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Interest Rates as Options

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Author Info
 Black, Fischer
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. Copyright 1995 by American Finance Association.

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Publisher Info
Article provided by American Finance Association in its journal Journal of Finance.

Volume (Year): 50 (1995)
Issue (Month): 5 (December)
Pages: 1371-76
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Handle: RePEc:bla:jfinan:v:50:y:1995:i:5:p:1371-76

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  1. Shane Miller & Eckhard Platen, 2004. "A Two-Factor Model for Low Interest Rate Regimes," Asia-Pacific Financial Markets, Springer, vol. 11(1), pages 107-133, March. [Downloadable!] (restricted)
    Other versions:
  2. Ruge-Murcia, F.J., 2002. "Some Implications of the Zero Lower Bound on Interest Rates for the Term Structure and Monetary Policy," Cahiers de recherche 06-2002, Centre interuniversitaire de recherche en économie quantitative, CIREQ. [Downloadable!]
    Other versions:
  3. Don H. Kim, 2008. "Zero bound, option-implied PDFs, and term structure models," Finance and Economics Discussion Series 2008-31, Board of Governors of the Federal Reserve System (U.S.). [Downloadable!]
  4. Don H Kim, 2007. "Spanned stochastic volatility in bond markets: a reexamination of the relative pricing between bonds and bond options," BIS Working Papers 239, Bank for International Settlements. [Downloadable!]
  5. Kenneth Kuttner, 2006. "Can Central Banks Target Bond Prices?," NBER Working Papers 12454, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  6. Antulio N. Bomfim, 2003. "Interest rates as options: assessing the markets' view of the liquidity trap," Finance and Economics Discussion Series 2003-45, Board of Governors of the Federal Reserve System (U.S.). [Downloadable!]
  7. Enlin Pan & Liuren Wu, 2004. "Taking Positive Interest Rates Seriously," Finance 0409013, EconWPA. [Downloadable!]
  8. Silverio Foresi & Alessandro Penati & George Pennacchi, 1997. "Estimating the cost of U.S. indexed bonds," Working Paper 9701, Federal Reserve Bank of Cleveland. [Downloadable!]
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