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One-Dimensional Pricing of CPPI


  • Louis Paulot
  • Xavier Lacroze


Constant Proportion Portfolio Insurance (CPPI) is an investment strategy designed to give participation in the performance of a risky asset while protecting the invested capital. This protection is, however, not perfect and the gap risk must be quantified. CPPI strategies are path dependent and may have American exercise which makes their valuation complex. A naive description of the state of the portfolio would involve three or even four variables. In this article we prove that the system can be described as a discrete-time Markov process in one single variable if the underlying asset follows a process with independent increments. This yields an efficient pricing scheme using transition probabilities. Our framework is flexible enough to handle most features of traded CPPIs including profit lock-in and other kinds of strategies with discrete-time reallocation.

Suggested Citation

  • Louis Paulot & Xavier Lacroze, 2011. "One-Dimensional Pricing of CPPI," Applied Mathematical Finance, Taylor & Francis Journals, vol. 18(3), pages 207-225.
  • Handle: RePEc:taf:apmtfi:v:18:y:2011:i:3:p:207-225 DOI: 10.1080/1350486X.2010.486571

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    References listed on IDEAS

    1. FRED ESPEN BENTH & JŪRATĖ SALTYTĖ BENTH & STEEN KOEKEBAKKER, 2007. "Putting a Price on Temperature," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 34(4), pages 746-767.
    2. Eckhard Platen & Jason West, 2004. "A Fair Pricing Approach to Weather Derivatives," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 11(1), pages 23-53, March.
    3. A. Zapranis & A. Alexandridis, 2008. "Modelling the Temperature Time-dependent Speed of Mean Reversion in the Context of Weather Derivatives Pricing," Applied Mathematical Finance, Taylor & Francis Journals, vol. 15(4), pages 355-386.
    4. Jewson,Stephen & Brix,Anders With contributions by-Name:Ziehmann,Christine, 2005. "Weather Derivative Valuation," Cambridge Books, Cambridge University Press, number 9780521843713, March.
    5. Sean D. Campbell & Francis X. Diebold, 2005. "Weather Forecasting for Weather Derivatives," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 6-16, March.
    6. Peter Alaton & Boualem Djehiche & David Stillberger, 2002. "On modelling and pricing weather derivatives," Applied Mathematical Finance, Taylor & Francis Journals, vol. 9(1), pages 1-20.
    7. Dorje Brody & Joanna Syroka & Mihail Zervos, 2002. "Dynamical pricing of weather derivatives," Quantitative Finance, Taylor & Francis Journals, vol. 2(3), pages 189-198.
    8. Jurate saltyte Benth & Fred Espen Benth & Paulius Jalinskas, 2007. "A Spatial-temporal Model for Temperature with Seasonal Variance," Journal of Applied Statistics, Taylor & Francis Journals, vol. 34(7), pages 823-841.
    9. M. Davis, 2001. "Pricing weather derivatives by marginal value," Quantitative Finance, Taylor & Francis Journals, vol. 1(3), pages 305-308, March.
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    12. Gneiting, Tilmann, 1999. "Radial Positive Definite Functions Generated by Euclid's Hat," Journal of Multivariate Analysis, Elsevier, vol. 69(1), pages 88-119, April.
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    Cited by:

    1. Schied, Alexander, 2014. "Model-free CPPI," Journal of Economic Dynamics and Control, Elsevier, vol. 40(C), pages 84-94.
    2. Alexander Schied, 2013. "Model-free CPPI," Papers 1305.5915,, revised Jan 2014.

    More about this item


    CPPI; portfolio insurance; option; pricing; gap risk; markov;


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