ABSTRACT
This chapter explains price interest rate options given the market prices of the entire zero-coupon bond price curve and its stochastic evolution. It analyses the theory underlying the methodology, which is decomposed into the one-factor case, the two-factor case, and the multiple-factor case. The key insight to be understood is how to determine when a given zero-coupon bond price curve evolution is arbitrage-free. This is a nontrivial exercise, and it is the primary contribution of the Heath, Jarrow, and Morton model to the academic literature. The chapter examines the restrictions that the assumption imposes upon the stochastic processes for the evolution of the entire zero-coupon bond price curve. The economic interpretation of condition is that, to prevent arbitrage, all zero-coupon bonds must have the same excess return per unit of risk. Otherwise, those zero-coupon bonds with higher excess returns, per unit of risk, are good buys.
