What is the expected return from investing in long-term bonds? What is the premium of holding long-term bonds compared to short-term bonds? The model developed in Chapter 15 also provides a methodology by which to gauge the risk premium that investors require in order to hold the more volatile long-term bonds compared to short-term bonds, or cash. In this chapter we introduce the notion of market price of risk, first in the Vasicek model and then in the general setting, and then show how to employ Monte Carlo simulations to study the risk embedded in interest rate securities. We conclude the chapter with the illustration of a simple macroeconomic model in which the size of the risk, the risk premium, and the market price of risk of nominal bonds is determined by key economic quantities, such as inflation risk, the business cycle, and the risk aversion of market participants.
Consider once again the Vasicek model of interest rates, developed in Chapter 15. The interest rate process is given by
In that chapter we show that no arbitrage implies that any interest rate security must satisfy the following fundamental pricing equation:
where, under the Vasicek assumption,