Models of yield curve and the term structure
This chapter summarizes the important developments in arbitrage-free pricing of securities. We focus exclusively on one-factor models of term structure and how they can be used to value fixed-income securities and their derivatives. We address the following models: random walk model of interest rates and mean-reverting interest rates, including the Cox, Ingersoll, and Ross model and the Vasicek model. We develop in detail the Black, Derman, and Toy model and show how it can be calibrated to market data on yields and volatilities. We briefly summarize many one-factor models and describe their differences. Finally, we illustrate the pricing of interest rate derivatives, including ...