Pricing interest rate derivatives and building a term structure of interest rates

Abstract

Interest rate derivatives are those instruments whose payoffs are dependent in some way on the level of interest rates. Therefore, to price these derivatives, we must build a term structure of interest rates viz. the yield curve. The models for pricing interest rate derivatives make the assumption that the probability distribution of an interest rate at a future point in time is lognormal. One popular model used for pricing these derivatives is the Black’s model. In this report, we estimate a yield curve for the Indian debt market using the Nelson-Siegel Method (also used by the NSE to generate the Zero Coupon Yield Curve) and using this curve price caps, floors, collars and swaptions. We provide working models to price these instruments for different values of the instrument parameters. We then point out the shortcomings of the Black’s model and discuss alternative approaches to overcome these limitations. Specifically, we talk of interest rate models of the short rate. Equilibrium and no-arbitrage models are briefly discussed and the second part of this project is the implementation of the General Hull-White model, a general one-factor model, as a recombining trinomial tree.