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Coherent chaos interest-rate models

Brody, Dorje and Hadjpetri, Stala (2015) Coherent chaos interest-rate models International Journal of Theoretical and Applied Finance, 18 (3), 1550016.


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The Wiener chaos approach to interest-rate modeling arises from the observation that in the general context of an arbitrage-free model with a Brownian filtration, the pricing kernel admits a representation in terms of the conditional variance of a square-integrable generator, which in turn admits a chaos expansion. When the expansion coefficients of the random generator factorize into multiple copies of a single function, the resulting interest-rate model is called "coherent", whereas a generic interest-rate model is necessarily "incoherent". Coherent representations are of fundamental importance because an incoherent generator can always be expressed as a linear superposition of coherent elements. This property is exploited to derive general expressions for the pricing kernel and the associated bond price and short rate processes in the case of a generic nth order chaos model, for each n ∈ ℕ. Pricing formulae for bond options and swaptions are obtained in closed form for a number of examples. An explicit representation for the pricing kernel of a generic incoherent model is then obtained by use of the underlying coherent elements. Finally, finite-dimensional realizations of coherent chaos models are investigated and we show that a class of highly tractable models can be constructed having the characteristic feature that the discount bond price is given by a piecewise-flat (simple) process.

Item Type: Article
Divisions : Faculty of Engineering and Physical Sciences > Mathematics
Authors :
Hadjpetri, Stala
Date : 7 May 2015
DOI : 10.1142/S0219024915500168
Copyright Disclaimer : Electronic version of an article published as International Journal of Theoretical and Applied Finance, 18(3), 2015, 1550016, DOI: 10.1142/S0219024915500168 © World Scientific Publishing Company.
Uncontrolled Keywords : Pricing kernel; Conditional variance; Representation; Wiener chaos; Expansion; Fock space; Coherent states
Depositing User : Claudio Svaluto
Date Deposited : 11 Oct 2018 08:57
Last Modified : 11 Oct 2018 08:57

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