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|Title:||Coherent chaos interest-rate models|
|Keywords:||Coherent states;Conditional variance representation;Fock space;Pricing kernel;Wiener chaos expansion|
|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.|
|Appears in Collections:||Dept of Mathematics Research Papers|
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