Abstrakt
Paper focuses on an econometric model known as the cusp within standard catastrophe theory. This model allows discontinuous change in a dependent variable for a small continuous change in parameters.
This model is given by stochastic di erential equation with cubic drift. The closed-form solution of density for this process is known only in the stationary case and this density belongs to the class of generalized exponential distributions, which allows for skewness, di erent tail shapes and multiple equilibria.
The transition density is approximated by the finite difference method and parameters are estimated using the maximum likelihood principle. An empirical example deals with the crash known as Black Monday, where parameters of the drift are driven by market fundamentals.