On Model Robustness of the Regime Switching Approach for Pegged Foreign Exchange Markets

We test the robustness of the regime switching model for pegged markets introduced in S. Drapeau, T. Wang, T. Wang (2021). In particular, two disputable underlying assumptions: 1) A Black and Scholes model with low volatility for the pre-depegging regime. 2) A thin tail distribution - Poisson type - for the time of the depegging. For the pre-depegging regime, we consider a bounded model within the peg -- from Ingersoll and Rady. For the depegging time, we consider fat tail distributions more in line with catastrophic events -- Pareto/Fr\'echet. We derive the option prices formula for each combination of these models. We then calibrate to option data from Hong Kong Dollars as well as Swiss Franc FX markets. In comparison to the benchmark model in S. Drapeau, T. Wang, T. Wang (2021), it turns out that the relevant resulting characteristics -- probability of a depegging before maturity, appreciation/depreciation at the depegging time as well as post-depegging volatility -- are strongly robust in terms of model choice for this regime switching approach. However, from a term structure perspective, fat tail distributions fit the data significantly better and provide more rational depegging probabilities for short and long maturities