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.

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.

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.

On the sources of business cycles in the G-7

This paper examines sources of cyclical movements in output, inflation and the term structure of interest rates. It employs a novel identification approach which uses the sign of the cross correlation function in response to shocks to catalog orthogonal disturbances. We find that demand shocks are the dominant source output, inflation and term structure fluctuations in six of the G-7 countries. Within the class of demand disturbances, nominal shocks are dominant, but their importance declined after 1982. Furthermore, there are no significant differences in the proportion of term structure variability explained by different structural sources at different horizons.

On the relevance of modeling volatility for pricing purposes

This paper presents a two-factor (Vasicek-CIR) model of the term structure of interest rates and develops its pricing and empirical properties. We assume that default free discount bond prices are determined by the time to maturity and two factors, the long-term interest rate and the spread. Assuming a certain process for both factors, a general bond pricing equation is derived and a closed-form expression for bond prices is obtained. Empirical evidence of the model's performance in comparisson with a double Vasicek model is presented. The main conclusion is that the modeling of the volatility in the long-term rate process can help (in a large amount) to fit the observed data can improve - in a reasonable quantity - the prediction of the future movements in the medium- and long-term interest rates. However, for shorter maturities, it is shown that the pricing errors are, basically, negligible and it is not so clear which is the best model to be used.

Forecasting the Yield Curve of Government Bonds: A Comparative Study

For the past 20 years, researchers have applied the Kalman filter to the modeling and forecasting the term structure of interest rates. Despite its impressive performance in in-sample fitting yield curves, little research has focused on the out-of-sample forecast of yield curves using the Kalman filter. The goal of this thesis is to develop a unified dynamic model based on Diebold and Li (2006) and Nelson and Siegel’s (1987) three-factor model, and estimate this dynamic model using the Kalman filter. We compare both in-sample and out-of-sample performance of our dynamic methods with various other models in the literature. We find that our dynamic model dominates existing models in medium- and long-horizon yield curve predictions. However, the dynamic model should be used with caution when forecasting short maturity yields

International evidence on the predictability of returns to securitized real estate assets: econometric models versus neural networks

The performance of various statistical models and commonly used financial indicators for forecasting securitised real estate returns are examined for five European countries: the UK, Belgium, the Netherlands, France and Italy. Within a VAR framework, it is demonstrated that the gilt-equity yield ratio is in most cases a better predictor of securitized returns than the term structure or the dividend yield. In particular, investors should consider in their real estate return models the predictability of the gilt-equity yield ratio in Belgium, the Netherlands and France, and the term structure of interest rates in France. Predictions obtained from the VAR and univariate time-series models are compared with the predictions of an artificial neural network model. It is found that, whilst no single model is universally superior across all series, accuracy measures and horizons considered, the neural network model is generally able to offer the most accurate predictions for 1-month horizons. For quarterly and half-yearly forecasts, the random walk with a drift is the most successful for the UK, Belgian and Dutch returns and the neural network for French and Italian returns. Although this study underscores market context and forecast horizon as parameters relevant to the choice of the forecast model, it strongly indicates that analysts should exploit the potential of neural networks and assess more fully their forecast performance against more traditional models.

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.

Business cycles in emerging economies : the role of interest rates

This paper documents the empirical relation between the interest rates that emerging economies face in international capital markets and their business cycles. It shows that the patterns observed in the data can be interpreted as the equilibrium of a dynamic general equilibrium model of a small open economy, in which (i) firms have to pay for a fraction of the input bill before production takes place, and (ii) preferences generate a labor supply that is independent of the interest rate. In our sample, interest rates are strongly countercyclical, strongly positively correlated with net exports, and they lead the cycle. Output is very volatile and consumption is more volatile than output. The sample includes data for Argentina during 1983-2000 and for four other large emerging economies, Brazil, Mexico, Korea, and Philippines, during 1994-2000. The model is calibrated to Argentina’s economy for the period 1983-1999. When the model is fed with actual US interest rates and the actual default spreads of Argentine sovereign interest rates, interest rates alone can explain forty percent of output fluctuations. When simulated technology shocks are added to the model, it can account for the main empirical regularities of Argentina’s economy during the period. A 1% increase in country risk causes a contemporaneous fall in output of 0.5 ’subsequent recovery. An increase in US rates causes output to fall by the same on impact and by almost 2% two years after the shock. The asymetry in the effect of shocks to US rates and country risk is due to the fact that US interest rates are more persistent than country risk and that there is a significant spillover effect from US interest rates to country risk.

Implied Hazard Rates Analysis Through Brazilian Corporate Debt

No Brasil, o mercado de crédito corporativo ainda é sub-aproveitado. A maioria dos participantes não exploram e não operam no mercado secundário, especialmente no caso de debêntures. Apesar disso, há inúmeras ferramentas que poderiam ajudar os participantes do mercado a analisar o risco de crédito e encorajá-los a operar esses riscos no mercado secundário. Essa dissertação introduz um modelo livre de arbitragem que extrai a Perda Esperada Neutra ao Risco Implícita nos preços de mercado. É uma forma reduzida do modelo proposto por Duffie and Singleton (1999) e modela a estrutura a termo das taxas de juros através de uma Função Constante por Partes. Através do modelo, foi possível analisar a Curva de Perda Esperada Neutra ao Risco Implícita através dos diferentes instrumentos de emissores corporativos brasileiros, utilizando Títulos de Dívida, Swaps de Crédito e Debêntures. Foi possível comparar as diferentes curvas e decidir, em cada caso analisado, qual a melhor alternativa para se tomar o risco de crédito da empresa, via Títulos de Dívida, Debêntures ou Swaps de Crédito.

Financial market reaction to central bank monetary policy communications under an inflation- targeting regime: the case of Brazil

Includes bibliography

A two-factor model of the U.K. yield curve

I model the forward premium in the U.K. gilt-edged market over the period 1982–96 using a two-factor general equilibrium model of the term structure of interest rates. The model permits the decomposition of the forward premium into separate components representing interest rate expectations, the risk premia associated with each of the underlying factors, and terms capturing the direct impact of the variances of the factors on the shape of the forward curve.