A Two-stage Approach for Estimating Jump-diffusion Model with Application to Daily Returns of USD/CNY Exchange Rates

The time series of daily returns of USD/CNY exchange rates suggest that there exists a leptokurtic feature (higher peak and fat tail) that results from some occasional jumps. So, we introduce the jump-diffusion model to describe the time series of daily returns. Since the traditional parameter estimation method, for example, MLE, can hardly detect the jumps exactly, then, we combine the jump detection method proposed by Lee and Mykland into the MLE method, formulate the two-stage approach for estimating the jump-diffusion model. Based on this, we further do some empirical results for daily returns of USD/CNY exchange rates, derive that the two-stage approach can fit the real data relatively better.