Beschreibung:
This paper proposes a simple bounded stochastic motion to model equity price dynamics under shocks. The stochastic process has a quasi-bounded boundary which can be breached if the probability leakage condition is met. The quasi-boundedness of the process at the boundary can thus provide an indicator of the possible risk of equities under price shocks or in distress. Empirical calibration of the model parameters of the proposed process for equities can be performed easily due to the availability of an analytically tractable probability density function which generates fat-tailed distributions consistent with empirical observations. The volatility and mean-reversion of the S&P500 dynamics calibrated by the process are positively and negatively co-integrated, respectively, with the VIX index representing the level of market distress. The process captures the high likelihood of Hertz's default about two months earlier, using only information until that point, and before the firm filed for Chapter 11 bankruptcy in May 2020 as a result of the COVID-19 pandemic. Empirical calibration of the process for GameStop's stock price shows that the short squeeze in the stock occurred when the condition for breaching the upper boundary was met on 14 January 2021, i.e., about two weeks before major short-sellers closed out their positions with significant losses. The trading volume of the stock was positively co-integrated with the probability leakage ratio.