Time-Varying Volatility and the Dynamic Behavior of the Term Structure (original) (raw)
Related papers
2005
We investigate whether bonds span the volatility risk in the U.S. Treasury market, as predicted by most 'affine' term structure models. To this end, we construct powerful and model-free empirical measures of the quadratic yield variation for a cross-section of fixed-maturity zero-coupon bonds ("realized yield volatility") through the use of high-frequency data. We find that the yield curve fails to span yield volatility, as the systematic volatility factors are largely unrelated to the cross-section of yields. We conclude that a broad class of affine diffusive, Gaussian-quadratic and affine jump-diffusive models is incapable of accommodating the observed yield volatility dynamics. An important implication is that the bond markets per se are incomplete and yield volatility risk cannot be hedged by taking positions solely in the Treasury bond market. We also advocate using the empirical realized yield volatility measures more broadly as a basis for specification testing and (parametric) model selection within the term structure literature.
Predictive Ability of the Volatility Yield Curve
This study applies the Nelson-Siegel model to volatilities of U.S. treasury yields between 2001 and 2016. The most significant finding is that curvature of the volatility yield curve has predictive ability for volatility levels. We use lagged curve characteristics and forward-looking indicators to forecast volatility curves and find that they consistently outperform benchmarks on long maturities, while producing mixed results on short maturities. Results are robust for European treasury yields.
An empirical analysis of unspanned risk for the U.S. yield curve
Lecturas de EconomÃa, 2016
In this paper, I formally test for the unspanning properties of liquidity premium risk in the context of a joint Gaussian affine term structure model for zero-coupon U.S. Treasury and TIPS bonds. In the model, the liquidity factor is regarded as an additional factor that does not span the yield curve, but improves the forecast of bond risk premia. I present empirical evidence suggesting that liquidity premium indeed helps to forecast U.S. bond risk premia in spite of not being linearly spanned by the information in the joint yield curve. In addition, I show that the liquidity factor does not affect the dynamics of bonds under the pricing measure, but does affect them under the historical measure. Further, variation in the TIPS liquidity premium predicts the future evolution of the traditional yield curve factors.
Term structure of volatilities and yield curve estimation methodology
Quantitative Finance, 2011
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Inferring Volatility from the Yield Curve
Journal of Mathematical Finance, 2015
In this paper, we assess how to recover the volatility of interest rates in the euro area money market, on the sole basis of the zero-coupon yield curve. Our primary result is that there exists an empirical regularity (linking rates and volatility) that takes a relatively simple mathematical form. We also show that the existence of such regularity cannot be explained by a reasoning based on the hypothesis of absence of opportunities of arbitrage since a continuous-time arbitrage-free model may produce instances of curves that are consistent with a continuum of level of volatilities. We exhibit an example for this.
Estimating the Term Structure of Volatility in Futures Yield - A Maximum Likelihood Approach
Social Science Research Network, 1995
The volatility structure of 90-day bill futures traded on the Sydney Futures Exchange is analysed within the framework of the Heath-Jarrow-Morton model. The method involves characterisation of the transition probability density function for the forward rate process represented by the stochastic differential equation in the arbitrage-free economy. Maximisation of the likelihood function then results in the estimates of the parameters of the volatility function. The volatility function is also used in a simulation of the preference-free stochastic differential equation for bill prices.
Bond price representations and the volatility of spot interest rates
Review of Quantitative Finance and Accounting, 1996
A common approach to modeling the term structure of interest rates in a single-factor economy is to assume that the evolution of all bond prices can be described by the current level of the spot interest rate. This article investigates the restrictions that this assumption imposes. Specifically, we show that this Markovian restriction, together with the no-arbitrage requirement, curtails the relationship of forward rates and their volatilities relative to spot-rate volatilities. Among such Markovian models, only a few provide simple analytical relationships between bond prices and the spot interest rate. This article identifies the class of spot-rate volatility specifications that permit simple analytical linkages to be derived between bond prices and interest rates. Included in the class are the volatility structures used by Vasicek and by Cox, Ingersoll, and Ross. Surprisingly, no other volatility structures permit simple analytical representations.
Interest Rate Risk - The Impact of the Yield Curve on Treasury Bill Returns
Advances in applied sciences, 2016
Interest rate risk involves the risk to earnings or capital arising from movement of interest rates. It arises from differences between the timing of rate changes and the timing of cash flows (re-pricing risk); changing rate relationships among yield curves that affect bank activities (basic risk); from changing rate relationships across the spectrum of maturities (yield curve risk); and from interest-rate-related options entrenched in bank products (option risk). This paper assessed the impact of the level, slope and curvature components of the yield curve on treasury bill returns using secondary data to draw quarterly yield curves for the various maturity periods. This approach was extended to capture the sensitivity to changes in the level, slope, and curvature of the term structure using the parameters of the dynamic [14] model to fit the term structure. The results revealed that, the shorter the yield to maturity the stable and better the returns or yield. Applying dynamic factor models, it was seen that, the slope factor representing the short term component had better returns compared to the medium term and the long term components. Also, the results revealed that, the 91 day T-bill which represents the short term component produced better and much stable returns compared with the 182 day T-bill and 1 year note representing the medium and long term components respectively.
Bond risk, bond return volatility, and the term structure of interest rates
International Journal of Forecasting, 2012
This paper explores time variation in bond risk, as measured by the covariation of bond returns with stock returns and with consumption growth, and in the volatility of bond returns. A robust stylized fact in empirical finance is that the spread between the yield on long-term bonds and short-term bonds forecasts positively future excess returns on bonds at varying horizons, and that the short-term nominal interest rate forecasts positively stock return volatility and exchange rate volatility. This paper presents evidence that movements in both the short-term nominal interest rate and the yield spread are positively related to changes in subsequent realized bond risk and bond return volatility. The yield spread appears to proxy for business conditions, while the short rate appears to proxy for inflation and economic uncertainty. A decomposition of bond betas into a real cash flow risk component, and a discount rate risk component shows that yield spreads have offsetting effects in each component. A widening yield spread is correlated with reduced cash-flow (or inflationary) risk for bonds, but it is also correlated with larger discount rate risk for bonds. The short rate forecasts only the discount rate component of bond beta.