Model Robustness of the Regime Switching Approach for the Usd-Hkd Pegged Foreign Exchange Market

Abstract

We test the robustness of the regime switching model for the pegged market USD-HKD introduced in S. Drapeau, Want T. and Wang T. (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 pegg -- from Ingersoll and Rady. For the depegging time, we consider fat tail distributions more in line with catastrophic events -- Pareto/Frechet. We derive the option prices formula for each combination of these models and calibrate it to the option data from USD-HKD. In comparison to the benchmark model in \citep{drapeau2019}, 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.