A Chaotic Approach to Interest Rate Modelling

Hughston, L P and Rafailidis, A. 2005. A Chaotic Approach to Interest Rate Modelling. Finance and Stochastics, 9(1), pp. 43-65. ISSN 0949-2984 [Article]

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This paper presents a new approach to interest rate dynamics. We consider the general family of arbitrage-free positive interest rate models, valid on all time horizons, in the case of a discount bond system driven by a Brownian motion of one or more dimensions. We show that the space of such models admits a canonical mapping to the space of square-integrable Wiener functionals. This is achieved by means of a conditional variance representation for the state price density. The Wiener chaos expansion technique is then used to formulate a systematic analysis of the structure and classification of interest rate models. We show that the specification of a first-chaos model is equivalent to the specification of an admissible initial yield curve. A comprehensive development of the second-chaos interest rate theory is presented in the case of a single Brownian factor, and we show that there is a natural methodology for calibrating the model to at-the-money-forward caplet prices. The factorisable second-chaos models are particularly tractable, and lead to closed-form expressions for options on bonds and for swaptions. In conclusion we outline a general

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January 2005Published

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07 Feb 2022 16:08

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07 Feb 2022 16:08

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