The implied volatility of U.S. interest rates: evidence from callable U. S. Treasuries

The prices for callable U.S. Treasury securities provide the sole source of evidence concerning the implied volatility of interest rates over the extended 1926-1994 period. This paper uses the prices of callable as well as non-callable Treasury instruments to estimate implied interest rate volatilities for the past sixty years, and, for the more recent 1989-1994 period, the cross-sectional term structures of implied interest rate volatility. We utilize these estimates to perform cross-sectional richness/cheapness analysis across callable Treasuries. Inter alia, we develop the optimal call policy for deferred \"Bermuda\"-style options for which prior notification of intent to call is required by introducing the concept of \"threshold volatility\" to measure the point when the time value of the embedded call option has been eroded to zero. Using this concept facilitates callable-bond valuation and documents the optimality of the Treasury's past call policy for U.S. government obligations.