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

Posted: 2 Jul 2021

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: 2008

Abstract

This paper points out that several known ways of modeling non-negative nominal interest rates lead to different implications for the risk-neutral distribution of the short rate that can be checked with options data. In particular, Black's boundary models (\"interest rates as options\") imply a probability density function (pdf) that contains a Dirac delta function and a cumulative distribution function (cdf) that is nonzero at the zero boundary, while models like the CIR and positive-definite quadratic-Gaussian (QG) models have a zero cdf at the boundary. Eurodollar futures options data are found to favor Black's boundary models: the CIR/QG models, even multifactor versions, have difficulty capturing option prices accurately not only in low interest rate environments but also in higher interest rate environments, and data in early 2008 provide an almost tangible signature of the Dirac delta function in Black's boundary pdf models. Options data also contradict the prediction of well-known models whose cdf is zero at the zero boundary, namely that the risk-neutral pdf is always positively skewed.

Suggested Citation

Kim, Don H., Zero Bound, Option-Implied Pdfs, and Term Structure Models (2008). FEDS Working Paper No. 2008-31, Available at SSRN: https://ssrn.com/abstract=3877824

Don H. Kim (Contact Author)

Board of Governors of the Federal Reserve System ( email )

20th Street and Constitution Avenue NW
Washington, DC 20551
United States

Do you have a job opening that you would like to promote on SSRN?

Paper statistics

Abstract Views
8
PlumX Metrics