Bayesian Inference in Markov Modulated Levy processes

Abstract

Levy Process are used in finance for Asset Modeling and Risk Management. Markov Modulated Levy Process(MMLP) are a more flexible class of Stochastic Processes which capture phase changes arising in economies by allowing jumps in drift and volatility, linked to hidden states of a Markov chain. Theses models have been used to model option prices, renewable energy markets as well as for risk quantification. While Bayesian inference methods exists for simpler regime-switching models, we aim to extend it to more complex MMLPs. Our approach involves applying Bayesian estimation techniques to recover the hidden states and the parameters associated with each state of the Markov Chain. We propose Markov Chain Monte Carlo algorithms to perform Bayesian inference for MMLPs. This will allow for a more data-driven analysis of asset returns with regime shifts and jumps