Constant Proportion Portfolio Insurance in Presence of Jumps in Asset Prices

Columbia University Center for Financial Engineering, Financial Engineering Report No. 2007-10

27 Pages Posted: 15 Oct 2007

See all articles by Rama Cont

Rama Cont

University of Oxford; CNRS

Peter Tankov

Ecole Polytechnique, Paris

Date Written: February 2007

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 non-negligible 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.

Keywords: Portfolio insurance, CPPI, Levy process, hedging, CPPI option, Value at Risk, jump-diffusion models

JEL Classification: G15

Suggested Citation

Cont, Rama and Tankov, Peter, Constant Proportion Portfolio Insurance in Presence of Jumps in Asset Prices (February 2007). Columbia University Center for Financial Engineering, Financial Engineering Report No. 2007-10. Available at SSRN: https://ssrn.com/abstract=1021084 or http://dx.doi.org/10.2139/ssrn.1021084

Rama Cont

University of Oxford ( email )

Mathematical Institute
Oxford, OX2 6GG
United Kingdom

HOME PAGE: http://https://www.maths.ox.ac.uk/people/rama.cont

CNRS ( email )

LPSM
Sorbonne University
Paris
France

HOME PAGE: http://rama.cont.perso.math.cnrs.fr/

Peter Tankov (Contact Author)

Ecole Polytechnique, Paris ( email )

route de Saclay
Palaiseau, 91128
France

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