IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v77y2007i2p196-203.html

Statistical options: Crash resistant financial contracts based on robust estimation

Author

Listed:
  • Ramprasath, L.
  • Singh, Kesar

Abstract

We propose a class of European-type options, which is named here as statistical options, utilizing robust location estimators from the statistics literature. The main motivating objective is to protect the buyer of a call option against a sudden drop in the security price or a put option against a sharp upward move. The vast literature on the asymptotics for the location estimator can be called upon to accurately approximate the prices of these options, when the price formulae are not obtainable in closed form. The statistician's eternal quest for robust estimators which are highly efficient under normality finds here another reason. A notion of limit loss option emerges as a special case, possessing practical appeal. The pricing of the options is carried out under the popular Black-Scholes model. A theory based on the jump diffusion processes ascertains that these robust options manage to nullify the effect of jump arrivals (or that of just the negative ones) in a limiting sense. Finally, a notion of ratio hedging is proposed for the statistical options.

Suggested Citation

  • Ramprasath, L. & Singh, Kesar, 2007. "Statistical options: Crash resistant financial contracts based on robust estimation," Statistics & Probability Letters, Elsevier, vol. 77(2), pages 196-203, January.
    • Handle: RePEc:eee:stapro:v:77:y:2007:i:2:p:196-203
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(06)00222-7
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. Miura, Ryozo, 1992. "A Note on Look-Back Options Based on Order Statistics," Hitotsubashi Journal of commerce and management, Hitotsubashi University, vol. 27(1), pages 15-28, November.
    2. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    3. Naik, Vasanttilak & Lee, Moon, 1990. "General Equilibrium Pricing of Options on the Market Portfolio with Discontinuous Returns," The Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 493-521.
    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. Mark Broadie & Jerome B. Detemple, 2004. "ANNIVERSARY ARTICLE: Option Pricing: Valuation Models and Applications," Management Science, INFORMS, vol. 50(9), pages 1145-1177, September.
    2. René Garcia & Richard Luger & Eric Renault, 2000. "Asymmetric Smiles, Leverage Effects and Structural Parameters," Working Papers 2000-57, Center for Research in Economics and Statistics.
    3. Sang Byung Seo & Jessica A. Wachter, 2019. "Option Prices in a Model with Stochastic Disaster Risk," Management Science, INFORMS, vol. 65(8), pages 3449-3469, August.
    4. Hongzhong Zhang, 2018. "Stochastic Drawdowns," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 10078.
    5. Nan Chen & S. G. Kou, 2009. "Credit Spreads, Optimal Capital Structure, And Implied Volatility With Endogenous Default And Jump Risk," Mathematical Finance, Wiley Blackwell, vol. 19(3), pages 343-378, July.
    6. Lam, K. & Chang, E. & Lee, M. C., 2002. "An empirical test of the variance gamma option pricing model," Pacific-Basin Finance Journal, Elsevier, vol. 10(3), pages 267-285, June.
    7. Ibáñez, Alfredo, 2008. "Factorization of European and American option prices under complete and incomplete markets," Journal of Banking & Finance, Elsevier, vol. 32(2), pages 311-325, February.
    8. C. He & J. Kennedy & T. Coleman & P. Forsyth & Y. Li & K. Vetzal, 2006. "Calibration and hedging under jump diffusion," Review of Derivatives Research, Springer, vol. 9(1), pages 1-35, January.
    9. Chenghu Ma, 2003. "Term Structure of Interest Rates in the Presence of Levy Jumps: The HJM Approach," Annals of Economics and Finance, Society for AEF, vol. 4(2), pages 401-426, November.
    10. Kozarski, R., 2013. "Pricing and hedging in the VIX derivative market," Other publications TiSEM 221fefe0-241e-4914-b6bd-c, Tilburg University, School of Economics and Management.
    11. Calvet, Laurent E. & Fisher, Adlai J., 2008. "Multifrequency jump-diffusions: An equilibrium approach," Journal of Mathematical Economics, Elsevier, vol. 44(2), pages 207-226, January.
    12. Melanie Cao & Batur Celik, 2021. "Valuation of bitcoin options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 41(7), pages 1007-1026, July.
    13. Garcia, R. & Renault, E., 1998. "Risk Aversion, Intertemporal Substitution, and Option Pricing," Cahiers de recherche 9801, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    14. Moreno, Manuel & Peña, Juan Ignacio, 1995. "On the term structure of Interbank interest rates: jump-diffusion processes and option pricing," DES - Working Papers. Statistics and Econometrics. WS 7074, Universidad Carlos III de Madrid. Departamento de Estadística.
    15. Oliver X. Li & Weiping Li, 2015. "Hedging jump risk, expected returns and risk premia in jump-diffusion economies," Quantitative Finance, Taylor & Francis Journals, vol. 15(5), pages 873-888, May.
    16. Blanchet-Scalliet, Christophette & El Karoui, Nicole & Martellini, Lionel, 2005. "Dynamic asset pricing theory with uncertain time-horizon," Journal of Economic Dynamics and Control, Elsevier, vol. 29(10), pages 1737-1764, October.
    17. Torben B. Rasmussen, 2009. "Jump Testing and the Speed of Market Adjustment," CREATES Research Papers 2009-08, Department of Economics and Business Economics, Aarhus University.
    18. Wang, Guanying & Wang, Xingchun & Shao, Xinjian, 2022. "Exchange options for catastrophe risk management," The North American Journal of Economics and Finance, Elsevier, vol. 59(C).
    19. Yi-Hao Lai & Yi-Chiuan Wang & Wei-Shih Chung, 2018. "Initial Jump and Recovering Jump in the S&P 500 Index Returns: A Jump-Recovering-Switching Approach," Journal of Economics and Management, College of Business, Feng Chia University, Taiwan, vol. 14(1), pages 51-66, February.
    20. Stephan Dieckmann & Michael Gallmeyer, 2006. "Pricing Rare Event Risk in Emerging Markets," 2006 Meeting Papers 305, Society for Economic Dynamics.

    More about this item

    Keywords

    ;

    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:eee:stapro:v:77:y:2007:i:2:p:196-203. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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.