IDEAS home Printed from https://ideas.repec.org/a/wly/apsmbi/v26y2010i2p142-156.html
   My bibliography  Save this article

Application in stochastic volatility models of nonlinear regression with stochastic design

Author

Listed:
  • Ping Chen
  • Jinde Wang

Abstract

In regression model with stochastic design, the observations have been primarily treated as a simple random sample from a bivariate distribution. It is of enormous practical significance to generalize the situation to stochastic processes. In this paper, estimation and hypothesis testing problems in stochastic volatility model are considered, when the volatility depends on a nonlinear function of the state variable of other stochastic process, but the correlation coefficient |ρ|≠±1. The methods are applied to estimate the volatility of stock returns from Shanghai stock exchange. Copyright © 2009 John Wiley & Sons, Ltd.

Suggested Citation

  • Ping Chen & Jinde Wang, 2010. "Application in stochastic volatility models of nonlinear regression with stochastic design," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 26(2), pages 142-156, March.
    • Handle: RePEc:wly:apsmbi:v:26:y:2010:i:2:p:142-156
    DOI: 10.1002/asmb.780
    as

    Download full text from publisher

    File URL: https://doi.org/10.1002/asmb.780
    Download Restriction: no
    File URL: https://libkey.io/10.1002/asmb.780?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. M. Avellaneda & A. Levy & A. ParAS, 1995. "Pricing and hedging derivative securities in markets with uncertain volatilities," Applied Mathematical Finance, Taylor & Francis Journals, vol. 2(2), pages 73-88.
    2. Reno, Roberto, 2006. "Nonparametric estimation of stochastic volatility models," Economics Letters, Elsevier, vol. 90(3), pages 390-395, March.
    3. Hull, John C & White, Alan D, 1987. "The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
    4. Tiku, Moti L. & Islam, M. Qamarul & Sazak, Hakan S., 2008. "Estimation in bivariate nonnormal distributions with stochastic variance functions," Computational Statistics & Data Analysis, Elsevier, vol. 52(3), pages 1728-1745, January.
    5. Davide Raggi, 2005. "Adaptive MCMC methods for inference on affine stochastic volatility models with jumps," Econometrics Journal, Royal Economic Society, vol. 8(2), pages 235-250, July.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Renò, Roberto, 2008. "Nonparametric Estimation Of The Diffusion Coefficient Of Stochastic Volatility Models," Econometric Theory, Cambridge University Press, vol. 24(5), pages 1174-1206, October.
    2. Hyungsok Ahn Adviti & Glen Swindle, 1997. "Misspecified asset price models and robust hedging strategies," Applied Mathematical Finance, Taylor & Francis Journals, vol. 4(1), pages 21-36.
    3. Gondzio, Jacek & Kouwenberg, Roy & Vorst, Ton, 2003. "Hedging options under transaction costs and stochastic volatility," Journal of Economic Dynamics and Control, Elsevier, vol. 27(6), pages 1045-1068, April.
    4. Jean-Pierre Fouque & Ning Ning, 2017. "Uncertain Volatility Models with Stochastic Bounds," Papers 1702.05036, arXiv.org.
    5. Davide Raggi & Silvano Bordignon, 2011. "Volatility, Jumps, and Predictability of Returns: A Sequential Analysis," Econometric Reviews, Taylor & Francis Journals, vol. 30(6), pages 669-695.
    6. Nappo, Giovanna & Marchetti, Fabio Massimo & Vagnani, Gianluca, 2023. "Traders’ heterogeneous beliefs about stock volatility and the implied volatility skew in financial options markets," Finance Research Letters, Elsevier, vol. 53(C).
    7. Carol Alexander & Leonardo Nogueira, 2007. "Model-free price hedge ratios for homogeneous claims on tradable assets," Quantitative Finance, Taylor & Francis Journals, vol. 7(5), pages 473-479.
    8. Larry G. Epstein & Shaolin Ji, 2013. "Ambiguous Volatility and Asset Pricing in Continuous Time," The Review of Financial Studies, Society for Financial Studies, vol. 26(7), pages 1740-1786.
    9. Lu, Xiaoping & Putri, Endah R.M., 2020. "A semi-analytic valuation of American options under a two-state regime-switching economy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 538(C).
    10. repec:dau:papers:123456789/5374 is not listed on IDEAS
    11. Joel Vanden, 2006. "Exact Superreplication Strategies for a Class of Derivative Assets," Applied Mathematical Finance, Taylor & Francis Journals, vol. 13(1), pages 61-87.
    12. Jan Maruhn & Morten Nalholm & Matthias Fengler, 2011. "Static hedges for reverse barrier options with robustness against skew risk: an empirical analysis," Quantitative Finance, Taylor & Francis Journals, vol. 11(5), pages 711-727.
    13. RØdiger Frey, 2000. "Superreplication in stochastic volatility models and optimal stopping," Finance and Stochastics, Springer, vol. 4(2), pages 161-187.
    14. Rüdiger Frey & Carlos A. Sin, 1999. "Bounds on European Option Prices under Stochastic Volatility," Mathematical Finance, Wiley Blackwell, vol. 9(2), pages 97-116, April.
    15. Simone Scotti, 2012. "Asset Pricing under uncertainty," Papers 1203.5664, arXiv.org.
    16. Sergei Fedotov & Sergei Mikhailov, 1998. "Option Pricing Model for Incomplete Market," Papers cond-mat/9807397, arXiv.org, revised Aug 1998.
    17. Lin, Lisha & Li, Yaqiong & Wu, Jing, 2018. "The pricing of European options on two underlying assets with delays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 495(C), pages 143-151.
    18. Samuel N. Cohen & Martin Tegn'er, 2018. "European Option Pricing with Stochastic Volatility models under Parameter Uncertainty," Papers 1807.03882, arXiv.org.
    19. Zaineb Mezdoud & Carsten Hartmann & Mohamed Riad Remita & Omar Kebiri, 2021. "$\alpha$-Hypergeometric Uncertain Volatility Models and their Connection to 2BSDEs," Papers 2108.06965, arXiv.org.
    20. Touzi, Nizar, 2000. "Direct characterization of the value of super-replication under stochastic volatility and portfolio constraints," Stochastic Processes and their Applications, Elsevier, vol. 88(2), pages 305-328, August.
    21. Carol Alexander & Leonardo M. Nogueira, 2006. "Hedging Options with Scale-Invariant Models," ICMA Centre Discussion Papers in Finance icma-dp2006-03, Henley Business School, University of Reading.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wly:apsmbi:v:26:y:2010:i:2:p:142-156. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: https://doi.org/10.1002/(ISSN)1526-4025 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.