Callable U.S. Treasury bonds: optimal calls, anomalies, and implied volatilities

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.Derivative securities ; Government securities

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.Government securities ; Interest rates ; Treasury bills

The bias in Black-Scholes/Black implied volatility: An analysis of equity and energy markets

In this paper we examine the extent of the bias between Black and Scholes (1973)/Black (1976) implied volatility and realized term volatility in the equity and energy markets. Explicitly modeling a market price of volatility risk, we extend previous work by demonstrating that Black-Scholes is an upward-biased predictor of future realized volatility in S&P 500/S&P 100 stock-market indices. Turning to the Black options-on-futures formula, we apply our methodology to options on energy contracts, a market in which crises are characterized by a positive correlation between price-returns and volatilities: After controlling for both term-structure and seasonality effects, our theoretical and empirical findings suggest a similar upward bias in the volatility implied in energy options contracts. We show the bias in both Black-Scholes/Black implied volatilities to be related to a negative market price of volatility risk. Copyright Springer Science+Business Media, LLC 2005Implied volatility, Energy markets, Black-Scholes,