Estimation of Random Volatility via Jump Diffusion Model

Abstract

We investigate the daily share prices of the Nikkei 225 stock market index to identify jump times of the stock index using a jump diffusion model, which consists of the Black-Scholes model with stochastic volatility and a compound Poisson process. Since the data of daily share prices of the Nikkei 225 stock index are observed at discrete times, it is difficult to find real jump times from the data. In this paper, we consider how to separate jump times from the observed times. The volatility of the stock index is estimated by the historical volatility from the observation of daily share prices. We also refer to the number of daily share prices for historical volatility and show that the number is essential for the accuracy of identifying of jump times.