IDEAS home Printed from https://ideas.repec.org/a/bla/mathfi/v8y1998i2p127-152.html
   My bibliography  Save this article

A Discrete Time Equivalent Martingale Measure

Author

Listed:
  • Robert J. Elliott
  • Dilip B. Madan

Abstract

An equivalent martingale measure selection strategy for discrete time, continuous state, asset price evolution models is proposed. The minimal martingale law is shown to generally fail to produce a probability law in this context. The proposed strategy, termed the extended Girsanov principle, performs a multiplicative decomposition of asset price movements into a predictable and martingale component with the measure change identifying the discounted asset price process to the martingale component. However, unlike the minimal martingale law, the resulting martingale law of the extended Girsanov principle leads to weak form efficient price processes. It is shown that the proposed measure change is relevant for economies in which investors adopt hedging strategies that minimize the variance of a risk adjusted discounted cost of hedging that uses risk adjusted asset prices in calculating hedging returns. Risk adjusted prices deflate asset prices by the asset's excess return. The explicit form of the change of measure density leads to tractable econometric strategies for testing the validity of the extended Girsanov principle. A number of interesting applications of the extended Girsanov principle are also developed. Copyright Blackwell Publishers 1998.

Suggested Citation

  • Robert J. Elliott & Dilip B. Madan, 1998. "A Discrete Time Equivalent Martingale Measure," Mathematical Finance, Wiley Blackwell, vol. 8(2), pages 127-152.
  • Handle: RePEc:bla:mathfi:v:8:y:1998:i:2:p:127-152
    as

    Download full text from publisher

    File URL: http://www.blackwell-synergy.com/doi/abs/10.1111/1467-9965.00048
    File Function: link to full text
    Download Restriction: Access to full text is restricted to subscribers.

    As the access to this document is restricted, you may want to search for a different version of it.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Guégan, Dominique & Ielpo, Florian & Lalaharison, Hanjarivo, 2013. "Option pricing with discrete time jump processes," Journal of Economic Dynamics and Control, Elsevier, vol. 37(12), pages 2417-2445.
    2. Chorro, C. & Guégan, D. & Ielpo, F., 2010. "Martingalized historical approach for option pricing," Finance Research Letters, Elsevier, vol. 7(1), pages 24-28, March.
    3. Beissner, Patrick & Rosazza Gianin, Emanuela, 2018. "The Term Structure of Sharpe Ratios and Arbitrage-Free Asset Pricing in Continuous Time," Rationality and Competition Discussion Paper Series 72, CRC TRR 190 Rationality and Competition.
    4. Christophe Chorro & Dominique Guegan & Florian Ielpo, 2008. "Option pricing under GARCH models with generalized hyperbolic innovations (I) : methodology," Documents de travail du Centre d'Economie de la Sorbonne b08037, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    5. Firoozi, Fathali, 2006. "On the martingale property of economic and financial instruments," International Review of Economics & Finance, Elsevier, vol. 15(1), pages 87-96.
    6. repec:hal:journl:halshs-00469529 is not listed on IDEAS
    7. Badescu Alex & Kulperger Reg & Lazar Emese, 2008. "Option Valuation with Normal Mixture GARCH Models," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 12(2), pages 1-42, May.
    8. Joan del Castillo & Juan-Pablo Ortega, 2011. "Hedging of time discrete auto-regressive stochastic volatility options," Papers 1110.6322, arXiv.org.
    9. Badescu, Alex & Elliott, Robert J. & Siu, Tak Kuen, 2009. "Esscher transforms and consumption-based models," Insurance: Mathematics and Economics, Elsevier, vol. 45(3), pages 337-347, December.
    10. repec:hal:journl:halshs-00611706 is not listed on IDEAS
    11. Liew, Chuin Ching & Siu, Tak Kuen, 2010. "A hidden Markov regime-switching model for option valuation," Insurance: Mathematics and Economics, Elsevier, vol. 47(3), pages 374-384, December.
    12. Huang, Shih-Feng & Tu, Ya-Ting, 2014. "Asymptotic distribution of the EPMS estimator for financial derivatives pricing," Computational Statistics & Data Analysis, Elsevier, vol. 73(C), pages 129-145.
    13. repec:hal:journl:halshs-00542475 is not listed on IDEAS
    14. Badescu, Alexandru & Elliott, Robert J. & Ortega, Juan-Pablo, 2014. "Quadratic hedging schemes for non-Gaussian GARCH models," Journal of Economic Dynamics and Control, Elsevier, vol. 42(C), pages 13-32.
    15. Badescu, Alexandru & Elliott, Robert J. & Ortega, Juan-Pablo, 2015. "Non-Gaussian GARCH option pricing models and their diffusion limits," European Journal of Operational Research, Elsevier, vol. 247(3), pages 820-830.
    16. Badescu, Alexandru M. & Kulperger, Reg J., 2008. "GARCH option pricing: A semiparametric approach," Insurance: Mathematics and Economics, Elsevier, vol. 43(1), pages 69-84, August.
    17. Badescu, Alexandru & Cui, Zhenyu & Ortega, Juan-Pablo, 2016. "A note on the Wang transform for stochastic volatility pricing models," Finance Research Letters, Elsevier, vol. 19(C), pages 189-196.
    18. : Andrea Gamba & Carmen Aranda Leon & Alessio Saretto, 2011. "Dynamic Capacity Choice, Dynamic Capital Structure and Credit Risk," Working Papers wpn11-03, Warwick Business School, Finance Group.
    19. Alexandru Badescu & Robert J. Elliott & Juan-Pablo Ortega, 2012. "Quadratic hedging schemes for non-Gaussian GARCH models," Papers 1209.5976, arXiv.org, revised Dec 2013.
    20. repec:hal:journl:halshs-00437927 is not listed on IDEAS
    21. Liu, Yanxin & Li, Johnny Siu-Hang & Ng, Andrew Cheuk-Yin, 2015. "Option pricing under GARCH models with Hansen's skewed-t distributed innovations," The North American Journal of Economics and Finance, Elsevier, vol. 31(C), pages 108-125.

    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:bla:mathfi:v:8:y:1998:i:2:p:127-152. 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: (Wiley-Blackwell Digital Licensing) or (Christopher F. Baum). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0960-1627 .

    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.

    We have no references for this item. You can help adding them by using 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.