In this dissertation, we consider the Hull-White term structure problem with the boundary value condition given as the payoff of a European bond option. We restrict ourselves to the case where the parameters of the Hull-White model are strictly positive constants and from the risk neutral valuation formula, we first derive simple closed–form expression for pricing European bond option in the Hull-White extended Vasicek model framework. As the European option can be exercised only on the maturity date, we then examine the case of early exercise opportunity commonly called American option. With the analytic representation of American bond option being very hard to handle, we are forced to resort to numerical experiments. To do it excellently, we transform the Hull-White term structure equation into the diffusion equation and we first solve it through implicit, explicit and Crank-Nicolson (CN) difference methods. As these standard finite difference methods (FDMs) require truncation of the domain from infinite to finite one, which may deteriorate the computational efficiency for American bond option, we try to build a CN method over an unbounded domain. We introduce an exact artificial boundary condition in the pricing boundary value problem to reduce the original to an initial boundary problem. Then, the CN method is used to solve the reduced problem. We compare our performance with standard FDMs and the results through illustration show that our method is more efficient and accurate than standard FDMs when we price American bond option. / Mathematical Sciences / (M.Sc. (Mathematics))

Thèse numérisée par la Division de la gestion de documents et des archives de l'Université de Montréal.

La spécificité de la tradition monétaire de Henry Thornton, Ralph George Hawtrey, John Maynard Keynes et John Richard Hicks, est de considérer le taux d'intérêt comme une variable influencée par la banque centrale. Ces auteurs peuvent être rattachés à une même tradition monétaire, différente de celle de Knut Wicksell, où le taux d'intérêt est déterminé par une variable réelle: le taux de profit. Dans la tradition de Thornton, le prêt et l'emprunt renvoient une vente et un achat de titres de dette. Ces derniers prennent une forme différente selon la période étudiée. Au dix-neuvième siècle, Thornton proposait que la Banque d'Angleterre contrôle, par des variations de son taux d'escompte, le prix de la liquidité de court-terme, étant la substituabilité des traites commerciales en monnaie. Un siècle plus tard, cette influence était effective. Cependant, au XXe siècle, avec le développement des marchés financiers, d'autre canaux de transmissions de la politique monétaire sont apparus. Bien que négligée par 1 littérature, une des controverses les plus représentatives de cette époque est celle d'Hawtre Keynes et Hicks. Ils conviennent que le taux court est un phénomène monétaire. En revanche, ils ne s'accordent pas sur la nature du taux long. Les débats portent sur la théorie pionnière d Keynes de la structure par terme des taux d'intérêt, les effets d'annonces, ainsi que les limite de l'arbitrage. / The specificity of the monetary tradition of Henry Thornton, Ralph George Hawtrey, John Maynard Keynes and John Richard Hicks is to consider the interest rate as mainly determined by the monetary policy. Those authors are part of the same monetary tradition, different that Knut Wicksell for whom the interest rate is a real variable: the rate of profit. The process of borrowing and lending, in the monetary tradition analyzed in my PhD thesis, corresponds to a sale and a purchase of debts. Debts take a different form according to the period studied. ln the nineteenth century, Thornton wrote that the Bank of England should be able to manage, by varying its discount rate, the price of short-term liquidity, which is the substitution of bills againt money. ln the twentieth century, other transmission channels of monetary policy appeared wit the evolution of financial markets. Although neglected by the literature, one of the most representative controversy at that time was between Hawtrey, Keynes and Hicks. All made a theory in which the short-term rate is a monetary phenomenon. They however disagreed on the nature of the long-term rate. The debate is on Keynes's pioneering theory of the term structur of interest rates, the announcement effects, and the limits to arbitrage.

Made available in DSpace on 2016-04-26T20:48:48Z (GMT). No. of bitstreams: 1 Jorge C Siqueira.pdf: 785030 bytes, checksum: 11ecce584ab79026b6028037746e40c4 (MD5) Previous issue date: 2007-05-16 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / ABSTRAT The purpose of this study is to present and discuss the main impacts the indexation profile and the term-structure of the public debt may inflict on the debt´s trajectory. The main result of the study suggests that there may exist a vicious circle stemming from the relationship between the rise of the short-term interest rate of the Brazilian economy and the growing-path behavior of its public debt. It is stated that this movement may be a consequence of the uniqueness of the structure of Brazilian public debt, which is largely composed by short-term securities pegged to the short-term interest rate of the economy (Selic). In order to demonstrate this statement, the approach taken up rests on two models of public debt administration and on the analysis of these models in reference to the behavior of the level and the profile of indexation and term-structure of the public debt between 1995 and 2005. Therefore, our effort seeks to present the workings of this supposed vicious circle and its impacts on the behavior of the Brazilian public debt. In addition, in order to estimate exercises which may, at some length, corroborate the main idea proposed by this study, we make use of some econometric tools, such as Vector auto-regressions models and Vector Erros Corretions / O objetivo desse trabalho é apresentar e discutir os principais impactos que o perfil de indexação e prazo da dívida pública brasileira podem exercer sobre a trajetória da dívida. O principal resultado desse trabalho sugere a existência de um círculo vicioso entre elevações na taxa de juros de curto prazo da economia brasileira e a evolução crescente da dívida pública. Sugere-se que esse movimento possa ser conseqüência da peculiaridade da dívida pública brasileira, que se traduz numa dívida representada em grande parte por títulos de curto prazo e indexados a taxa de juros de curto prazo da economia (Selic). Para isso, utiliza-se uma abordagem que envolve a apresentação de dois modelos de administração de dívida pública e a análise desses modelos em conjunto com a evolução do nível e do perfil de indexação e prazo da dívida pública brasileira durante o período de 1995 - 2005. Dessa maneira, tenta-se apresentar o funcionamento desse suposto círculo vicioso e seus impactos para a evolução da dívida pública brasileira. Ainda utiliza-se o instrumental econométrico dos modelos Vetores auto-regressivos (VAR) e Vetores de Correção de Erros (VEC) para se estimarem exercícios que de certa forma corroboram a principal idéia sugerida nesse trabalho

本篇論文擴充Ang et al. (2007)之基本架構,分別建構台灣各式月資料與季資料的物價指數預測模型,並進行預測以及實證分析。我們用以衡量通貨膨脹率的指標為 CPI 年增率與核心CPI 年增率。我們比較貨幣模型、成本加成模型、6 種不同設定的菲力浦曲線模型、3 種期限結構模型、隨機漫步模型、 AO 模型、ARIMA 模型、VAR 模型、主計處(DGBAS)、中經院(CIER) 及台經院(TIER) 之預測。藉由此研究,我們可以完整評估出文獻上常用之各式月資料及季資料預測模型的優劣。 我們實證結果顯示,在月資料預測模型樣本外預測績效表現方面, ARIMA 模 型對 2 種通貨膨脹率指標的樣本外預測能力表現最好。至於季資料預測模型樣本外預測績效表現, ARIMA 模型對未來核心 CPI 年增率的樣本外預測能力表現最好; 然而,對於 CPI 年增率為預測目標的預測模型則不存在最佳的模型。此外,實證分析中我們也發現本研究所建構的模型預測表現仍遜於主計處的預測,但部份模型的樣本外預測能力表現則比中經院與台經院的預測為佳。 / This paper compares the forecasting performance of inflation in Taiwan. We conduct various inflation forecasting methods (models) for two inflation measures(CPI growth rate and core-CPI growth rate) by using monthly and quarterly data. Besides the models of Ang et al. (2007), we also consider some macroeconomic models for comparison. We compare some Monetary models, Mark-up models, six variants of Phillips curve models, three variants of term structure models, a Random walk model, an AO model, an ARIMA model, and a VAR model. We also compare the forecast ability of these model with three different survey forecasts (the DGBAS, CIER, and TIER surveys). We summarized our findings as follows. The best monthly forecasting model for both inflation measures is ARIMA model. For quarterly core-CPI inflation, ARIMA model is also the best model; however, when comparing the quarterly forecasts for CPI inflation, there does not exist the best one. Besides, we also found that the DGBAS survey outperforms all of our forecasting methods/models, but some of our forecasting models are better than the CIER and TIER surveys in terms of MAE.

Thèse numérisée par la Division de la gestion de documents et des archives de l'Université de Montréal

Insurance contracts will be reported at fair values on insurers’ balance sheets from 2010. In this thesis, we will review the conceptual and theoretical backbone of the insurance fair valuation project while providing a summary of the key features of the fair valuation project. Then, we will conduct a case study aimed at finding, under the fair valuation regime, the best asset allocation strategy for a particular business unit that carries a hypothetical annuity portfolio using a single modelling framework for valuation, risk calculation and business appraisal.

Submitted by Daniela Kubudi Glasman (dkubudi@gmail.com) on 2014-06-23T17:18:45Z No. of bitstreams: 1 tese_DanielaKubudi_final.pdf: 1329488 bytes, checksum: 78a5e9b2527544313ec47b6425dbeb07 (MD5) / Approved for entry into archive by BRUNA BARROS (bruna.barros@fgv.br) on 2014-10-27T16:31:57Z (GMT) No. of bitstreams: 1 tese_DanielaKubudi_final.pdf: 1329488 bytes, checksum: 78a5e9b2527544313ec47b6425dbeb07 (MD5) / Approved for entry into archive by Marcia Bacha (marcia.bacha@fgv.br) on 2014-11-13T13:38:37Z (GMT) No. of bitstreams: 1 tese_DanielaKubudi_final.pdf: 1329488 bytes, checksum: 78a5e9b2527544313ec47b6425dbeb07 (MD5) / Made available in DSpace on 2014-11-13T13:39:30Z (GMT). No. of bitstreams: 1 tese_DanielaKubudi_final.pdf: 1329488 bytes, checksum: 78a5e9b2527544313ec47b6425dbeb07 (MD5) Previous issue date: 2013-02-25 / This thesis consists of three works that analyses the term structure of interest rates using different datasets and models. Chapter 1 proposes a parametric interest rate model that allows for segmentation and local shocks in the term structure. Adopting U.S. Treasury data, two versions of this segmented model are implemented. Based on a sequence of 142 forecasting experiments, the proposed models are compared to established benchrnarks and find that they outperform in out-of-sample forecasting results, specially for short-term maturities and for the 12-month horizon forecast. Chapter 2 adds no-arbitrage restrictions when estimating a dynamic gaussian polynomial term structure model for the Brazilian interest rate market. This article propose an important approximation of the time series of term structure risk factors, that allows to extract the risk premium embedded in interest rate zero coupon instruments without having to run a fui! optimization of a dynamic model. This methodology has the advantage to be easily implemented and provides a good approximation for the term structure risk premia that can be used in many applications. Chapter 3 models the joint dynamic of nominal and real yields using an affine macro-finance no-arbitrage term structure model in order to decompose the break even inflation rates into inflation risk premiums and inflation expectations in the US market. The Yields-Only and the Macro version of this model are implemented and the estimated inflation risk premiums obtained are small and quite stable during the sample period, but have differences when comparing the two versions of the model. / Esta tese é composta de três artigos que analisam a estrutura a termo das taxas de juros usando diferentes bases de dados e modelos. O capítulo 1 propõe um modelo paramétrico de taxas de juros que permite a segmentação e choques locais na estrutura a termo. Adotando dados do tesouro americano, duas versões desse modelo segmentado são implementadas. Baseado em uma sequência de 142 experimentos de previsão, os modelos propostos são comparados à benchmarks e concluí-se que eles performam melhor nos resultados das previsões fora da amostra, especialmente para as maturidades curtas e para o horizonte de previsão de 12 meses. O capítulo 2 acrescenta restrições de não arbitragem ao estimar um modelo polinomial gaussiano dinâmico de estrutura a termo para o mercado de taxas de juros brasileiro. Esse artigo propõe uma importante aproximação para a série temporal dos fatores de risco da estrutura a termo, que permite a extração do prêmio de risco das taxas de juros sem a necessidade de otimização de um modelo dinâmico completo. Essa metodologia tem a vantagem de ser facilmente implementada e obtém uma boa aproximação para o prêmio de risco da estrutura a termo, que pode ser usada em diferentes aplicações. O capítulo 3 modela a dinâmica conjunta das taxas nominais e reais usando um modelo afim de não arbitagem com variáveis macroeconômicas para a estrutura a termo, afim de decompor a diferença entre as taxas nominais e reais em prêmio de risco de inflação e expectativa de inflação no mercado americano. Uma versão sem variáveis macroeconômicas e uma versão com essas variáveis são implementadas e os prêmios de risco de inflação obtidos são pequenos e estáveis no período analisado, porém possuem diferenças na comparação dos dois modelos analisados.

In this dissertation, we consider the Hull-White term structure problem with the boundary value condition given as the payoff of a European bond option. We restrict ourselves to the case where the parameters of the Hull-White model are strictly positive constants and from the risk neutral valuation formula, we first derive simple closed–form expression for pricing European bond option in the Hull-White extended Vasicek model framework. As the European option can be exercised only on the maturity date, we then examine the case of early exercise opportunity commonly called American option. With the analytic representation of American bond option being very hard to handle, we are forced to resort to numerical experiments. To do it excellently, we transform the Hull-White term structure equation into the diffusion equation and we first solve it through implicit, explicit and Crank-Nicolson (CN) difference methods. As these standard finite difference methods (FDMs) require truncation of the domain from infinite to finite one, which may deteriorate the computational efficiency for American bond option, we try to build a CN method over an unbounded domain. We introduce an exact artificial boundary condition in the pricing boundary value problem to reduce the original to an initial boundary problem. Then, the CN method is used to solve the reduced problem. We compare our performance with standard FDMs and the results through illustration show that our method is more efficient and accurate than standard FDMs when we price American bond option. / Mathematical Sciences / (M.Sc. (Mathematics))

Cette thèse est organisée en trois chapitres. Dans le premier chapitre, qui est co-écrit avec Ilze Kalnina, nous proposons un test statistique pour évaluer l’adéquation de la volatilité idiosyncratique comme mesure du risque idioyncratique. Nous proposons un test statistique qui est basé sur l’idée qu’un bon proxy du risque idiosyncratique devrait être non correélé à travers les actifs financiers. Nous démontrons que l’estimation de la volatililité est sujet à des erreurs qui rendent le test non standard. Nous proposons un modèle à facteurs qui permet de réduire sinon éliminer les corrélations dans la volatilité idiosyncratique, avec comme ultime but d’ aboutir à un facteur qui satisfait mieux aux critères souhaités du risque idiosyncratique. Dans le deuxième chapitre de ma thèse, qui est co-écrit avec Christian Dorion et Pierre Chaigneau, nous proposons une méthodologie pour étudier l’importance des risques d’ordres supérieurs dans la valorisation des actifs financiers. A la suite de Kraus and Litzenberger (1976) et Harvey and Siddique (2000a), beaucoup d’études ont analysé l’aversion aux risques de skewness et kurtosis de façon inconditionnelle. Dans ce chapitre, nous proposons une méthodogie qui permet de faire une analyse conditionnelle assez précise de l’aversion au risques d’ordres superieurs. Notre étude complémente la littérature dans la mesure ou nous étudions aussi la valuation des risques d’ordre plus élevé que la kurtosis à savoir l’hyperskewness et l’hyperkurtosis qui sont théoriquement valorisés dans certaines fonction d’utilité comme le CRRA. Dans le dernier chapitre de ma thése, j’étudie la structure à terme de la prime de risque pour le risque de co-skewness, un risque qui mesure l’asymmétrie systématique dans les actions individuelles. Nous y proposons une méthode assez générale qui permet de faire une analyze mutli-horizon contrairement à la plupart des études existantes. / This thesis is organized in three chapters. In the first chapter (which is co-authored with Ilze Kalnina), we propose a statistical test to assess the adequacy of the most popular measure of idiosyncratic risk, which is the idiosyncratic volatility. Our test statistic exploits the idea that a “good" measure of the idiosyncratic risk should be uncorrelated in the cross-section. Using in-fill asymptotics, we study the theoretical properties of the test and find that it has a non-standard behaviour due to various biases induced by the latency of the idiosyncratic volatility. Moreover, we propose a regression model that can be used to reduce if not eliminate the cross-sectional dependences in assets idiosyncratic volatilities. The second chapter of my thesis is the fruit of a colaboration with Christian Dorion and Pierre Chaigneau. In this chapter, we study the relevance of higher-order risk aversion in asset pricing. The evidence in Kraus and Litzenberger (1976) and Harvey and Siddique (2000a) has spurred the literature on the estimation of the risk premiums attached to skewness and kurtosis risk in addition to the standard variance risk. However, most of these studies focus on the estimation of unconditional premiums or average premiums. In this chapter, we propose a methodology that allows to accurately estimate the time-varying higher-order risk aversions using options prices. Our study complements the literature as we also study the higher-order risks beyond the kurtosis such as hyperskewness and hyperkurtosis risks which are valued by a CRRA investor. . In my third chapter, I study the term-structure of price of co-skewness risk. Co-Skewness risk captures the portion of the stock returns asymmetry that arises as a result of market returns asymmetry. I propose a general methodology that allows to study the multi-horizon pricing of this risk in contrast to many existing studies.