polynomials and can be computed;without the need for numerical procedures or special functions. Recent results on;the exploding behavior of the forward smile in the Heston model are confirmed and;generalized to a wider class of local-stochastic volatility models. We illustrate the;effectiveness of the technique through some numerical tests.

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