Modelling exchange rate returns: which flexible distribution to use?

It is well known that the normal distribution is inadequate in capturing the skewed and heavy-tailed behaviour of exchange rate returns. To this end, various flexible distributions that are capable of modelling the asymmetric and tailed behaviour of returns have been proposed. In this paper, we investigate the performance of the generalized lambda distribution (GLD) to capture the skewed and leptokurtic behaviour of exchange rate returns. We do this by conducting a comprehensive numerical study to compare the performance of the GLD against the performances of the skewed t distribution, the unbounded Johnson family of distributions and the normal inverse Gaussian (NIG) distribution. Our results suggest that in terms of the value-at-risk and expected shortfall, the GLD shows at least similar performance to the skewed t distribution and the NIG distribution. Considering the ease in GLD's use for random variate generation in Monte Carlo simulations, we conclude that the GLD can be a good alternative in various financial applications where modelling of the heavy tail behaviour is critical.