re Libor models - skew parametrization
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re Libor models - skew parametrization
 
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Well, if you allow an arbitrary skew parametrization the SDEs are no
longer solvable even when the drift is zero. All modelling is a compromise between tractability and realism, displaced diffusion is just as tractable as log-normal and so is a natural choice. The volatilities in the model are to be interpreted as the volatilities of the displaced log-rates. If all your displacements are equal then there is no loss of time homogeneity. If they are not clearly there is. As to what is usual, well that's always an interesting question... regards Mark ------------------------------------------------------------------------------ _______________________________________________ QuantLib-users mailing list [hidden email] https://lists.sourceforge.net/lists/listinfo/quantlib-users |
Antwort: re Libor models - skew parametrization
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ok, of course. But I we at least had
dF = ( b F(t) * (1-b) F(0) ) ... with b rate specific constants (as now the displacements are), the interpretation of the volatilities would be lognormal at the money, tractability is the same, time homogenity of volatilites would be pretty much preserved, wouldn't it? Of course these are modelling issues and I don't say that it has to be changed. Just thoughts and discussion points. Best regards Peter Mark joshi <mark.joshi@gmail .com> An [hidden email] 31.03.2009 11:41 et Kopie Thema [Quantlib-users] re Libor models - skew parametrization Well, if you allow an arbitrary skew parametrization the SDEs are no longer solvable even when the drift is zero. All modelling is a compromise between tractability and realism, displaced diffusion is just as tractable as log-normal and so is a natural choice. The volatilities in the model are to be interpreted as the volatilities of the displaced log-rates. If all your displacements are equal then there is no loss of time homogeneity. If they are not clearly there is. As to what is usual, well that's always an interesting question... regards Mark ------------------------------------------------------------------------------ _______________________________________________ QuantLib-users mailing list [hidden email] https://lists.sourceforge.net/lists/listinfo/quantlib-users ------------------------------------------------------------------------------------------------------------------------------------------------------ WGZ BANK AG Westdeutsche Genossenschafts-Zentralbank Sitz: Düsseldorf, Registergericht: Amtsgericht Düsseldorf, HRB 52363 Vorstand: Werner Böhnke (Vors.), Karl-Heinz Moll, Thomas Ullrich, Hans-Bernd Wolberg Vorsitzender des Aufsichtsrats: Dieter Philipp Ueber das Internet versandte E-Mails koennen unter fremdem Namen erstellt oder inhaltlich veraendert werden. Aus diesem Grund sind unsere als E-Mail verschickten Nachrichten grundsaetzlich keine rechtsverbindlichen Erklaerungen. Der Inhalt dieser E-Mail samt Anlagen ist vertraulich und u. U. rechtlich geschuetzt. Der Inhalt ist ausschließlich an einen bestimmten Empfaenger gerichtet. Eine Weitergabe, die Herstellung von Kopien oder der sonstige Gebrauch durch Nichtadressaten ist nicht erlaubt. Messages sent by e-mail can be manipulated by third parties. For this reason our e-mail messages are generally not legally binding. This electronic message (including any attachments) contains confidential information and may be privileged or otherwise protected from disclosure. The information is intended to be for the use of the intended addressee only. Please be aware that any copy, distribution or use of the contents of this message by any other person than the intended addressee is prohibited. ------------------------------------------------------------------------------ _______________________________________________ QuantLib-users mailing list [hidden email] https://lists.sourceforge.net/lists/listinfo/quantlib-users |
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