Forecasting the term structure of volatility of crude oil price changes

Peer reviewed

Estimating the term structure of volatility and fixed income derivative pricing

Estimating the parameters of the instantaneous spot interest rate process is of crucial importance for pricing fixed income derivative securities. This paper presents an estimation for the parameters of the Gaussian interest rate model for pricing fixed income derivatives based on the term structure of volatility. We estimate the term structure of volatility for US treasury rates for the period 1983 - 1995, based on a history of yield curves. We estimate both conditional and first differences term structures of volatility and subsequently estimate the implied parameters of the Gaussian model with non-linear least squares estimation. Results for bond options illustrate the effects of differing parameters in pricing.

Hedging options in a garch environment: testing the term structure of stochastic volatility models

This paper develops a methodology for testing the term structure of volatility forecasts derived from stochastic volatility models, and implements it to analyze models of S&P500 index volatility. U sing measurements of the ability of volatility models to hedge and value term structure dependent option positions, we fmd that hedging tests support the Black-Scholes delta and gamma hedges, but not the simple vega hedge when there is no model of the term structure of volatility. With various models, it is difficult to improve on a simple gamma hedge assuming constant volatility. Ofthe volatility models, the GARCH components estimate of term structure is preferred. Valuation tests indicate that all the models contain term structure information not incorporated in market prices.

The economic determinants of the Brazilian nominal term structure of interest rates

The purpose of this study is to identify the effects of monetary policy and macroeconomic shocks on the dynamics of the Brazilian term structure of interest rates. We estimate a near-VAR model under the identification scheme proposed by Christiano et al. (1996, 1999). The results resemble those of the US economy: monetary policy shocks that flatten the term structure of interest rates. We find that monetary policy shocks in Brazil explain a significantly larger share of the dynamics of the term structure than in the USA. Finally, we analyse the importance of standard macroeconomic variables (e. g. GDP, inflation and measure of country risk) to the dynamics of the term structure in Brazil.

The problem of estimating the volatility of zero coupon bond interest rate

Financial literature and financial industry use often zero coupon yield curves as input for testing hypotheses, pricing assets or managing risk. They assume this provided data as accurate. We analyse implications of the methodology and of the sample selection criteria used to estimate the zero coupon bond yield term structure on the resulting volatility of spot rates with different maturities. We obtain the volatility term structure using historical volatilities and Egarch volatilities. As input for these volatilities we consider our own spot rates estimation from GovPX bond data and three popular interest rates data sets: from the Federal Reserve Board, from the US Department of the Treasury (H15), and from Bloomberg. We find strong evidence that the resulting zero coupon bond yield volatility estimates as well as the correlation coefficients among spot and forward rates depend significantly on the data set. We observe relevant differences in economic terms when volatilities are used to price derivatives.

Three essays on the term structure of interest rates

A PhD Dissertation, presented as part of the requirements for the Degree of Doctor of Philosophy from the NOVA - School of Business and Economics

How do current term structure model behave beyond the last liquid point?: A comparison of the DNS and Smith-Wilson methods

A Work Project, presented as part of the requirements for the Award of a Master’s Double Degree in Finance from Maastricht University and NOVA – School of Business and Economics

Term Structure Dynamics, Macro-Finance Factors and Model Uncertainty

This paper extends the Nelson-Siegel linear factor model by developing a flexible macro-finance framework for modeling and forecasting the term structure of US interest rates. Our approach is robust to parameter uncertainty and structural change, as we consider instabilities in parameters and volatilities, and our model averaging method allows for investors' model uncertainty over time. Our time-varying parameter Nelson-Siegel Dynamic Model Averaging (NS-DMA) predicts yields better than standard benchmarks and successfully captures plausible time-varying term premia in real time. The proposed model has significant in-sample and out-of-sample predictability for excess bond returns, and the predictability is of economic value.

On the term structure of Interbank interest rates: Jump-diffusion processes and option pricing

In this paper we study the dynamic behavior of the term structureof Interbank interest rates and the pricing of options on interest ratesensitive securities. We posit a generalized single factor model withjumps to take into account external influences in the market. Daily datais used to test for jump effects. Qualitative examination of the linkagebetween Monetary Authorities' interventions and jumps are studied. Pricingresults suggests a systematic underpricing in bonds and call options ifthe jumps component is not included. However, the pricing of put optionson bonds presents indeterminacies.

Stock returns, term structure, inflation and real activity: An international perspective

This paper analyses the empirical interdependences among assetreturns, real activity and inflation from a multicountry and internationalpoint of view. We find that nominal stock returns are significantly relatedto inflation only in the US, that the US term structure of interest ratespredicts both domestic and foreign inflation rates while foreign termstructures do not have this predictive power and that innovations in inflationand exchange rates induce insignificant responses of real and financialvariables. An interpretation of the dynamics and some policy implicationsof the results are provided.

Speculative dynamics in the term structure of interest rates

When long maturity bonds are traded frequently and traders have non-nestedinformation sets, speculative behavior in the sense of Harrison and Kreps (1978) arises.Using a term structure model displaying such speculative behavior, this paper proposesa conceptually and observationally distinct new mechanism generating time varying predictableexcess returns. It is demonstrated that (i) dispersion of expectations about futureshort rates is sufficient for individual traders to systematically predict excess returns and(ii) the new term structure dynamics driven by speculative trade is orthogonal to publicinformation in real time, but (iii) can nevertheless be quantified using only publicly availableyield data. The model is estimated using monthly data on US short to medium termTreasuries from 1964 to 2007 and it provides a good fit of the data. Speculative dynamicsare found to be quantitatively important, potentially accounting for a substantial fractionof the variation of bond yields and appears to be more important at long maturities.

Risk management under a two-factor model of the term structure of interest rates

This paper presents several applications to interest rate risk managementbased on a two-factor continuous-time model of the term structure of interestrates previously presented in Moreno (1996). This model assumes that defaultfree discount bond prices are determined by the time to maturity and twofactors, the long-term interest rate and the spread (difference between thelong-term rate and the short-term (instantaneous) riskless rate). Several newmeasures of ``generalized duration" are presented and applied in differentsituations in order to manage market risk and yield curve risk. By means ofthese measures, we are able to compute the hedging ratios that allows us toimmunize a bond portfolio by means of options on bonds. Focusing on thehedging problem, it is shown that these new measures allow us to immunize abond portfolio against changes (parallel and/or in the slope) in the yieldcurve. Finally, a proposal of solution of the limitations of conventionalduration by means of these new measures is presented and illustratednumerically.

A two-mean reverting-factor model of the term structure of interest rates

This paper presents a two--factor model of the term structure ofinterest rates. We assume that default free discount bond prices aredetermined by the time to maturity and two factors, the long--term interestrate and the spread (difference between the long--term rate and theshort--term (instantaneous) riskless rate). Assuming that both factorsfollow a joint Ornstein--Uhlenbeck process, a general bond pricing equationis derived. We obtain a closed--form expression for bond prices andexamine its implications for the term structure of interest rates. We alsoderive a closed--form solution for interest rate derivatives prices. Thisexpression is applied to price European options on discount bonds andmore complex types of options. Finally, empirical evidence of the model'sperformance is presented.

Term structure of interest rates. European financial integration

In this paper we estimate, analyze and compare the term structures of interest rates in six different countries over the period 1992-2004. We apply the Nelson-Siegel model to obtain the term structures of interest rates at weekly intervals. A total of 4,038 curves are estimated and analyzed. Four European Monetary Union countries¿Spain, France, Germany and Italy¿are included. The UK is also included as a European non-member of the Monetary Union. Finally the US completes the analysis. The goal is to determine the differences in the shapes of the term structure of interest rates among these countries. Likewise, we can determine the most usual term structure shapes that appear for each country.*****