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A Discrete Time Equivalent Martingale Measure

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  • Robert J. Elliott
  • Dilip B. Madan
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    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.

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    Bibliographic Info

    Article provided by Wiley Blackwell in its journal Mathematical Finance.

    Volume (Year): 8 (1998)
    Issue (Month): 2 ()
    Pages: 127-152

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    Handle: RePEc:bla:mathfi:v:8:y:1998:i:2:p:127-152

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    Cited by:
    1. 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.
    2. Joan del Castillo & Juan-Pablo Ortega, 2011. "Hedging of time discrete auto-regressive stochastic volatility options," Papers 1110.6322, arXiv.org.
    3. repec:hal:journl:halshs-00281585 is not listed on IDEAS
    4. repec:hal:journl:halshs-00376756 is not listed on IDEAS
    5. Christophe Chorro & Dominique Guegan & Florian Ielpo, 2009. "Martingalized historical approach for option pricing," Documents de travail du Centre d'Economie de la Sorbonne 09021, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    6. Firoozi, Fathali, 2006. "On the martingale property of economic and financial instruments," International Review of Economics & Finance, Elsevier, vol. 15(1), pages 87-96.
    7. : 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.
    8. Dominique Guegan & Florian Ielpo & Hanjarivo Lalaharison, 2011. "Option pricing with discrete time jump processes," Documents de travail du Centre d'Economie de la Sorbonne 11037r, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne, revised Apr 2012.
    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. 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.
    11. 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.
    12. repec:hal:journl:halshs-00437927 is not listed on IDEAS
    13. 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.
    14. 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.
    15. repec:hal:journl:halshs-00469529 is not listed on IDEAS

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