Jump Diffusion and {\alpha}-Stable Techniques for the Markov Switching Approach to Financial Time Series

TL;DR

This paper compares Jump Diffusion and {\

Contribution

It provides a detailed comparison of two advanced models for financial time series, highlighting the robustness and computational trade-offs of each.

Findings

Jump diffusion model is highly robust and accurate for financial data.

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paper_type":"empirical"}}}

Abstract

We perform a detailed comparison between a Markov Switching Jump Diffusion Model and a Markov Switching {\alpha}-Stable Distribution Model with respect to the analysis of non-stationary data. We show that the jump diffusion model is extremely robust, flexible and accurate in fitting of financial time series. A thorough computational study involving the two models being applied to real data, namely, the S&P500 index, is provided. The study shows that the jump-diffusion model solves the over-smoothing issue stated in (Di Persio and Frigo, 2016), while the {\alpha}-stable distribution approach is a good compromise between computational effort and performance in the estimate of implied volatility, which is a major problem widely underlined in the dedicated literature.