ジャンプ拡散過程による時系列解析とその応用

抄録

We investigate daily share prices of the Nikkei 225 stock index to identify jump times of the stock index using a jump-diffusion model which consists of the Black-Scholes model with a 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 data. The volatility of the stock index is estimated by the historical volatility from the observation of some daily share prices. We also refer to the number of daily share prices for the historical volatility and show that the number is essential for the accuracy of the identification of jump times.