Delta-Hedging of Interest Rate Risk in Longterm Contracts - An Application of the Cairns-Model

Abstract

Long-term portfolios consisting of assets and liabilities often exhibit a significant sensitivity to changes in interest rates. For the management of the interest rate risk arising from such portfolios asset managers usually use duration based approaches like the PV01-method. In the meanwhile the model family proposed by Cairns (2004) proclaims to deliver arbitrage-free valuation of interest rate derivatives and an ideal framework for the management of long-term interest rate risks.

In the following paper, we use the two-factor version of the Cairns-model in order to hedge interest rates of long-term portfolios and in order to test the hedge-effiectiveness of the commonly used PV01-approach. For this purpose we first derive interest rate sensitivity measures on the basis of the Cairns-model. Based on the extended Kalman-fillter approach, we calibrate the model and demonstrate the behavior of the sensitivity measures derived. We then use these measures in order to hedge interest rate risks of a pension-fund-like portfolio. The hedging-strategy we introduce for this purpose is based on plain vanilla interest rate swaps, it is rule-based and model independent. We then put the Cairns-model and PV01 approach to the test using one historical path (European interest rates, June 2000 - June 2010) as well as on the basis of a Monte Carlo simulation. Both analysis show that the strategy delivered is quite robust in eliminating interest rate risks. Interestingly, our analysis actually underlines the practicability and compatibility of the PV01-approach.

Keywords: Cairns Model, Delta Hedging, Interest Rate Risk, Extended Kalman-Filter, Swap-Overlay, DV01, PV01, Duration Gap

JEL Classification: E43, E47, G12, G23, C13