One-Dimensional Pricing of CPPI
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.
References listed on IDEAS
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- Rama Cont & Peter Tankov, 2007.
"Constant Proportion Portfolio Insurance in presence of Jumps in Asset Prices,"
- Rama Cont & Peter Tankov, 2009. "Constant proportion portfolio insurance in presence of jumps in asset prices," Post-Print hal-00445646, HAL.
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- 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. Full references (including those not matched with items on IDEAS)
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