Study of the approaches to term structure modelling and their applications in the pricing of interest rate derivatives

Abstract

The theory of the term structure of interest rates has evolved greatly over the last fifty years. This evolution has been largely motivated by the growth of the markets and their diverse needs. Simple explanations like the liquidity preference hypotheses could not explain idiosyncratic movements in the yield curve. They could neither help in pricing derivatives based on interest rates. Newer, better models had therefor to be introduced. This study aims primarily at understanding the birth and growth of the models that explain the behavior of interest rates. The study divides interest rate models into three broad segments: • Early models – simple theories like expectations hypothesis, liquidity preference, preferred habitat. • Yield Models – the study discusses three generations of yield curve models here o First Generation Models- Models of the short rate. o Second Generation Models- Tree based models two factor models o Third Generation Models- Models that consider terminal decoration. • Later, more sophisticated models like the HJM model. In analyzing these models rather than employing a purely mathematical approach, the study attempts to blend the mathematical foundations of the models with the needs of the market that drove their evolution. By doing this, it aims to make the reader aware of both the theory and the practical considerations that went behind them. The second part of the study aims at calibrating the first generation yield curve models in the Indian context. This has become relevant in the context of the introduction of exchange traded interest rate derivatives recently in India. Extending the work done by Varna (1996), it calibrates a set of eight, fortnightly (14 day) and monthly rates between 1998 and 2003. The study said, it goes on to normality is violated in India and conclusively proves it to be so. More unrestrictive methods of calibration like the Generalized Method of Moments may allow better calibration and hence a better fit . The study recommends that jump- diffusion models may provide better ways to model these rates.