Using the Laplace transform approach, we compute the expected value and the variance of the error of a hedging strategy for a contingent claim when trading in discrete time. The method applies to a fairly general class of models, including Black-Scholes, Merton's jump-diffusion and Normal Inverse Gaussian, and to several interesting strategies, as the Black-Scholes delta, the Wilmott's improveddelta and the local optimal one. With this approach, also transaction costs may be treated. The results obtained are not asymptotical approximations but exact and efficient formulas, valid for any number of trading dates. They can also be employed under model mispecification, to measure the influence of model risk on a hedging strategy.

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This paper proposes a calibration algorithm that fits multi-factor Gaussian models to the implied volatilities of caps using the respective minimal consistent family to infer the forward rate curve. The algorithm is applied to three forward rate volatility structures and their combination to form two-factor models. The efficiency of the consistent calibration is evaluated through comparisons with non-consistent methods. The selection of the number of factors and of the volatility functions is supported by a Principal Component Analysis. Models are evaluated in terms of in-sample and out-of-sample data fitting as well as stability of parameter estimates. The results are analyzed mainly focusing on the capability of fitting the market implied volatility curve and, in particular, of reproducing its characteristic humped shape.

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We consider the problem of measuring the performance of a dynamic strategy, re-balanced at a discrete set of dates, with the objective of hedging a claim in an incomplete market driven by a general multi-dimensional affine process. The main purpose of the paper is to propose a method to efficiently compute the expected value and variance of the hedging error of the strategy. Representing the payoff of the claim as an inverse Laplace transform, we are able to obtain semi-explicit formulas for strategies satisfying a certain property. The result is quite general and can be applied to a very rich class of models and strategies, including Delta hedging. We provide illustrations for the case of the Heston stochastic volatility model.