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Title: | Coherent chaos interest-rate models |
Authors: | Brody, DC Hadjipetri, S |
Keywords: | Coherent states;Conditional variance representation;Fock space;Pricing kernel;Wiener chaos expansion |
Issue Date: | 2015 |
Publisher: | World Scientific Publishing Co. Pte., Ltd. |
Citation: | International Journal of Theoretical and Applied Finance, 18(3): 1550016, (2015) |
Abstract: | 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 eachn 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. |
Description: | Electronic version of an article published as International Journal of Theoretical and Applied Finance, 18, 3, 2015, pp. 1550016. doi:10.1142/S0219024915500168 © copyright World Scientific Publishing Company, https://www.worldscientific.com/doi/abs/10.1142/S0219024915500168 |
URI: | https://www.worldscientific.com/doi/abs/10.1142/S0219024915500168 https://bura.brunel.ac.uk/handle/2438/10950 |
DOI: | https://doi.org/10.1142/S0219024915500168 |
ISSN: | 0219-0249 |
Appears in Collections: | Dept of Mathematics Research Papers |
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