Chapter

Short-Rate Term Structure Models

Term Structure Modeling

  1. Alexander Levin PhD

Published Online: 15 DEC 2012

DOI: 10.1002/9781118182635.efm0122

Encyclopedia of Financial Models

Encyclopedia of Financial Models

How to Cite

Levin, A. 2012. Short-Rate Term Structure Models. Encyclopedia of Financial Models. .

Author Information

  1. Director, Financial Engineering, Andrew Davidson & Co., Inc.

Publication History

  1. Published Online: 15 DEC 2012

Abstract

Market randomness makes the fair value of a financial instrument an expectation. It also requires a rigorous quantification of the dynamics of interest rates; that is, a well-defined interest rate model. Prices of interest rate options and options embedded in bonds such as corporate or agency callable debts, mortgage-backed securities, and asset-backed securities will firmly depend on this modeling work. Contemporary interest rate models employ the available information about currently observed forward rates and vanilla European options and are “calibrated” to them. The relationships between bond rates should preclude arbitrage. Some analytically tractable models ensure these properties explicitly. Selecting the “best” term structure model is becoming more a conscientious task and less a matter of taste. Measuring “volatility skew” for widely traded swaptions is a simple technique that yields rich results. Another method is computing volatility indexes produced by different models and tracking their stability. Recent trading history confirms normalization of the swaption market making the Hull-White model, the extended Cox-Ingersoll-Ross model, or the squared Gaussian model more attractive than formerly popular lognormal models. Single-factor models cannot value accurately curve options or some exotic derivatives that are exposed to the yield curve shape and require multifactor modeling work. The affine theory offers a systematic method of constructing such models. It also allows for jump-diffusion extensions that may be necessary to explain volatility smile; that is, an excessive convexity of the Black volatility as a function of strike.

Keywords:

  • short-rate volatility;
  • mean reversion;
  • normality;
  • lognormality;
  • arbitrage-free relationship;
  • analytical tractability;
  • calibration;
  • Black volatility;
  • volatility index;
  • volatility skew;
  • volatility smile;
  • affine modeling framework;
  • diffusion;
  • jumps;
  • multifactor models