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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.

This paper investigates the linear/nonlinear long-run and short-run dynamic relationships between oil prices and two implied volatilities, oil price volatility index (OVX) and stock index options volatility index (VIX), representing panic gauges. The results show that there is a long-run equilibrium relationship between oil prices and OVX (VIX) using the linear autoregressive distributed lag (ARDL)-bounds test. Likewise, while using the nonlinear autoregressive distributed lag (NARDL)-bounds test, not only does a long-run equilibrium relationship exist, but also the rising OVX (VIX) has a greater negative influence on oil prices than the declining OVX (VIX), thus indicating that a long-run, asymmetric cointegration exists between the variables. Furthermore, OVX (VIX) oil prices have a linear Granger causality, while for the nonlinear Granger causality test, oil prices have a bidirectional relation with OVX (VIX). In addition, we find that once major international political and economic events occur, structural changes in oil prices change the behavior of oil prices, and thus panic indices, thereby switching from a linear relationship to a nonlinear one. The empirical results of this study provide market participants with more valuable information.

Abstract This article assesses the impact of exogenous variables in GARCH models, when applied to volatility forecasts for the Brazilian USD-BRL currency market. As exogenous variables, we used the realized variance, based on high frequency data, and the FXVol index, based on market implied volatility data. This is the first study to use the FXVol index and to investigate its effects on Brazilian foreign exchange volatility. The results indicate statistical significance of the superiority of the extended models when predicting volatility. We conclude that high frequency data and market implied volatility contain relevant information with respect to USD-BRL currency volatility. These find ings are relevant for hedgers, speculators and practitioners in general.