投稿日: 2012/04/11 10:52:51
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日時： 2012年5月25日（金）19:00～20:30
場所： 立命館大学 東京キャンパス (サピアタワー8階)
講師： 長谷川貴博 （金融テクノロジー専門会社 ファイナンシャル・エンジニア）
タイトル: Pricing Nikkei225 VI Futures and Estimating Model Parameters with MCMC Method in R and R-package
アブストラクト:
In this article, I present a closed-form and exact solution for pricing futures of Nikkei Stock Average Volatility Index (Nikkei 225 VI) in a stochastic volatility model with simultaneous jumps in both the asset price and volatility processes. The pricing formula proposed in this article is derived in [ZL11a] for someone to price VIX futures. VIX and Nikkei 225 VI have been developed under the same policies that the volatility index (i.e., VIX or Nikkei 225 VI) is inferred in the volatility of the stock index expected in one month and is computed from the option prices (premiums) in the stock option markets. For this reason, the pricing formula in [ZL11a] can be directly applicable to pricing Nikkei 225 VI futures.
To price Nikkei 225 VI futures with the newly derived formula in [ZL11a], I am required to estimate all parameters of the model which I assume as the dynamics of stock index price. In this research, I program the algorithm of the Markov Chain Monte Carlo (MCMC) method in R and R-package, and I estimate all parameters with MCMC method from the daily-returns of Nikkei 225.
I prove the newly derived formula with same technique in [ZL11a], estimate all parameters with MCMC method from daily-returns of Nikkei 225, and price the Nikkei 225 VI futures empirically.
[ZL11a]:S., P., Zhu, G., H., Lian, An Analytical Formula for VIX Futures and Its Applications, The Journal of Futures Markets, Vol. 00, No. 00, 1-25 (2011).