On the geometry of interest rate models
 
 
Description:  The purpose of this talk is to give an overview of some recent work concerning the structural and geometric properties of the evolution of the forward rate curve in an arbitrage free bond market. The main problems to be discussed are as follows.
1. When is a given forward rate model consistent with a given family of forward rate curves?
2. When can the inherently infinite dimensional forward rate process be realized by means of a finite dimensional state space model. We consider interest rate models of Heath-Jarrow-Morton type, where the forward rates are driven by a multidimensional Wiener process, and where the volatility is allowed to be an arbitrary smooth functional of the present forward rate curve. Within this framework we give necessary and sufficient conditions for consistency, as well as for the existence of a finite dimensional realization, in terms of the forward rate volatilities. We also study stochastic volatility HJM models, and we provide a systematic method for the construction of concrete realisations.
No previous knowledge of finance is assumed.

Tomas Björk is professor in the Department of Finance of the Stockholm School of Economics (KTH) since 1998. He is well known for his contributions in continuous time finance. Tomas Björk has given several invited and plenary talks at some of the most reputable events in mathematical finance and applied stochastics. He has served as co-editor or associate editor in the journals Mathematical Finance, Finance and Stochastics, Annals of Applied Probability, and Finance India. Professor Björk was elected teacher of the year in KTH on several occasions. He gave a number of international courses and lectures and held several visiting positions such as those in Cambridge, Pisa, and Princeton. He is the author of the book "Arbitrage Theory in Continuous Time", published by Oxford University Press (1998, 2004).
Area(s):
Start Date:  2008-05-07
Start Time:   11.00
Speaker:  Tomas Björk (Stockholm School of Economics, Sweden)
Place:  Sala 2.4 - Departamento de Matemática
URL:  http://www.hhs.se/Finance/People/ShowPerson.htm?personid=37
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