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Constant proportion portfolio insurance in presence of jumps in asset prices

Author

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  • Rama Cont

    () (LPMA - Laboratoire de Probabilités et Modèles Aléatoires - UPMC - Université Pierre et Marie Curie - Paris 6 - UPD7 - Université Paris Diderot - Paris 7 - CNRS - Centre National de la Recherche Scientifique, Center for Financial Engineering, Columbia University - Columbia University [New York])

  • Peter Tankov

    () (LPMA - Laboratoire de Probabilités et Modèles Aléatoires - UPMC - Université Pierre et Marie Curie - Paris 6 - UPD7 - Université Paris Diderot - Paris 7 - CNRS - Centre National de la Recherche Scientifique)

Abstract

Constant proportion portfolio insurance (CPPI) allows an investor to limit downside risk while retaining some upside potential by maintaining an exposure to risky assets equal to a constant multiple of the cushion, the difference between the current portfolio value and the guaranteed amount. Whereas in diffusion models with continuous trading, this strategy has no downside risk, in real markets this risk is nonnegligible and grows with the multiplier value. We study the behavior of CPPI strategies in models where the price of the underlying portfolio may experience downward jumps. Our framework leads to analytically tractable expressions for the probability of hitting the floor, the expected loss, and the distribution of losses. This allows to measure the gap risk but also leads to a criterion for adjusting the multiplier based on the investor's risk aversion. Finally, we study the problem of hedging the downside risk of a CPPI strategy using options. The results are applied to a jump-diffusion model with parameters estimated from returns series of various assets and indices.

Suggested Citation

  • Rama Cont & Peter Tankov, 2009. "Constant proportion portfolio insurance in presence of jumps in asset prices," Post-Print hal-00445646, HAL.
  • Handle: RePEc:hal:journl:hal-00445646
    DOI: 10.1111/j.1467-9965.2009.00377.x
    Note: View the original document on HAL open archive server: https://hal.archives-ouvertes.fr/hal-00445646
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    Cited by:

    1. Hamidi, Benjamin & Maillet, Bertrand & Prigent, Jean-Luc, 2014. "A dynamic autoregressive expectile for time-invariant portfolio protection strategies," Journal of Economic Dynamics and Control, Elsevier, vol. 46(C), pages 1-29.
    2. Chris Kenyon & Andrew Green, 2016. "Option-Based Pricing of Wrong Way Risk for CVA," Papers 1609.00819, arXiv.org, revised Oct 2016.
    3. Branger, Nicole & Mahayni, Antje & Schneider, Judith C., 2010. "On the optimal design of insurance contracts with guarantees," Insurance: Mathematics and Economics, Elsevier, vol. 46(3), pages 485-492, June.
    4. Sami Attaoui & Vincent Lacoste, 2013. "A scenario-based description of optimal American capital guaranteed strategies," Finance, Presses universitaires de Grenoble, vol. 34(2), pages 65-119.
    5. De Franco, Carmine & Tankov, Peter, 2011. "Portfolio insurance under a risk-measure constraint," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 361-370.
    6. Louis Paulot & Xavier Lacroze, 2009. "Efficient Pricing of CPPI using Markov Operators," Papers 0901.1218, arXiv.org.
    7. Dorn, Jochen, 2010. "Modeling of CPDOs - Identifying optimal and implied leverage," Journal of Banking & Finance, Elsevier, vol. 34(6), pages 1371-1382, June.
    8. Raquel M. Gaspar, 2016. "On Path–dependency of Constant Proportion Portfolio Insurance strategies," EcoMod2016 9381, EcoMod.
    9. Louis Paulot & Xavier Lacroze, 2009. "One-Dimensional Pricing of CPPI," Papers 0905.2926, arXiv.org, revised Feb 2010.
    10. Alexandre Hocquard & Nicolas Papageorgiou & Bruno Remillard, 2015. "The payoff distribution model: an application to dynamic portfolio insurance," Quantitative Finance, Taylor & Francis Journals, vol. 15(2), pages 299-312, February.
    11. Sami Attaoui & Vincent Lacoste, 2013. "A scenario-based description of optimal American capital guaranteed strategies," Post-Print hal-00867667, HAL.
    12. repec:spr:annopr:v:260:y:2018:i:1:d:10.1007_s10479-017-2638-5 is not listed on IDEAS

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