A new Fourier transform algorithm for value-at-risk

In this paper, we introduce a new Fourier method for computing value-at-risk for a portfolio with derivatives and for return models with fat tails. The new method does not assume that the characteristic function for the return model is known explicitly. We define a class of admissible models for returns and present statistical evidence that supports our approach. We discuss the details of the algorithm. The paper concludes with two applications of value-at-risk. Both examples illustrate the effect that changes in the models for portfolio value and for risk factor returns have on the value-at-risk surface.