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Journal of Finance Vol. 50 No. 5 1995

Interest Rates as Options

Fischer Black1,2

1 Goldman, Sachs & Co. I am grateful to Chi-Fu Huang and Wei-Tong Shu for discussions of these issues, and to Wei-Tong Shu for producing the graphs. [Note from the Managing Editor: Fischer Black submitted this paper on May 1, 1995. His submission letter stated: “I would like to publish this, though I · 2 Goldman, Sachs & Co. I am grateful to Chi-Fu Huang and Wei-Tong Shu for discussions of these issues, and to Wei-Tong Shu for producing the graphs. [Note from the Managing Editor: Fischer Black submitted this paper on May 1, 1995. His submission letter stated: "I would like to publish this, though I

Abstract

Since people can hold currency at a zero nominal interest rate, the nominal short rate cannot be negative. The real interest rate can be and has been negative, since low risk real investment opportunities like filling in the Mississippi delta do not guarantee positive returns. The inflation rate can be and has been negative, most recently (in the United States) during the Great Depression. The nominal short rate is the “shadow real interest rate” (as defined by the investment opportunity set) plus the inflation rate, or zero, whichever is greater. Thus the nominal short rate is an option. Longer term interest rates are always positive, since the future short rate may be positive even when the current short rate is zero. We can easily build this option element into our interest rate trees for backward induction or Monte Carlo simulation: just create a distribution that allows negative nominal rates, and then replace each negative rate with zero.

DOI
10.1111/j.1540-6261.1995.tb05182.x
Volume
50
Issue
5
Pages
1371-1376
Language
en
Sources
openalex crossref

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