The Market Price of Risk for Affine Interest Rate Term Structures

Abstract

This paper examines the market price of risk for discount bond prices under an affine term structure of interest rates. The usual relation plays two roles. First, it is the definition of market price of risk and, second, it provides a no arbitrage condition for the discount bond market. Here the relation defines the market price of risk for more general situations, but includes the processes which give rise to markets with no arbitrage. This allows a separate study of the no arbitrage condition. We solve for the parameters in the general case of affine term structure with constant parameters. The parameters depend explicitly on the market price of risk. Moreover, observations of the yield rate process do not, in general, uniquely determine the market price of risk.