On Pricing Kernels and Finite State Variable Heath Jarrow Morton Models

Posted: 12 May 2000

See all articles by George Pennacchi

George Pennacchi

University of Illinois

Peter H. Ritchken

Case Western Reserve University - Department of Banking & Finance

L. Sankarasubramanian

affiliation not provided to SSRN

Abstract

Once a pricing kernel is established, bond prices and all other interest rate claims can be computed. Alternatively, the pricing kernel can be deduced from observed prices of bonds and selected interest rate claims. Examples of the former approach include the celebrated Cox, Ingersoll and Ross (1985) model and the more recent model of Constantinides (1992). Examples of the latter include the Black, Derman and Toy (1990) model and the Heath, Jarrow and Morton paradigm (1992) (hereafter HJM). In general, these latter models are not Markov. Fortunately, when suitable restrictions are imposed on the class of volatility structures of forward rates, then finite state variable HJM models do emerge. This article provides a linkage between the finite state variable HJM models, which use observables to induce a pricing kernel, and the alternative approach, which proceeds directly to price after a complete specification of a pricing kernel. Given such linkages, we are able to explicitly reveal the relationship between state-variable models, such as Cox, Ingersoll and Ross, and the finite state-variable HJM models. In particular, our analysis identifies the unique map between the set of investor forecasts about future levels of the drift of the pricing kernel and the manner by which these forecasts are revised, to the shape of the term structure and its volatility. For an economy with square root innovations, the exact mapping is made transparent.

JEL Classification: G13, E43, G12

Suggested Citation

Pennacchi, George G. and Ritchken, Peter H. and Sankarasubramanian, L., On Pricing Kernels and Finite State Variable Heath Jarrow Morton Models. REVIEW OF DERIVATIVES RESEARCH, Vol. 1 No. 1. Available at SSRN: https://ssrn.com/abstract=7455

George G. Pennacchi (Contact Author)

University of Illinois ( email )

4041 BIF, Box 25
515 East Gregory Drive
Champaign, IL 61820
United States
217-244-0952 (Phone)

HOME PAGE: http://www.business.illinois.edu/gpennacc/

Peter H. Ritchken

Case Western Reserve University - Department of Banking & Finance ( email )

10900 Euclid Ave.
Cleveland, OH 44106-7235
United States
216-368-3849 (Phone)
216-368-4776 (Fax)

L. Sankarasubramanian

affiliation not provided to SSRN

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