Abstract
Modeling the interest-rate evolution through the instantaneous short rate has some advantages, mostly the large liberty one has in choosing the related dynamics. For example, for one-factor short-rate models one is free to choose the drift and instantaneous volatility coefficient in the related diffusion dynamics as one deems fit, with no general restrictions. We have seen several examples of possible choices in Chapter 3. However, short-rate models have also some clear drawbacks. For example, an exact calibration to the initial curve of discount factors and a clear understanding of the covariance structure of forward rates are both difficult to achieve, especially for models that are not analytically tractable.
I decided I’d spent too much time philosophizing. It is, unfortunately, one of my character flaws. J’onn J’onnz in “Martian Manhunter annual” 2, 1999, DC Comics.
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References
Even the celebrated LIBOR market model was developed starting from instantaneous-forward-rate dynamics in Brace, Gatarek and Musiela (1997), although it is possible to obtain it also through the change-of-numeraire approach, as we will see in the next chapter.
We refer to Li, Ritchken and Sankarasubramanian (1995a) for a detailed description of all the calculations above.
When modeling humped volatility structures, many other specifications can of course be considered. For example the term between square brackets in (5.10) can be generalized to be any polynomial in (T — t). It is disputable however whether there exists a simpler characterization than (5.10) and for which (a), (b), (c) and (d) hold.
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© 2001 Springer-Verlag Berlin Heidelberg
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Brigo, D., Mercurio, F. (2001). The Heath-Jarrow-Morton (HJM) Framework. In: Interest Rate Models Theory and Practice. Springer Finance. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-04553-4_5
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DOI: https://doi.org/10.1007/978-3-662-04553-4_5
Publisher Name: Springer, Berlin, Heidelberg
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