Markov Regime-Switching in-Mean Model with Tempered Stable Distribution

Markov Regime-Switching (MRS) model is a widely used approach to model the actuarial and financial data with potential structural breaks. In the original MRS model, the innovation series is assumed to follow a Normal distribution, which cannot accommodate fat-tailed properties commonly present in empirical data. Many existing studies point out that this problem can lead to inconsistent estimates of the MRS model. To overcome it, the Student’s t-distribution and General Error Distribution (GED) are two most popular alternatives. However, a recent study argues that those distributions lack in stability under aggregation and suggests using the $$\alpha $$α-stable distribution instead. The issue of the $$\alpha $$α-stable distribution is that its second moment does not exist in most cases. To address this issue, the tempered stable distribution, which retains most characteristics of the $$\alpha $$α-stable distribution and has defined moments, is a natural candidate. In this paper, we conduct systematically designed simulation studies to demonstrate that the MRS model with tempered stable distribution uniformly outperforms that with Student’s t-distribution and GED. Our empirical study on the implied volatility of the S&P 500 options (VIX) also leads to the same conclusions. Therefore, we argue that the tempered stable distribution could be widely used for modelling the actuarial and financial data in general contexts with an MRS-type specification. We also expect that this method will be more useful in modelling more volatile financial data from China and other emerging markets.