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 by Drapeau et al. [How rational are the option prices of the Hong Kong dollar exchange rate? J. Derivatives, 2021, 28(3), 140–161]. In particular, there are two disputable underlying assumptions: (1) a Black and Scholes model with low volatility for the pre-depegging regime and (2) a thin tail distribution—Exponential 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/Fréchet. We derive the option prices formula for each combination of these models. We then calibrate to option data from USD-HKD as well as EUR-CHF. In comparison to the benchmark model in Drapeau et al. [How rational are the option prices of the Hong Kong dollar exchange rate? J. Derivatives, 2021, 28(3), 140–161], 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.