Interest Rates as Options

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...

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Bibliographic Details
Published in:The Journal of finance (New York) 1995-12, Vol.50 (5), p.1371-1376
Main Author: BLACK, FISCHER
Format: Article
Language:English
Subjects:
Capital costs
Economic theory
Financial instruments
Inflation rates
Interest rates
Investment risk
Market prices
Monte Carlo simulation
Nominal interest rates
Options markets
Underground economies
Yield curves
Yield to maturity
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Summary: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.
ISSN:0022-1082
1540-6261
DOI:10.1111/j.1540-6261.1995.tb05182.x