Pricing Fixed-Income Securities in an Information-Based Framework

Abstract

The purpose of this article is to introduce a class of information-based models for the pricing of fixed-income securities. We consider a set of continuous-time processes that describe the flow of information concerning market factors in a monetary economy. The nominal pricing kernel is assumed to be given at any specified time by a function of the values of information processes at that time. Using a change-of-measure technique, we derive explicit expressions for the prices of nominal discount bonds and deduce the associated dynamics of the short rate of interest and the market price of risk. The interest rate positivity condition is expressed as a differential inequality. An example that shows how the model can be calibrated to an arbitrary initial yield curve is presented. We proceed to model the price level, which is also taken at any specified time to be given by a function of the values of the information processes at that time. A simple model for a stochastic monetary economy is introduced in which the prices of the nominal discount bonds and inflation-linked notes can be expressed in terms of aggregate consumption and the liquidity benefit generated by the money supply.

Key Words:

• fixed-income securities
• interest rate theory
• inflation-linked securities
• incomplete information
• non-linear filtering

Acknowledgements

The authors are grateful to J. Akahori, D. C. Brody, H. Gretarsson, M. Hinnerich, T. Honda, E. Hoyle, E. Mackie, R. Miura, K. Ohashi, P. A. Parbhoo, G. Sarais, J. Sekine and W. T. Shaw for useful discussions. We are grateful to the seminar participants at Ritsumeikan University, Kusatsu, Japan, the KIER-TMU International Workshop on Financial Engineering 2009, Tokyo, and ICS Hitotsubashi University, Tokyo, for helpful comments. LPH acknowledges support from Lloyds TSB, Shell International and the Aspen Center for Physics.