Chapter

One‐Factor Diffusion Models

Claus Munk

in Fixed Income Modelling

Published in print June 2011 | ISBN: 9780199575084
Published online September 2011 | e-ISBN: 9780191728648 | DOI: http://dx.doi.org/10.1093/acprof:oso/9780199575084.003.0007
One‐Factor Diffusion Models

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This chapter introduces one-factor diffusion models of the term structure of interest rates, including the famous models of Vasicek and Cox, Ingersoll, and Ross. The one-factor models assume that the short rate contains all the information about the term structure that is relevant for pricing and hedging interest rate-dependent claims, and that the short rate follows a diffusion process. Special attention is given to the so-called affine models. In each model, the pricing of bonds, forwards and futures on bonds, Eurodollar futures, and European options on bonds is discussed. The pricing techniques applied are those developed in earlier chapters: the solution of a partial differential equation or the computation of the expected payoff under a suitable risk-adjusted probability measure.

Keywords: affine models; Merton's model; Vasicek's model; Cox–Ingersoll–Ross model; generalized affine models; estimation

Chapter.  22782 words.  Illustrated.

Subjects: Financial Markets

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