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Atlanta Fed Working Papers


Callable U.S. Treasury Bonds: Optimal Calls, Anomalies, and Implied Volatilities

Robert R. Bliss and Ehud I. Ronn
Federal Reserve Bank of Atlanta
Working Paper 97-1
March 1997

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Previous studies on interest rate derivatives have been limited by the relatively short history of most traded derivative securities. The prices for callable U.S. Treasury securities, available for the period 1926–95, provide the sole source of evidence concerning the implied volatility of interest rates over this extended period. Using the prices of callable, as well as non-callable, Treasury instruments, this paper estimates implied interest rate volatilities for the past seventy years. Our technique for estimating implied volatilities enables us to address two important issues concerning callable bonds: the apparent presence of negative embedded option values and the optimal policy for calling these, and similarly structured, deferred-exercise embedded option bonds.

In examining the issue of negative option value callable bonds, our technique enables us to extend significantly both the sample period and sample breadth beyond those covered by other investigators of this phenomenon and to resolve the inconsistencies in their results. We show that the frequency of mispriced bonds is time-varying and that there also exist irrationally underpriced bonds. Critically, both anomalies are shown to be related to volatility-insensitive, away-from-the-money bonds.

In contrast to the naive call decision rules suggested by previous authors, we develop the option-theoretic optimal call policy for deferred-exercised "Bermuda"-style options for which prior notification of intent to call is required. We do this by introducing the concept of "threshold volatility" to measure the point at which the time value of the embedded call option has been eroded to zero. By using this concept, we address the valuation of such bonds and document the frequent optimality of the Treasury's past call decisions for U.S. government obligations.

JEL classification: G13, H63

Key words: Optimal call decision, implied interest rate volatility, callable U.S. Treasury bond mispricing


This is a much-revised version of Working Paper 95-12, "The Implied Volatility of U.S. Interest Rates: Evidence from Callable U.S. Treasuries." The authors acknowledge the helpful comments and suggestions of David Brown, Andreas Grünbrichler, Robert Litzenberger, and finance seminar participants at the University of Texas at Austin, the Norwegian School of Management, Merrill Lynch International (London), the Federal Reserve Board of Governors, the University of Warwick, the Federal Reserve Bank of Atlanta, Case Western Reserve University, the Federal Reserve Bank of Chicago, and the University of Mannheim. Earlier drafts of this paper were presented at the 1994 Cornell University/Queen's University Derivative Securities Conference, the 1994 Wisconsin Finance Symposium, the 1995 Meetings of the Western Finance Association, and the 1996 Federal Reserve System Meeting on Financial Markets and Instruments. Financial support from the University of Texas at Austin College and Graduate School of Business is gratefully acknowledged. The authors would also like to thank Merrill Lynch & Co. for providing data in support of this project. The views expressed here are those of the authors and not necessarily those of the Federal Reserve Bank of Atlanta or the Federal Reserve System. Any remaining errors are the authors' responsibility.

Please address questions of substance to Robert R. Bliss, Research Department, Federal Reserve Bank of Atlanta, 104 Marietta Street, N.W., Atlanta, Georgia 30303-2713, 404/498-8757, 404/498-8814 (fax), robert.bliss@atl.frb.org; and Ehud I. Ronn, Department of Finance, College and Graduate School of Business, University of Texas at Austin, Austin, Texas 78712-1179, 512/471-5853, 512/471-5073 (fax), eronn@mail.utexas.edu.

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