A Poisson process with random intensity for modeling financial stability

Stock market crashes are hazardous for financial stability and usually modeled via Poisson processes having a predetermined fixed intensity. This study uses a more general framework by allowing the intensity to be random in order to model rare events called the “unpredictable unknowns”. Three stock indices, namely Japan Nikkei 225, US Dow Jones Industrial Average and Turkish BIST 100 are analyzed. Simulation results indicate that in stable markets, we encounter fewer unpredictable unknowns compared to unstable ones. However, it is also shown that stable markets are more prone to severe financial crises.