Efficient Pricing of CPPI using Markov Operators

TL;DR

This paper introduces a fast, accurate method for pricing CPPI and related options by reformulating the strategy as a Markov process, enabling efficient computation and analysis of gap risk.

Contribution

The paper presents a novel Markov operator-based approach for pricing CPPI strategies and options, improving speed and accuracy over traditional Monte Carlo methods.

Findings

The method efficiently handles tail events and path-dependent features.

It allows natural incorporation of features like profit lock-in and coupons.

The approach enables analysis of factors influencing gap risk.

Abstract

Constant Proportion Portfolio Insurance (CPPI) is a strategy designed to give participation in a risky asset while protecting the invested capital. Some gap risk due to extreme events is often kept by the issuer of the product: a put option on the CPPI strategy is included in the product. In this paper we present a new method for the pricing of CPPIs and options on CPPIs, which is much faster and more accurate than the usual Monte-Carlo method. Provided the underlying follows a homogeneous process, the path-dependent CPPI strategy is reformulated into a Markov process in one variable, which allows to use efficient linear algebra techniques. Tail events, which are crucial in the pricing are handled smoothly. We incorporate in this framework linear thresholds, profit lock-in, performance coupons... The American exercise of open-ended CPPIs is handled naturally through backward propagation. Finally we use our pricing scheme to study the influence of various features on the gap risk of CPPI strategies.