Une méthode d'inférence bayésienne pour les modèles espace-état affines faiblement identifiés appliquée à une stratégie d'arbitrage statistique de la dynamique de la structure à terme des taux d'intérêt

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Affine processes, arbitrage-Free Term structures of legendre polynomials,and option pricing

Multivariate Affine term structure models have been increasingly used for pricing derivatives in fixed income markets. In these models, uncertainty of the term structure is driven by a state vector, while the short rate is an affine function of this vector. The model is characterized by a specific form for the stochastic differential equation (SDE) for the evolution of the state vector. This SDE presents restrictions on its drift term which rule out arbitrages in the market. In this paper we solve the following inverse problem: Suppose the term structure of interest rates is modeled by a linear combination of Legendre polynomials with random coefficients. Is there any SDE for these coefficients which rules out arbitrages? This problem is of particular empirical interest because the Legendre model is an example of factor model with clear interpretation for each factor, in which regards movements of the term structure. Moreover, the Affine structure of the Legendre model implies knowledge of its conditional characteristic function. From the econometric perspective, we propose arbitrage-free Legendre models to describe the evolution of the term structure. From the pricing perspective, we follow Duffie et al. (2000) in exploring Legendre conditional characteristic functions to obtain a computational tractable method to price fixed income derivatives. Closing the article, the empirical section presents precise evidence on the reward of implementing arbitrage-free parametric term structure models: The ability of obtaining a good approximation for the state vector by simply using cross sectional data.

Is the supply of long-term debt independent of the term premia? Evidence from Portugal

An important assumption in the statistical analysis of the financial market effects of the central bank’s large scale asset purchase program is that the "long-term debt stock variables were exogenous to term premia". We test this assumption for a small open economy in a currency union over the period 2000M3 to 2015M10, via the determinants of short- term financing relative to long-term financing. Empirical estimations indicate that the maturity composition of debt does not respond to the level of interest rate or to the term structure. These findings suggest a lower adherence to the cost minimization mandate of debt management. However, we find that volatility and relative market size respectively decrease and increase short-term financing relative to long-term financing, while it decreases with an increase in government indebtedness.

Some bounds of loss in classical semideterministic immunization

Since Samuelson, Redington and Fisher and Weil, duration and immunization are very important topics in bond portfolio analysis from both a theoretical and a practical point of view. Many results have been established, especially in semi-deterministic framework. As regards, however, the loss may be sustained, we do not think that the subject has been investigated enough, except for the results found in the wake of the theorem of Fong and Vasicek. In this paper we present some results relating to the limitation of the loss in the case of local immunization for multiple liabilities.

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.

Aplicação de um software de cálculo automático na verificação aos estados limites de utilização em estruturas de Betão Armado

Actualmente e cada vez mais, são concebidos e utilizados programas de cálculo automático de Engenharia na realização de projectos de edifícios, que proporcionam aos engenheiros uma possibilidade avançada e rápida de execução, simulação e análise de edifícios para estruturas complexas e de elevada dimensão. Contudo, será necessário que os resultados deverão ser fiáveis de modo a não existirem consequências no comportamento real da estrutura a longo prazo. O presente relatório de estágio, refere-se à verificação aos estados limites de utilização (tensões, fendilhação e deformação) segundo o Eurocódigo 2, de uma estrutura porticada em betão armado, nomeadamente de um pórtico central pertencente a essa mesma estrutura recorrendo ao programa de cálculo automático da Autodesk o Robot Structural Analysis Professional 2014. O objectivo principal do presente trabalho consiste na comparação de resultados referente aos estados limites últimos e de utilização, pelos diferentes módulos de dimensionamento Required e Provided Reinforcement presentes no programa Robot. É destacado no final do relatório, considerando uma disposição de armadura optada analiticamente para o pórtico, uma análise comparativa de resultados referente aos estados limites de utilização entre o comando Typical Reinforcement do módulo Provided Reinforcement e por expressões analíticas. Refere-se contudo que, o procedimento do método analítico teve como base de cálculo uma aplicação desenvolvida para a verificação de elementos de betão armado aos estados limites de utilização segundo o Eurocódigo 2, com o nome de XD-Conserv tendo sido também comparado os resultados finais do mesmo.

Principal component analysis of the yield curve

A Work Project, presented as part of the requirements for the Award of a Masters Degree in Finance from the NOVA – School of Business and Economics

Fitting the yield curve

A Work Project, presented as part of the requirements for the Award of a Masters Degree in Finance from the NOVA – School of Business and Economics

Machine learning Gaussian short rate

Dissertação para obtenção do Grau de Doutor em Estatística e Gestão do Risco

Trading the differences in expectations between the CDS and bond markets

This paper uses the framework developed by Vrugt (2010) to extract the recovery rate and term-structure of risk-neutral default probabilities implied in the cross-section of Portuguese sovereign bonds outstanding between March and August 2011. During this period the expectations on the recovery rate remain firmly anchored around 50 percent while the instantaneous default probability increases steadily from 6 to above 30 percent. These parameters are then used to calculate the fair-value of a 5-year and 10- year CDS contract. A credit-risk-neutral strategy is developed from the difference between the market price of a CDS of the same tenors and the fair-value calculated, yielding a sharpe ratio of 3.2

Dynamic Option Adjusted Spread and the Value of Mortgage Backed Securities (Draft 1)

We extend a reduced form model for pricing pass-through mortgage backed securities (MBS) and provide a novel hedging tool for investors in this market. To calculate the price of an MBS, traders use what is known as option-adjusted spread (OAS). The resulting OAS value represents the required basis points adjustment to reference curve discounting rates needed to match an observed market price. The OAS suffers from some drawbacks. For example, it remains constant until the maturity of the bond (thirty years in mortgage-backed securities), and does not incorporate interest rate volatility. We suggest instead what we call dynamic option adjusted spread (DOAS). The latter allows investors in the mortgage market to account for both prepayment risk and changes of the yield curve.

Dynamic Option Adjusted Spread and the Value of Mortgage Backed Securities (Draft 2)

We extend a reduced form model for pricing pass-through mortgage backed securities (MBS) and provide a novel hedging tool for investors in this market. To calculate the price of an MBS, traders use what is known as option-adjusted spread (OAS). The resulting OAS value represents the required basis points adjustment to reference curve discounting rates needed to match an observed market price. The OAS suffers from some drawbacks. For example, it remains constant until the maturity of the bond (thirty years in mortgage-backed securities), and does not incorporate interest rate volatility. We suggest instead what we call dynamic option adjusted spread (DOAS), which allows investors in the mortgage market to account for both prepayment risk and changes of the yield curve.

Co-Movement, Spillovers and Excess Returns in Global Bond Markets

This paper investigates global term structure dynamics using a Bayesian hierarchical factor model augmented with macroeconomic fundamentals. More than half of the variation in bond yields of seven advanced economies is due to global co-movement, which is mainly attributed to shocks to non-fundamentals. Global fundamentals, especially global inflation, affect yields through a ‘policy channel’ and a ‘risk compensation channel’, but the effects through two channels are offset. This evidence explains the unsatisfactory performance of fundamentals-driven term structure models. Our approach delineates asymmetric spillovers in global bond markets connected to diverging monetary policies. The proposed model is robust as identified factors has significant explanatory power of excess returns. The finding that global inflation uncertainty is useful in explaining realized excess returns does not rule out regime changing as a source of non-fundamental fluctuations.

Monetary policy with signal extraction from the bond market

Monetary policy is conducted in an environment of uncertainty. This paper sets upa model where the central bank uses real-time data from the bond market togetherwith standard macroeconomic indicators to estimate the current state of theeconomy more efficiently, while taking into account that its own actions influencewhat it observes. The timeliness of bond market data allows for quicker responsesof monetary policy to disturbances compared to the case when the central bankhas to rely solely on collected aggregate data. The information content of theterm structure creates a link between the bond market and the macroeconomythat is novel to the literature. To quantify the importance of the bond market asa source of information, the model is estimated on data for the United Statesand Australia using Bayesian methods. The empirical exercise suggests that thereis some information in the US term structure that helps the Federal Reserve toidentify shocks to the economy on a timely basis. Australian bond prices seemto be less informative than their US counterparts, perhaps because Australia is arelatively small and open economy.

Speculation, risk premia and expectations in the yield curve

An affine asset pricing model in which traders have rational but heterogeneous expectations aboutfuture asset prices is developed. We use the framework to analyze the term structure of interestrates and to perform a novel three-way decomposition of bond yields into (i) average expectationsabout short rates (ii) common risk premia and (iii) a speculative component due to heterogeneousexpectations about the resale value of a bond. The speculative term is orthogonal to public informationin real time and therefore statistically distinct from common risk premia. Empirically wefind that the speculative component is quantitatively important accounting for up to a percentagepoint of yields, even in the low yield environment of the last decade. Furthermore, allowing for aspeculative component in bond yields results in estimates of historical risk premia that are morevolatile than suggested by standard Affine Gaussian term structure models which our frameworknests.