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One-Dimensional Pricing of CPPI

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  • Louis Paulot
  • Xavier Lacroze

Abstract

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 paper we prove that the system can be described as a discrete-time Markov process in one single variable if the underlying asset follows a homogeneous process. 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, 2009. "One-Dimensional Pricing of CPPI," Papers 0905.2926, arXiv.org, revised Feb 2010.
  • Handle: RePEc:arx:papers:0905.2926
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    File URL: http://arxiv.org/pdf/0905.2926
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    References listed on IDEAS

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    1. Rama Cont & Peter Tankov, 2007. "Constant Proportion Portfolio Insurance in presence of Jumps in Asset Prices," Working Papers hal-00129413, HAL.
    2. S. G. Kou, 2002. "A Jump-Diffusion Model for Option Pricing," Management Science, INFORMS, vol. 48(8), pages 1086-1101, August.
    3. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
    4. P. Bertrand & J.L. Prigent, 2000. "Portfolio Insurance : The extreme Value of the CCPI Method," THEMA Working Papers 2000-49, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
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