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Efficient Pricing of CPPI using Markov Operators

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  • Louis Paulot
  • Xavier Lacroze

Abstract

Constant Proportion Portfolio Insurance (CPPI) is a strategy designed to give participation in a risky asset while protecting the invested capital. Some gap risk due to extreme events is often kept by the issuer of the product: a put option on the CPPI strategy is included in the product. In this paper we present a new method for the pricing of CPPIs and options on CPPIs, which is much faster and more accurate than the usual Monte-Carlo method. Provided the underlying follows a homogeneous process, the path-dependent CPPI strategy is reformulated into a Markov process in one variable, which allows to use efficient linear algebra techniques. Tail events, which are crucial in the pricing are handled smoothly. We incorporate in this framework linear thresholds, profit lock-in, performance coupons... The American exercise of open-ended CPPIs is handled naturally through backward propagation. Finally we use our pricing scheme to study the influence of various features on the gap risk of CPPI strategies.

Suggested Citation

  • Louis Paulot & Xavier Lacroze, 2009. "Efficient Pricing of CPPI using Markov Operators," Papers 0901.1218, arXiv.org.
    • Handle: RePEc:arx:papers:0901.1218
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    References listed on IDEAS

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    1. Rama Cont & Peter Tankov, 2009. "Constant Proportion Portfolio Insurance In The Presence Of Jumps In Asset Prices," Mathematical Finance, Wiley Blackwell, vol. 19(3), pages 379-401, July.
    2. Albanese, Claudio, 2006. "Operator Methods, Abelian Processes And Dynamic Conditioning," MPRA Paper 5246, University Library of Munich, Germany, revised 06 Nov 2007.
    3. S. G. Kou, 2002. "A Jump-Diffusion Model for Option Pricing," Management Science, INFORMS, vol. 48(8), pages 1086-1101, August.
    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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    Cited by:

    1. Louis Paulot & Xavier Lacroze, 2009. "One-Dimensional Pricing of CPPI," Papers 0905.2926, arXiv.org, revised Feb 2010.
    2. Zieling, Daniel & Mahayni, Antje & Balder, Sven, 2014. "Performance evaluation of optimized portfolio insurance strategies," Journal of Banking & Finance, Elsevier, vol. 43(C), pages 212-225.

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