Essential Classes of Interest Rate Models and Their Use

PETER FITTON

Manager, Scientific Development CreditXpert Inc.

JAMES F. McNATT, CFA

Executive Vice President, ValueWealth Services

Abstract: Models of the term structure of interest rates have become increasingly important in financial modeling. However, the understanding of these models by practitioners has not always kept pace with the breadth of the application of these models. In particular, misinterpretation of the proper uses of a particular model can lead to significant errors. The confusion regarding these models has arisen because of the overuse and misuse of the term “arbitrage-free.”

In this entry, we attempt to clear up some of the most commonly misconstrued aspects of interest rate models: the choice between an arbitrage-free or equilibrium model, and the choice between risk neutral or realistic parame-terizations of a model. These two dimensions define four classes of model forms, each of which has its own proper use.

Much of the confusion has arisen from overuse and misuse of the term “arbitrage-free.” Virtually all finance practitioners believe that market participants quickly take advantage of any opportunities for risk-free arbitrage among financial assets, so that these opportunities do not exist for long; thus, the term “arbitrage-free” sounds as if it would be a good characteristic for any model to have. Simply based on these positive connotations, it almost seems hard to believe that anyone would ...

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