Capital Protection: Modeling the CPPI Portfolio
Alessandro Paolo Luigi Cipollini
Deutsche Bank, Fixed Income Research; Università Degli Studi del Sacro Cuore di Milano - Laboratory of Statistics; University of Milan-Bicocca - Department of Mathematics and Applications
August 27, 2008
The aim of the paper is to introduce a rigorous mathematical modellization of the Constant Proportion Portfolio Insurance (CPPI), with as principal aims: to capture the characteristic of the portfolio's distribution, to analyze the properties of the return/risk profile and to identify a procedure through it is possible to produce reliable future target returns. Particular stress has been made in order to produce closed formulas that may lead to easy Monte-Carlo simulation estimates. Moreover as attempt to hedge the CPPI portfolio's risks, the approach followed relies on classical replication techniques: the closing out effect and the gap risk are faced by acting on the CPPI as on a self-financed hedging strategy and converting it in a synthetic derivative. In addition to put an extra protection it has been studied the case of Vanilla options having as underlying the CPPI portfolio's value at maturity and as strike the protected amount. Two are the CPPI portfolios analyzed. As first it has been considered the known case of a CPPI portfolio whose risky exposure is non-constrained and whose floor consists in the risk-less bond. As second, it has been tested the mathematical model on the case of a CPPI whose portfolio's risky exposure is constrained and whose floor is rebalanced at any time of the financial horizon.
Number of Pages in PDF File: 36
Keywords: Capital protection, CPPI, Non-arbitrage price, Monte-Carlo methods
JEL Classification: G10, G11, G12, C0
Date posted: September 20, 2008
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