Abstract:
We consider a continuous time stochastic process which exhibits a regime-switch in the dynamics accordingly to a certain threshold. This process is solution to a stochastic differential equation with piecewise constant coefficients. We introduce and analyze estimators for the diffusion coefficient, the drift coefficient and the threshold level. We consider the local volatility model associated to this SDE and apply our estimators to time series of daily prices of several assets, finding evidence of leverage effect (negative correlation between prices and volatilies) and of mean-reversion effects in the dynamics of the prices. (Joint work with Antoine Lejay)