Bond indifference prices

Abstract

In a market with stochastic interest rates, we consider an investor who can either (i) invest all of his wealth in a money market account or (ii) purchase zero-coupon bonds and invest the remainder of his wealth in the money market account. The indifference price of the zero-coupon bond is the price at which the investor could achieve the same expected utility under both strategies. In an affine term structure setting, we show that the indifference price of the zero-coupon bond is the root of an integral equation, when the investor's utility function is of exponential or power form. As an example, we compute the indifference price and the corresponding indifference yield curve in the Vasicek model and conduct sensitivity analysis to study the impact of various parameters on the yield curve. Furthermore, we discuss the choice of numéraire and its impact on the indifference prices.

Keywords:

• Bond
• Pricing
• Risk neutral
• Stochastic interest
• Yield

Acknowledgments

The authors are grateful to an anonymous referee for his/her encouraging comments.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1 Please see the report (https://www.sifma.org/wp-content/uploads/2017/08/US-Fact-Book-2018-SIFMA.pdf) from Securities Industry and Financial Markets Association (SIFMA).

2 ‘Currency’ here means a fiat currency (e.g. US dollar) and will be fixed throughout this paper.

Additional information

Funding

Bin Zou acknowledges partial support through a start-up grant from the University of Connecticut.