On Carr and Lee's correlation immunization strategy

TL;DR

This paper analyzes Carr and Lee's correlation immunization strategy, demonstrating its uniqueness in producing real-valued hedging portfolios under nonzero correlation and confirming its effectiveness through Monte Carlo experiments.

Contribution

It proves that the correlation immunization strategy is the only one yielding real-valued portfolios with nonzero correlation and validates its practical effectiveness via simulations.

Findings

Correlation immunization minimizes pricing errors with nonzero correlation.

It is the only strategy producing real-valued portfolios under these conditions.

Monte Carlo results confirm its robustness and effectiveness.

Abstract

In their seminal work Carr and Lee (2008) show how to robustly price and replicate a variety of claims written on the quadratic variation of a risky asset under the assumption that the asset's volatility process is independent of the Brownian motion that drives the asset's price. Additionally, they propose a correlation immunization strategy that minimizes the pricing and hedging error that results when the correlation between the risky asset's price and volatility is nonzero. In this paper, we show that the correlation immunization strategy is the only strategy among the class of strategies discussed in Carr and Lee (2008) that results in real-valued hedging portfolios when the correlation between the asset's price and volatility is nonzero. Additionally, we perform a number of Monte Carlo experiments to test the effectiveness of Carr and Lee's immunization strategy. Our results indicate that the correlation immunization method is an effective means of reducing pricing and hedging errors that result from nonzero correlation.