Computing Quantiles in Regime-Switching Jump-Diffusions with Application to Optimal Risk Management: a Fourier Transform Approach

Abstract: In this paper we consider the problem of calculating the quantiles of a risky position, the dynamic of which is described as a continuous time regime-switching jump-diffusion, by using Fourier Transform methods. Furthermore, we study a classical option-based portfolio strategy which minimizes the Value-at-Risk of the hedged position and show the impact of jumps and switching regimes on the optimal strategy in a numerical example. However, the analysis of this hedging strategy, as well as the computational technique for its implementation, is fairly general, i.e. it can be applied to any dynamical model for which Fourier transform methods are viable.