Pricing Nikkei 225 Options Using Realized Volatility
This article analyzes whether daily realized volatility, which is the sum of squared intraday returns over a day, is useful for option pricing. Different realized volatilities are calculated with or without taking account of microstructure noise and with or without using overnight and lunch-time returns. ARFIMA, ARFIMAX, HAR, HARX models are employed to specify the dynamics of realized volatility. ARFIMA and HAR models can capture the long-memory property and ARFIMAX and HARX models can also capture the asymmetry in volatility depending on the sign of previous day's return. Option prices are derived under the assumption of risk-neutrality. For comparison, GARCH, EGARCH and FIEGARCH models are estimated using daily returns, where option prices are derived by assuming the risk-neutrality and by using the Duan (1995) method in which the assumption of risk-neutrality is relaxed. Main results using the Nikkei 225 stock index and its put options prices are: (1) ARFIMAX model with daily realized volatility performs best, (2) the Hansen and Lunde ( 2005a) adjustment without using overnight and lunch-time returns can improve the performance, (3) if the Hansen and Lunde (2005a), which also plays a role to remove the bias caused by the microstructure noise by setting the sample mean of realized volatility equal to the sample variance of daily returns, is used, the other methods for taking account of microstructure noise do not necessarily improve the performance and (4) the Duan (1995) method does not improve the performance compared with assuming the risk neutrality.
|Date of creation:||Aug 2011|
|Date of revision:|
|Contact details of provider:|| Postal: 2-1-1 Nihonbashi, Hongoku-cho, Chuo-ku, Tokyo 103|
Web page: http://www.imes.boj.or.jp/
More information through EDIRC
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Daisuke Nagakura & Toshiaki Watanabe, 2015.
"A State Space Approach to Estimating the Integrated Variance under the Existence of Market Microstructure Noise,"
Journal of Financial Econometrics,
Society for Financial Econometrics, vol. 13(1), pages 45-82.
- Daisuke Nagakura & Toshiaki Watanabe, 2010. "A State Space Approach to Estimating the Integrated Variance under the Existence of Market Microstructure Noise," Global COE Hi-Stat Discussion Paper Series gd09-115, Institute of Economic Research, Hitotsubashi University.
- Daisuke Nagakura & Toshiaki Watanabe, 2011. "A State Space Approach to Estimating the Integrated Variance under the Existence of Market Microstructure Noise," Global COE Hi-Stat Discussion Paper Series gd11-200, Institute of Economic Research, Hitotsubashi University.
- Bandi, Federico M. & Russell, Jeffrey R., 2011. "Market microstructure noise, integrated variance estimators, and the accuracy of asymptotic approximations," Journal of Econometrics, Elsevier, vol. 160(1), pages 145-159, January.
- Bollerslev, Tim & Ole Mikkelsen, Hans, 1999. "Long-term equity anticipation securities and stock market volatility dynamics," Journal of Econometrics, Elsevier, vol. 92(1), pages 75-99, September.
- Makoto Takahashi & Yasuhiro Omori & Toshiaki Watanabe, 2007.
"Estimating Stochastic Volatility Models Using Daily Returns and Realized Volatility Simultaneously,"
CIRJE-F-515, CIRJE, Faculty of Economics, University of Tokyo.
- Takahashi, Makoto & Omori, Yasuhiro & Watanabe, Toshiaki, 2009. "Estimating stochastic volatility models using daily returns and realized volatility simultaneously," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2404-2426, April.
- MEDDAHI, Nour, 2001.
"A Theoretical Comparison Between Integrated and Realized Volatilies,"
Cahiers de recherche
2001-26, Universite de Montreal, Departement de sciences economiques.
- Nour Meddahi, 2002. "A theoretical comparison between integrated and realized volatility," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(5), pages 479-508.
- Meddahi, N., 2001. "A Theoretical Comparison Between Integrated and Realized Volatilies," Cahiers de recherche 2001-26, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
- Tim Bollerslev, 1986.
"Generalized autoregressive conditional heteroskedasticity,"
EERI Research Paper Series
EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
- Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
- Bandi, Federico M. & Russell, Jeffrey R. & Yang, Chen, 2008. "Realized volatility forecasting and option pricing," Journal of Econometrics, Elsevier, vol. 147(1), pages 34-46, November.
- Harris, Lawrence, 1990. "Estimation of Stock Price Variances and Serial Covariances from Discrete Observations," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 25(03), pages 291-306, September.
- Baillie, Richard T. & Bollerslev, Tim & Mikkelsen, Hans Ole, 1996.
"Fractionally integrated generalized autoregressive conditional heteroskedasticity,"
Journal of Econometrics,
Elsevier, vol. 74(1), pages 3-30, September.
- Tom Doan, . "RATS programs to replicate Baillie, Bollerslev, Mikkelson FIGARCH results," Statistical Software Components RTZ00009, Boston College Department of Economics.
- Christian Conrad & Berthold R. Haag, 2006. "Inequality Constraints in the Fractionally Integrated GARCH Model," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 4(3), pages 413-449.
- Peter Reinhard Hansen & Zhuo (Albert) Huang & Howard Howan Shek, . "Realized GARCH: A Complete Model of Returns and Realized Measures of Volatility," CREATES Research Papers 2010-13, School of Economics and Management, University of Aarhus.
- Pierre Giot & Sébastien Laurent, 2002.
"Modelling Daily Value-at-Risk Using Realized Volatility and ARCH Type Models,"
Computing in Economics and Finance 2002
52, Society for Computational Economics.
- Giot, Pierre & Laurent, Sebastien, 2004. "Modelling daily Value-at-Risk using realized volatility and ARCH type models," Journal of Empirical Finance, Elsevier, vol. 11(3), pages 379-398, June.
- Giot Pierre & Laurent Sebastien, 2001. "Modelling daily value-at-risk using realized volatility and arch type models," Research Memorandum 014, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
- Bollerslev, Tim & Ole Mikkelsen, Hans, 1996.
"Modeling and pricing long memory in stock market volatility,"
Journal of Econometrics,
Elsevier, vol. 73(1), pages 151-184, July.
- Tom Doan, . "RATS program to replicate Bollerslev-Mikkelson(1996) FIEGARCH models," Statistical Software Components RTZ00173, Boston College Department of Economics.
- Schoffer, Olaf, 2003. "HY-A-PARCH: A stationary A-PARCH model with long memory," Technical Reports 2003,40, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
When requesting a correction, please mention this item's handle: RePEc:ime:imedps:11-e-18. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Kinken)
If references are entirely missing, you can add them using this form.