Thesis advisor: Robert Murphy / In order for the Euro to be successful over time, certain conditions must be satisfied. First, the economies of the countries need to be similar so that a policy change does not cripple certain economies when it attempts to help others. Therefore, convergence among the interest rates of the different countries will be tested. Also, since the Euro has removed the individual monetary policies, the countries only have fiscal policy to use for stabilization of their economies. Provisions have been in place to prevent countries from overspending, which creates pressure for devaluation of the Euro. This paper will provide evidence that these countries have shown convergence in their economies since the inception of the Euro. It will also explore the literature surrounding the opinions about the role of fiscal policy. Together, these two topics will be used to support the belief that the Euro will be sustained in the future. / Thesis (BA) — Boston College, 2007. / Submitted to: Boston College. College of Arts and Sciences. / Discipline: Economics Honors Program.

利率模型廣泛應用於利率衍生品的定價。為了吻合實證利率的分佈和隱含波動率，一種可能的辦法是用Lévy過程替換Hull- White模型中的布朗隨機變量的利率模型，但是這種方法很難實施。本文建立了一種有效的網絡數值方法對利率進行估測。利用Lévy過程的馬爾可夫性質， FFT網絡實質上是多項樹模型的擴展。這種數值方法的優勢在於一直固定不變的狀態點，對現時利率期限結構的超級校準以及基於對Lévy過程的特徵方程的快速傅裡葉變換(FFT) 去恢復概率密度函數以實現轉移概率的計算過程。這種網絡數值方法對利率衍生品的定價與利率樹類似。對利率上限期權和交換期權的解析解和數值解的比較表明網絡數值方法是準確和有效的。FFT網絡還可以對百慕達式利率交換期權以及美式期權進行定價。最後， FFT網絡被擴展去適應路徑依賴變量，因此，能對利率依賴的結構性票據進行定價，比如目標贖回票據和範團積息結構票據。 / Short rate models are widely used in valuing interest rate derivatives. To fit empirical distribution of interest rates and implied volatility, a possible way is to replace Brownian motion by a Lévy process in short rate models. However, this approach is difficult to implement. This thesis establishes an efficient network approach for interest rate valuation. The FFT-network is essentially an extension of multinomial tree model, taking advantage of the Markov property of Lévy processes. Its fixed and unchanged states at all time, super-calibration ability to the current term structure, and elegant computation procedure for transition probabilities using the fast Fourier transform (FFT) from the characteristic function of Lévy processes make it attractive and distinct from other numerical methods. The interest rate derivatives value is determined in a way similar to that of the tree approach. The comparison between the closed-form solution of interest rate caplets and swaptions and the numerical results under the network demonstrates that the proposed network is accurate and efficient. In addition, the FFT-network can also be used to pricing the Bermudan swaption and American-style option. Finally, the FFT-network is expanded to accommodate path-dependent variables, and hence can be used for pricing some path-dependent structured notes, such as the target redemption notes and range of accrual notes. / Detailed summary in vernacular field only. / Xu, Zhuolu. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2012. / Includes bibliographical references (leaves 91-93). / Abstracts also in Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Preliminaries --- p.4 / Chapter 2.1 --- Elementary techniques --- p.4 / Chapter 2.1.1 --- Characteristic function --- p.4 / Chapter 2.1.2 --- Cumulant generating function --- p.5 / Chapter 2.1.3 --- Fourier Transform --- p.6 / Chapter 2.1.4 --- Fast Fourier Transform (FFT) --- p.8 / Chapter 2.2 --- Lévy Processes --- p.10 / Chapter 2.2.1 --- Definition --- p.10 / Chapter 2.2.2 --- Lévy-Khintchine --- p.11 / Chapter 2.2.3 --- Lévy Processes in Interest Rate --- p.13 / Chapter 2.3 --- Hull-White Model --- p.13 / Chapter 2.3.1 --- Model setup --- p.14 / Chapter 2.3.2 --- Interest rate caps --- p.15 / Chapter 2.3.3 --- European Swaptions --- p.16 / Chapter 2.3.4 --- A Tree-building procedure --- p.19 / Chapter 3 --- HW-Lévy Model --- p.20 / Chapter 3.1 --- Model Setup --- p.20 / Chapter 3.2 --- The Characteristic Function --- p.22 / Chapter 3.3 --- Analytic result on interest rate derivatives --- p.26 / Chapter 4 --- Valuation: FFT Network Model --- p.35 / Chapter 4.1 --- Drawbacks of Tree Approach --- p.35 / Chapter 4.2 --- FFT Network Setup --- p.37 / Chapter 4.3 --- Transition Probability Matrix --- p.38 / Chapter 4.4 --- Yield Curve Fitting --- p.42 / Chapter 4.5 --- Pricing Algorithm under FFT Network --- p.45 / Chapter 4.5.1 --- European Interest Rate Derivatives Pricing --- p.45 / Chapter 4.5.2 --- Bermudan Interest Rate Derivatives Pricing --- p.49 / Chapter 5 --- Extended FFT Network for Path-dependent Structured Notes --- p.55 / Chapter 5.1 --- Extended FFT-netwok --- p.55 / Chapter 5.2 --- Target Redemption Notes (TARN) --- p.61 / Chapter 6 --- Numerical Study --- p.69 / Chapter 6.1 --- Numerical Scheme --- p.69 / Chapter 6.2 --- Numerical Examples --- p.74 / Chapter 7 --- Conclusion --- p.89 / Bibliography --- p.91

Wong, Tsz-Lim. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references (leaves 48-51). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Reduced-Form Model --- p.5 / Chapter 2.1 --- Information and Probabilistic Framework --- p.6 / Chapter 2.2 --- Poisson and Cox Process --- p.6 / Chapter 2.3 --- The Building Blocks of Pricing --- p.8 / Chapter 2.4 --- Comparing the Recovery Models --- p.10 / Chapter 3 --- General Equilibrium Model --- p.12 / Chapter 3.1 --- State Variables --- p.12 / Chapter 3.2 --- Investment Opportunities --- p.14 / Chapter 3.3 --- Preferences --- p.15 / Chapter 3.4 --- The Term Structure of Defaultable Bonds --- p.17 / Chapter 4 --- Methodologies --- p.24 / Chapter 5 --- SNP and EMM --- p.27 / Chapter 5.1 --- SNP Density --- p.27 / Chapter 5.2 --- EMM Estimation --- p.29 / Chapter 6 --- Empirical Results --- p.31 / Chapter 6.1 --- Data Description --- p.31 / Chapter 6.2 --- Estimation Results --- p.33 / Chapter 7 --- Conclusion --- p.42 / Chapter A --- Extended Nelson and Siegel Model --- p.44 / Chapter B --- Moment-Matching of the CIR Model --- p.46 / Bibliography --- p.48

Lai, Ka Lun. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references (leaves 75-77). / Abstracts in English and Chinese. / Chapter Chapter 1 --- Introduction --- p.1 / Chapter Chapter 2 --- Multivariate Threshold Time Series Model --- p.14 / Chapter 2.1 --- The Multivariate TAR Models --- p.14 / Chapter 2.2 --- Testing for Nonlinearity --- p.15 / Chapter 2.3 --- Model Selection and Estimation --- p.22 / Chapter 2.4 --- Bivariate TAR Models --- p.26 / Chapter 2.5 --- Applications --- p.27 / Chapter Chapter 3 --- Comparative Study of Interest Rates --- p.34 / Chapter 3.1 --- Background --- p.34 / Chapter 3.2 --- The Importance of Modelling Interest Rates --- p.40 / Chapter 3.3 --- The Scope of Study --- p.41 / Chapter 3.4 --- Major Findings --- p.42 / Chapter Chapter 4 --- Conclusion --- p.71 / Reference --- p.80

Tam Chak Yue, Ben. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1997. / Includes bibliographical references (leaves 49-51). / Chapter 1. --- Introduction --- p.3 / Chapter 2. --- Money and Growth in the neoclassical production function --- p.7 / Chapter 2.1 --- The Real Competitive Equilibrium --- p.8 / Chapter 2.2 --- The Monetary Competitive Equilibrium with the Cash-in-Advance approach --- p.11 / Chapter 2.3 --- Alternative Approach: Money-in-Utility-Function --- p.16 / Chapter 2.4 --- Alternative Approach: Transaction Cost --- p.20 / Chapter 3. --- Three Approaches with Endogenous Leisure --- p.25 / Chapter 3.1 --- The Real Competitive Equilibrium --- p.26 / Chapter 3.2 --- The Alternative Approaches to Interest Rate Smoothing --- p.28 / Chapter 3.2.1 --- The Cash-in-Advance Approach --- p.28 / Chapter 3.2.2 --- The Money-in-Utility-Function Approach --- p.29 / Chapter 3.2.3 --- The Transaction Cost Approach --- p.30 / Chapter 4. --- Money and Growth in an Economy with Endogenous Growth --- p.35 / Chapter 4.1 --- The Real Competitive Equilibrium of Ak Model --- p.36 / Chapter 4.2 --- The Alternative Approaches --- p.37 / Chapter 4.2.1 --- The Cash-in-Advance Approach --- p.37 / Chapter 4.2.2 --- The Money-in-Utility-Function Approach --- p.39 / Chapter 4.2.3 --- The Transaction Cost Approach --- p.40 / Chapter 5. --- Concluding Remark --- p.44 / Appendix --- p.46 / Chapter A1. --- The First Order Condition of The MIUF Approach with Endogenous Leisure --- p.46 / Chapter A2. --- The First Order Condition of The TC Approach with Endogenous Leisure --- p.46 / Chapter A3. --- The Transitional Dynamics of Ak Model with The money-in-utility-function Approach --- p.47 / Literature Cited --- p.50

Chow, Chui Ngan. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2008. / Includes bibliographical references (leaves 76-79). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Interest Rate Models --- p.6 / Chapter 2.1 --- Short Rate Models --- p.7 / Chapter 2.2 --- Heath-Jarrow-Morton Framework --- p.8 / Chapter 2.3 --- Bond Market Models (BMM) --- p.9 / Chapter 3 --- Mortality Models --- p.13 / Chapter 3.1 --- Deterministic Survival Functions --- p.13 / Chapter 3.2 --- Stochastic Mortality Models --- p.15 / Chapter 4 --- Guaranteed Annuity Options under BMM --- p.16 / Chapter 4.1 --- Model Settings --- p.17 / Chapter 4.1.1 --- Financial Variables --- p.17 / Chapter 4.1.2 --- Mortality --- p.19 / Chapter 4.2 --- Guaranteed annuity option --- p.21 / Chapter 4.3 --- Numerical results --- p.23 / Chapter 4.3.1 --- Simulation Study --- p.24 / Chapter 4.3.2 --- Empirical results --- p.29 / Chapter 5 --- Longevity Bond Market Models --- p.34 / Chapter 5.1 --- Model Settings --- p.35 / Chapter 5.1.1 --- Theoretical Settings --- p.35 / Chapter 5.1.2 --- Risk-free Bonds and Longevity Bonds --- p.36 / Chapter 5.2 --- Applications on Potential Mortality-Linked Products --- p.41 / Chapter 5.3 --- Numerical Results --- p.45 / Chapter 5.3.1 --- Simulation Settings --- p.46 / Chapter 5.3.2 --- Simulation Results --- p.49 / Chapter 6 --- Conclusion --- p.53 / Chapter A --- Equation Derivation --- p.56 / Chapter A.l --- Proof for Proposition (4.2.1) --- p.56 / Chapter A.2 --- Proof for Proposition (4.2.2) --- p.58 / Chapter A.3 --- Proof for Proposition (5.3.1) --- p.61 / Chapter A.4 --- Proof for Proposition (5.3.2) --- p.66 / Chapter B --- Results --- p.71 / Chapter B.l --- Valuation Results for GAO under BMM --- p.71 / Chapter B.1.1 --- Simulation Situations --- p.71 / Chapter B.1.2 --- Calibration Results --- p.72 / Chapter B.1.3 --- Valuation Results --- p.74

Este trabalho apresenta uma abordagem inovadora para a modelagem do risco cambial. Ao invés de utilizar regressões de MQO \"equação por equação\", explora-se a correlação contemporânea e estrutural entre os choques de preferência num sistema de equações de precificação de ativos. Estima-se um modelo via SUR em uma amostra de excessos de retorno de países entre 1999Q1 e 2014Q2, utilizando-se novos fatores de risco associados ao PIB das diferentes economias. O modelo empírico é derivado de preferências que são consistentes com um problema de economia aberta, em contraste com a abordagem habitual que utiliza o crescimento do consumo de bens duráveis e não-duráveis como fatores de risco. A estratégia econométrica escolhida leva a uma melhora significativa da precisão das quantidades de risco (betas) estimadas. A relação positiva entre taxas de juros e quantidades de risco, contudo, não é corroborada para todos os betas. / This thesis presents an innovative approach for modeling currency risk. Instead of using equation by equation OLS, we explore the structural contemporaneous correlation between preference shocks across a system of asset pricing equations. SUR regressions as well as new risk factors lead to a marked improvement in efficiency for the estimation of the quantities of risk (betas) in a sample of country excess returns from 1999Q1 to 2014Q2. However, the monotonic relation between interest rates and quantities of risk is not statistically significant for all betas. Our model is derived from preferences that are consistent to an open economy problem, in contrast to the typical approach of using durable and non-durable consumption growth as risk factors.

Esta dissertação é um estudo empírico que relaciona variáveis fiscais como dívida pública e déficit primário com a taxa de juros nominal de longo prazo, relação, que na literatura empírica como um todo, é bastante ambígua. Quando separamos, desta literatura, os trabalhos que incluem expectativas de déficits, obtemos resultados positivos e significantes, ou seja, que a contenção fiscal reduz a taxa de juros de longo prazo. Ainda nesta literatura, poucos trabalhos fazem uso de dados de painel devido à pouca disponibilidade de dados. Dessa forma, usamos um painel com 25 países e dados anuais entre 1980 e 2009. Assim, estimam-se modelos estáticos e dinâmicos em que a taxa de juros nominal de longo prazo é explicada pela dívida pública e, principalmente, o déficit primário, controlando a existência de efeitos fixos para países e anos. Utilizamos, em seguida, modelos não-lineares, para captar efeitos das variáveis fiscais de forma não-linear e com variáveis interativas. Encontra-se uma relação positiva entre as variáveis, indicando que um aumento no déficit primário leva a um aumento na taxa de juros nominal de longo prazo. A magnitude do efeito estimado é semelhante a outros estudos feitos com dados em painel. Os resultados apontam que um aumento em um ponto percentual do déficit primário leva a um aumento de zero a 10 bps sobre a taxa de juros nominal de longo prazo. Já para a dívida pública encontramos que, ao contrário do que esperaríamos pela teoria, que seu efeito sobre a taxa de juros nominal de longo prazo é insignificante e menor do que o encontrado na maior parte da literatura, menos de 2 bps, mas semelhante aos de outros trabalhos. Ao contrário de toda literatura para dados em painel, incluímos também a expectativa de déficits, variável que deveria incorporar mais informação do que somente o déficit corrente e, por isso, nossos resultados deveriam ser mais significantes. No entanto, estas variáveis não estão disponíveis para muito anos e, portanto, para esta parte do trabalho nossa amostra se reduz para 1996-2009. Contudo, ao fazermos as mesmas estimações que as anteriores, mas com a expectativa de déficit obtemos coeficientes para o déficit primário insignificantes, nem sempre positivos e baixos. Este resultado parece ser devido à amostra reduzida que temos para expectativa de déficit. / This dissertation is an empirical study that tries to capture the relationship between fiscal variables, such as the public debt and the primary deficit, and the long-term nominal interest rates, a relationship that in the empirical literature as a whole is very ambiguous. However, when, in this literature, we look only at papers that include expected deficits, we obtain positive and significant results. In the same set of studies, few use panel data due to low data availability. We use a panel with 25 countries and annual data between 1980 and 2009. We estimate static and dynamic models in which the long-term nominal interest rate is explained by the public debt and, especially, the primary deficit by controlling for the existence of fixed effects for countries and years. We then estimate non-linear models to capture the non-linear and interactive effects of fiscal variables on interest rates. We find a positive and statistically significant relationship between these variables, indicating that the primary deficit has a positive impact on the long-term nominal interest rate. The magnitude of the estimated effect is similar to other studies with panel data. They show that a one percentage point increase in the primary deficit leads to an increase from zero to 10 bps in the long-term nominal interest rate. As for the public debt, we find that, contrary to what we would expect from economic theory, its effect on the long-term nominal interest rate is negligible and smaller than that found in most of the literature, less than 2 bps, but similar to other panel studies. Unlike the rest of the literature that uses panel data, we included deficit expectations that would incorporate more information than just the current primary deficit and would, therefore, give us more statistically significant results. However, these variables are not available for large periods of time for a panel of countries and, therefore, for this part of our study, our sample is reduced to the period 1996-2009. This time, even though we estimate the same models, but now with the deficit expectations, we now obtain statistically insignificant, sometimes negative and lower coefficients for the primary deficit. Nevertheless, these results seem to be due to the small sample size we have for deficit expectations.

A condução da política monetária vem sendo descrita pela literatura recente por meio de uma regra forward-looking do tipo \"Taylor\". Neste contexto, o que a literatura identifica como o Princípio de Taylor indica que, para que haja uma política de controle inflacionário efetiva, o coeficiente de resposta dos juros nominais a um desvio da expectativa de inflação em relação à meta deve ser maior do que um. Deste modo, se este desvio for positivo, será provocado um aumento nos juros reais. No entanto, tomando uma Equação de Fischer também em termos expectacionais, a derivação da Regra nos leva a crer que tal princípio pode ser questionado, sendo necessário que este coeficiente supere ( ) t rr + 1 , ou seja, um mais os juros reais. Neste trabalho é estimada uma Regra de Taylor para o caso brasileiro, país com elevadas taxas de juros reais, buscando comparar o valor deste coeficiente ao valor de ( ) t rr + 1 . O método consiste em um Time-Varying Parameter (TVP), onde os parâmetros seguem passeios aleatórios. São utilizadas diversas combinações de dados. Os resultados mostraram uma política bastante agressiva por parte do Banco Central brasileiro em todos os períodos de análise. / The conduction of monetary policy is being described by recent literature through a forward-looking Taylor rule. In this context, what literature identifies as the Taylor Principle indicates that, for an efficient policy of inflation control, the coefficient of the response of nominal interest rates from the deviation of the inflation expectations in relation to the target should be more than one. If this deviation is positive, it will cause an increase in real interest rates. However, the derivation of the rule shows that this principle can be questioned, and the coefficient must be more than ( ) t rr + 1 , one plus the real interest rate. In this work we estimate a Taylor rule for Brazil, country with high real interest rates, trying to compare the coefficient value to ( ) t rr + 1 . The method consists in a Time-Varying Parameter (TVP), where the parameters follow a random walk process. Varied data combinations are used. The results show a very aggressive policy by the Central Bank in all periods of analysis.

This thesis consists of two related parts. In the first part we conduct an empirical examination of the dynamics of Australian interest rates of six different maturities, covering the whole yield curve. This direct study of the long rates is quite novel. We use maximum likelihood estimation on a variety of models and find some results that are in stark contrast to previous studies. We estimate Poisson-jump diffusion (PJD) models and find very strong evidence for the existence of jumps in all daily interest rate series. We find that the PJD model fits short-rate data significantly better than a Bernoulli-jump diffusion model. We also estimate the CKLS model for our data and find that the only model not rejected for all six maturities is the CEV model in stark contrast to previous findings. Also, we find that the elasticity of variance estimate in the CKLS model is much higher for the short-rates than for the longer rates where the estimate is only about 0.25, indicating that different dynamics seem to be at work for different maturities. We also found that adding jumps to the simple diffusion model gives a larger improvement than comes from going from the simple diffusion to the CKLS model. In the second part of the thesis we examine the Flesaker and Hughston (FH) term structure model. We derive the dynamics of the short rate under both the original measure and the risk-neutral measure, and show that some criticisms of the bounds for the short rate may not be significant in actual applications. We also derive the dynamics of bond prices in the FH model and compare them to the HJM model. We also extend the FH model by allowing the martingale to follow a jump-diffusion process, rather than just a diffusion process. We derive the unique change of measure that guarantees the family of bond prices is arbitrage-free. We derive prices for caps and swaptions, and extend the results to include Bermudan swaptions and show how to price options with the jump-diffusion version of the FH model.