The price and risk of guaranteed interest rate products

Abstract

This paper examines the utility indifference price of interest rate products and the risk associated with these. Such products can be compared with put options and are here considered to be written on a non-tradeable asset which can be hedged with a correlated asset. Initially, we look at the case where both the tradeable and non-tradeable assets can be modeled by two geometric Brownian motions. This model is later extended to the case where it is assumed that the tradeable asset follows a Lévy process. The paper is based on the article ’Utility indifference pricing of interest-rate guarantees’ by Fred Espen Benth and Frank Proske, but is meant to be an independent paper. The definitions of the utility indifference price and the residual risk remaining after hedging are the same as in their paper. The residual risk is measured with several different risk measures such as Value at Risk, Conditional Value at Risk and Expected Shortfall. These measures, with others, are closely examined and evaluated. Numerical examples are included showing that the utility indifference price is lower for negative correlation than for positive and that the price can be even lower if the tradeable asset follows a Lévy process. Thus, if e.g. life companies can hedge in assets allowing jumps, and that are negatively correlated with their pension fund, they may offer lower prices with practically unaltered measures of risk. Analysis of the pricing and hedging of interest rate guarantees are not only relevant for life companies, but also for other financial institutions offering investment products where there is a guaranteed least rate of return.