REVEALING THE MARKET PRICE OF RISK FROM THE SHORT‐TERM RATE PROCESS

This paper shows that for a large class of single and multi‐factor term structure models, including the affine class, the market price of risk is directly related to the parameters of the stochastic processes of the underlying factors of the economy. It is shown that the market price of risk is proportional to the limit of the volatility of zero coupon bond returns. This means that the market price of risk is not entirely arbitrary. Not only it must be consistent with no arbitrage conditions, also it must be consistent with the parameters of stochastic processes of the factors that describe the economy. If the market price of risk is not correctly specified, then it could lead to profit opportunities of the type discussed in Backus et al (1996). Another consequence of our result is that in empirical tests of interest rate processes, the market price of risk should not be specified exogenously since its value is a function of the parameters of the model. We extend our result to forward processes. The market price of risk is shown to be a function of the volatility of the forward rate processes.