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Title: Spanning GARCH: Pricing uncertainty in the very long run Authors:  Abderrahim Taamouti - Durham University Business School (United Kingdom) [presenting]
Abstract: High-order moments derivatives, such as variance and skewness swaps, are increasingly popular risk management tools for Foreign Exchange exposures. We propose a simple Fourier inversion-based method to estimate the risk neutral value of a spanning contract contingent on the future outcome of an asset price. The price of the contract can computed by a single quadrature evaluation of the characteristic function and is easily implemented for moment swaps beyond variance, such as skewness and kurtosis. Indeed, even fractional moment swaps are admissible in this framework and can be estimated directly from spot and yield curve data via maximum likelihood. We show that the predicted moment swaps based on our approach - with the characteristic function computed using a GARCH model- perform well against both option implied variance and skewness swaps and traded variance swaps.