Estimation of Jump Times in Daily Share Prices of Nikkei 225 Stock Index using a Jump Diffusion Model

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  • 日経225平均株価指数の日次収益率分析におけるジャンプ拡散過程モデルの同定とその低頻度で振幅の大きなジャンプ時点推定への応用について
  • ニッケイ 225 ヘイキン カブカ シスウ ノ ヒナミ シュウエキリツ ブンセキ ニ オケル ジャンプ カクサン カテイ モデル ノ ドウテイ ト ソノ テイヒンド デ シンプク ノ オオキナ ジャンプ ジテン スイテイ エ ノ オウヨウ ニ ツイテ

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We investigate the 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 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.

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