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

TL;DR

This paper develops a Fourier Transform method to compute quantiles of positions modeled by regime-switching jump-diffusions, and applies it to optimize risk management strategies considering jumps and regime changes.

Contribution

It introduces a general Fourier Transform approach for quantile calculation in complex stochastic models and demonstrates its application to risk management strategies.

Findings

Quantiles can be efficiently computed using Fourier methods in regime-switching jump-diffusions.

Jumps and regime switches significantly affect optimal risk management strategies.

The proposed method is versatile and applicable to various models with Fourier transform feasibility.

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.