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From: Greg Frank
Affiliation:
Address: gfrank5@home.com
Date: 17 Dec 2000
Time: 11:26:04
Hi:
Black Derman Toy (BDT) is an example of a short rate interest rate model. 'Short' refers to the entity driving the model. The short rate is the interest rate over the shortest measured period and is intended to approximate the instantaneous rate of return. It does not mean you are confined to modeling 'short' term instruments.
Given the short rate, you posit a particular stochastic process it must follow. FOr example, BDT assumes lognormal evolution with a particular mean reversion structure, while Hull-White assumes normal processes, etc. This allows you to build a term structure consistent with both observations (discount factors stripped out of bond curves, etc) and the assumed dynamics. You can model the entire term structure using this approach.
And there are problems, of course. While you may be able to model a 30y rate based on observations of the ON, the connection with reality becomes rather tenuous. This is why multi-factor models have been developed that allow modeling of sets of interest rate processes distributed across the term structure. Generalized Heath-Jarrow-Morton (HJM) models are the most widely used framework. The problem with them is keeping them up to date, as calibration becomes a very time consuming activity. A lot of trading desks still get a lot of mileage using simple one-factor models for that reason.
Regards,
Greg
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