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 role of no-arbitrage on forecasting: lessons from a parametric term structure model

Parametric term structure models have been successfully applied to innumerous problems in fixed income markets, including pricing, hedging, managing risk, as well as studying monetary policy implications. On their turn, dynamic term structure models, equipped with stronger economic structure, have been mainly adopted to price derivatives and explain empirical stylized facts. In this paper, we combine flavors of those two classes of models to test if no-arbitrage affects forecasting. We construct cross section (allowing arbitrages) and arbitrage-free versions of a parametric polynomial model to analyze how well they predict out-of-sample interest rates. Based on U.S. Treasury yield data, we find that no-arbitrage restrictions significantly improve forecasts. Arbitrage-free versions achieve overall smaller biases and Root Mean Square Errors for most maturities and forecasting horizons. Furthermore, a decomposition of forecasts into forward-rates and holding return premia indicates that the superior performance of no-arbitrage versions is due to a better identification of bond risk premium.

A model to estimate the US term structure of interest rates

The US term structure of interest rates plays a central role in fixed-income analysis. For example, estimating accurately the US term structure is a crucial step for those interested in analyzing Brazilian Brady bonds such as IDUs, DCBs, FLIRBs, EIs, etc. In this work we present a statistical model to estimate the US term structure of interest rates. We address in this report all major issues which drove us in the process of implementing the model developed, concentrating on important practical issues such as computational efficiency, robustness of the final implementation, the statistical properties of the final model, etc. Numerical examples are provided in order to illustrate the use of the model on a daily basis.

Essays on the monetary aspects of the term structure of nominal interest rates

Interest rates are key economic variables to much of finance and macroeconomics, and an enormous amount of work is found in both fields about the topic. Curiously, in spite of their common interest, finance and macro research on the topic have seldom interacted, using different approaches to address its main issues with almost no intersection. Concerned with interest rate contingent claims, finance term structure models relate interest rates to lagged interest rates; concerned with economic relations and macro dynamics, macro models regress a few interest rates on a wide variety of economic variables. If models are true though simplified descriptions of reality, the relevant factors should be captured by both the set of bond yields and that of economic variables. Each approach should be able to address the other field concerns with equal emciency, since the economic variables are revealed by the bond yields and these by the economic variables.

Term structure dynamics and no-arbitrage under the Taylor rule

A determinação da taxa de juros estrutura a termo é um dos temas principais da gestão de ativos financeiros. Considerando a grande importância dos ativos financeiros para a condução das políticas econômicas, é fundamental para compreender a estrutura que é determinado. O principal objetivo deste estudo é estimar a estrutura a termo das taxas de juros brasileiras, juntamente com taxa de juros de curto prazo. A estrutura a termo será modelado com base em um modelo com uma estrutura afim. A estimativa foi feita considerando a inclusão de três fatores latentes e duas variáveis ​​macroeconômicas, através da técnica Bayesiana da Cadeia de Monte Carlo Markov (MCMC).

Essays in macroeconomy and dynamic term-structure models

This thesis is composed of three articles with the subjects of macroeconomics and - nance. Each article corresponds to a chapter and is done in paper format. In the rst article, which was done with Axel Simonsen, we model and estimate a small open economy for the Canadian economy in a two country General Equilibrium (DSGE) framework. We show that it is important to account for the correlation between Domestic and Foreign shocks and for the Incomplete Pass-Through. In the second chapter-paper, which was done with Hedibert Freitas Lopes, we estimate a Regime-switching Macro-Finance model for the term-structure of interest rates to study the US post-World War II (WWII) joint behavior of macro-variables and the yield-curve. We show that our model tracks well the US NBER cycles, the addition of changes of regime are important to explain the Expectation Theory of the term structure, and macro-variables have increasing importance in recessions to explain the variability of the yield curve. We also present a novel sequential Monte-Carlo algorithm to learn about the parameters and the latent states of the Economy. In the third chapter, I present a Gaussian A ne Term Structure Model (ATSM) with latent jumps in order to address two questions: (1) what are the implications of incorporating jumps in an ATSM for Asian option pricing, in the particular case of the Brazilian DI Index (IDI) option, and (2) how jumps and options a ect the bond risk-premia dynamics. I show that jump risk-premia is negative in a scenario of decreasing interest rates (my sample period) and is important to explain the level of yields, and that gaussian models without jumps and with constant intensity jumps are good to price Asian options.

Economic cycles and term structure: application to Brazil

The objective of this work is to describe the behavior of the economic cycle in Brazil through Markov processes which can jointly model the slope factor of the yield curve, obtained by the estimation of the Nelson-Siegel Dynamic Model by the Kalman filter and a proxy variable for economic performance, providing some forecasting measure for economic cycles

Stochastic growth and monetary policy: the impacts on the term structure of interest rates

This paper builds a simple, empirically-verifiable rational expectations model for term structure of nominal interest rates analysis. It solves an stochastic growth model with investment costs and sticky inflation, susceptible to the intervention of the monetary authority following a policy rule. The model predicts several patterns of the term structure which are in accordance to observed empirical facts: (i) pro-cyclical pattern of the level of nominal interest rates; (ii) countercyclical pattern of the term spread; (iii) pro-cyclical pattern of the curvature of the yield curve; (iv) lower predictability of the slope of the middle of the term structure; and (v) negative correlation of changes in real rates and expected inflation at short horizons.

Evaluating the existence of structural change in the brazilian term structure of interest: evidence based on cointegration models with structural break

This paper investigates whether there is evidence of structural change in the Brazilian term structure of interest rates. Multivariate cointegration techniques are used to verify this evidence. Two econometrics models are estimated. The rst one is a Vector Autoregressive Model with Error Correction Mechanism (VECM) with smooth transition in the deterministic coe¢ cients (Ripatti and Saikkonen [25]). The second one is a VECM with abrupt structural change formulated by Hansen [13]. Two datasets were analysed. The rst one contains a nominal interest rate with maturity up to three years. The second data set focuses on maturity up to one year. The rst data set focuses on a sample period from 1995 to 2010 and the second from 1998 to 2010. The frequency is monthly. The estimated models suggest the existence of structural change in the Brazilian term structure. It was possible to document the existence of multiple regimes using both techniques for both databases. The risk premium for di¤erent spreads varied considerably during the earliest period of both samples and seemed to converge to stable and lower values at the end of the sample period. Long-term risk premiums seemed to converge to inter-national standards, although the Brazilian term structure is still subject to liquidity problems for longer maturities.

A comparison of test of non-linear cointegration with an application to the predictability of US interest rates using the term structure

We evaluate the forecasting performance of a number of systems models of US shortand long-term interest rates. Non-linearities, induding asymmetries in the adjustment to equilibrium, are shown to result in more accurate short horizon forecasts. We find that both long and short rates respond to disequilibria in the spread in certain circumstances, which would not be evident from linear representations or from single-equation analyses of the short-term interest rate.

Precificação de derivativos de taxa de juros utilizando o modelo HJM multifatorial com estrutura de volatilidade não paramétrica

Com o objetivo de precificar derivativos de taxas de juros no mercado brasileiro, este trabalho foca na implementação do modelo de Heath, Jarrow e Morton (1992) em sua forma discreta e multifatorial através de uma abordagem numérica, e, que possibilita uma grande flexibilidade na estimativa da taxa forward sob uma estrutura de volatilidade baseada em fatores ortogonais, facilitando assim a simulação de sua evolução por Monte Carlo, como conseqüência da independência destes fatores. A estrutura de volatilidade foi construída de maneira a ser totalmente não paramétrica baseada em vértices sintéticos que foram obtidos por interpolação dos dados históricos de cotações do DI Futuro negociado na BM&FBOVESPA, sendo o período analisado entre 02/01/2003 a 28/12/2012. Para possibilitar esta abordagem foi introduzida uma modificação no modelo HJM desenvolvida por Brace e Musiela (1994).

Ensaios sobre inflação e política monetária

Esta tese tem por objetivo principal o estudo da relação entre atividade econômica, inflação e política monetária no tocante a três aspectos importantes. O primeiro, a perspectiva histórica da evolução da relação entre atividade e inflação no pensamento econômico. O segundo, a análise da dinâmica inflacionária utilizando um modelo com fundamentação microeconômica, no caso a curva de Phillips Novo-Keynesiana, com uma aplicação ao caso brasileiro. O terceiro, a avaliação da eficiência dos mecanismos de sinalização de política monetária utilizados pelo Banco Central no Brasil com base nos movimentos na estrutura a termo da taxa de juros com a mudança da meta da Selic. O elemento central que une estes ensaios é a necessidade do formulador de política econômica compreender o impacto significativo das ações de política monetária na definição do curso de curto prazo da economia real para atingir seus objetivos de aliar crescimento econômico com estabilidade de preços. Os resultados destes ensaios indicam que o modelo Novo-Keynesiano, resultado de um longo desenvolvimento na análise econômica, constitui-se numa ferramenta valiosa para estudar a relação entre atividade e inflação. Uma variante deste modelo foi empregada para estudar com relativo sucesso a dinâmica inflacionária no Brasil, obtendo valores para rigidez da economia próximos ao comportamento observado em pesquisas de campo. Finalmente, foi aliviada a previsibilidade das ações do Banco Central para avaliar o estágio atual de desenvolvimento do sistema de metas no Brasil, através da reação da estrutura a termo de juros às mudanças na meta da taxa básica (Selic). Os resultados indicam que comparando o período de 2003 a 2008 com 2000 a 2003, verificamos que os resultados apontam para o aumento da previsibilidade das decisões do Banco Central. Este fato pode ser explicado por alguns fatores: o aprendizado do público sobre o comportamento do Banco Central; a menor volatilidade econômica no cenário econômico e o aperfeiçoamento dos mecanismos de sinalização e da própria operação do sistema de metas. Comparando-se o efeito surpresa no Brasil com aqueles obtidos por países que promoveram mudanças significativas para aumentar a transparência da política monetária no período de 1990 a 1997, observa-se que o efeito surpresa no Brasil nas taxas de curto prazo reduziu-se significativamente. No período de 2000 a 2003, o efeito surpresa era superior aos de EUA, Alemanha e Reino Unido e era da mesma ordem de grandeza da Itália. No período de 2003 a 2008, o efeito surpresa no Brasil está próximo dos valores dos EUA e Alemanha e inferiores aos da Itália e Reino Unido.

Pricing the option adjust spread of Brazilian Eurobonds

This paper presents results of a pricing system to compute the option adjusted spread ("DAS") of Eurobonds issued by Brazilian firms. The system computes the "DAS" over US treasury rates taktng imo account the embedded options present on these bonds. These options can be calls ("callable bond"), puts ("putable bond") or combinations ("callable and putable bond"). The pricing model takes into account the evolution of the term structure along time, is compatible with the observable market term structure and is able to compute risk measures such as duration and convexity, and pricing and hedging of options on these bonds. Examples show the ejJects of the embedded options on the spread and risk measures as well as the ejJects on the spread due to variations on the volatility parameters ofthe short rate.