Zero Bound, Option-Implied PDFs, and Term Structure Models

33 Pages Posted: 28 May 2008 Last revised: 31 May 2009

See all articles by Don H. Kim

Don H. Kim

Board of Governors of the Federal Reserve System

Multiple version iconThere are 2 versions of this paper

Date Written: May 28, 2009


Federal Reserve's decision (in December 2008) to lower its target funds rate all the way to the range of "0 to 1/4 percent'' has brought the issue of the zero bound in nominal interest rates into a sharp focus. This paper develops techniques for analyzing the risk-neutral probability density functions (pdf) of the short rate arising from certain interest rate models that respect the presence of the zero bound. In particular, this paper derives the pdf of a one-factor Black's boundary model (showing that it contains the so-called Dirac delta function), and also comes up with flexible pdf forms that are consistent with Black's boundary behavior. In addition, this paper develops a fast method for the computation of option prices for the risk-neutral distribution implied by another class of positive interest rate models, those that show a "CIR-like'' zero-boundary behavior (multifactor CIR models and quadratic-Gaussian models). The asymptotic behavior of the pdf at vanishing interest rates (which highlights the effect of different boundary behaviors on the pdf) is also derived for well-known models. Applying these techniques to data on eurodollar futures options from May 1998 to April 2008, this paper finds some support for Black's boundary behavior, and at the same time finds problems with models that have a CIR-like zero-boundary behavior.

Keywords: zero bound, options, risk-neutral pdf, term structure models

JEL Classification: E43, G13

Suggested Citation

Kim, Don H., Zero Bound, Option-Implied PDFs, and Term Structure Models (May 28, 2009). Available at SSRN: or

Don H. Kim (Contact Author)

Board of Governors of the Federal Reserve System ( email )

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