Financial crashes as endogenous jumps: estimation, testing and forecasting

This paper provides an econometric approach for forecasting financial crashes based on diffusion processes with time-varying parameters that are driven by market fundamentals. Under a polynomial drift function, one obtains a cusp stochastic process that entails a generalized exponential stationary distribution. This class of densities is quite convenient as it allows for skewness, different tail shapes and even multimodality, which corresponds to multiple equilibria. Movements from one equilibrium to another, due to changes in the market fundamentals, then relates to crashes. Methods for fitting and evaluating this sort of diffusion processes are proposed to enable the estimation and forecast of crash events. Finally, an empirical assessment is carried out by tracking the likelihood of a crash during the Swedish twin crises in the early 1990s.