Forward and Futures Prices with Markovian Interest-Rate Processes

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.

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Pricing Claims Under GARCH-Level Dependent Interest Rate Processes

Management Science ◽

10.1287/mnsc.47.12.1693.10238 ◽

2001 ◽

Vol 47 (12) ◽

pp. 1693-1711 ◽

Cited By ~ 8

Author(s):

V. Cvsa ◽

P. Ritchken

Keyword(s):

Interest Rate ◽

Rate Processes

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ESTIMATES OF THE SHORT-TERM RATE PROCESS IN AN ARBITRAGE-FREE FRAMEWORK

International Journal of Theoretical and Applied Finance ◽

10.1142/s0219024904002566 ◽

2004 ◽

Vol 07 (05) ◽

pp. 577-589 ◽

Cited By ~ 1

Author(s):

HOSSEIN KAZEMI ◽

MAHNAZ MAHDAVI ◽

BRETT SALAZAR

Keyword(s):

Interest Rate ◽

Factor Models ◽

Rate Process ◽

Short Term ◽

Constant Elasticity ◽

General Process ◽

No Arbitrage ◽

Time Period ◽

Rate Processes ◽

Almost All

This paper uses a new restriction imposed by the no-arbitrage condition on interest rate processes to estimate the parameters of the short-term rates for US, France, UK and Germany. A general process that nests almost all previous one-factor models is estimated. The results show that the volatility structure of US short-term rate is similar to the processes suggested by Duffie and Kahn [9] or Chan et al. [4] depending on the proxy used for the short-term rate and the time period covered by the study. The volatility structures of the short-term rates in France and Germany do not have constant elasticity with respect to the short-term rate, while the elasticity of UK's short-term rate is constant and equal to 1.5.

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