Coherent chaos interest-rate models

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/S0219024915500168The 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

Entropy and Information in the Interest Rate Term Structure

Associated with every positive interest term structure there is a probability density function over the positive half-line. This fact can be used to turn the problem of term structure analysis into a problem in the comparison of probability distributions, an area well developed in statistics, known as information geometry. The information-theoretic and geometric aspects of term structures thus arising are here illustrated. In particular, we introduce a new term structure calibration methodology based on maximization of entropy, and also present some new families of interest rate models arising naturally in this context

Pricing the Quality Option In Treasury Bond Futures

This article develops a model for pricing the quality option embedded in the Treasury bond futures contract. Since the option value is set relative to a large family of deliverable bond prices, it is important for the theoretical bond prices to match up to the observed prices. Hence an arbitrage-based model is used where the forward rate process is initialized at its current observable value. A model for valuing the quality option in an otherwise identical forward contract is also established. This permits the quality option and marking to market costs to be separately quantified. Support is provided for the common practice of pricing Treasury bond futures contracts as forward contracts with an embedded forward quality option. Copyright 1992 Blackwell Publishers.