Bond indifference prices and indifference yield curves

TL;DR

This paper derives explicit formulas for bond indifference prices and yield curves in a stochastic interest rate market, using affine models and utility functions, with practical computations in the Vasicek model.

Contribution

It introduces a method to compute bond indifference prices and yield curves explicitly in affine term structure models with exponential or power utility functions.

Findings

Explicit indifference price formulas derived

Indifference yield curves computed in Vasicek model

Results interpreted within the affine term structure framework

Abstract

In a market with stochastic interest rates, we consider an investor who can either (i) invest all if his money in a savings account or (ii) purchase zero-coupon bonds and invest the remainder of his wealth in a savings account. The indifference price of the bond is the price for which the investor could achieve the same expected utility under both scenarios. In an affine term structure setting, under the assumption that an investor has a utility function in either exponential or power form, we show that the indifference price of a zero-coupon bond is the root of an integral expression. As an example, we compute bond indifference prices and the corresponding indifference yield curves in the Vasicek setting and interpret the results.