One-Dimensional Pricing of CPPI

TL;DR

This paper introduces a simplified one-dimensional Markov process model for pricing CPPI strategies, enabling efficient valuation while capturing key features like profit lock-in and discrete rebalancing.

Contribution

It proves that CPPI strategies can be modeled as a single-variable Markov process under certain conditions, simplifying valuation of complex, path-dependent strategies.

Findings

Efficient pricing scheme using transition probabilities.

Model accommodates profit lock-in and discrete rebalancing.

Reduces complexity from multi-variable to single-variable analysis.

Abstract

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.