Dissertations / Theses on the topic 'One-factor interest rate models'

The uncertainty attached to future movements of interest rates is an essential part of the Financial Decision Theory and requires an awareness of the stochastic movement of these rates. Several approaches have been proposed for modeling the one-factor short rate models where some lead to arbitrage-free term structures. However, no definite consensus has been reached with regard to the best approach for interest rate modeling. In this work, we briefly examine the existing one-factor interest rate models and calibrate Vasicek and Hull-White (Extended Vasicek) Models by using Turkey'
s term structure. Moreover, a trinomial interest rate tree is constructed to represent the evolution of Turkey&rsquo
s zero coupon rates.

Includes bibliographical references
This paper revisits pricing and hedging differences presented by Z. Guan, et. al., 2008 from a South African context. The Asset Liabilities Management (ALM) departments in large financial institutions are plagued by a number of problems. Among them is the choice of interest rate model for managing the risks associated with mortgage (home loan) repay-ments. This paper will address these problems by comparing various one-factor models, including Hull-White, Black-Karasinski and CIR models for the pricing and hedging of long-term Bermudan Swaptions which resembles mortgage loans in banks' books.

Includes bibliographical references (leaves 33-36).
This paper presents the results of Gaussian estimation of the South African short-term interest rate. It uses the same Gaussian estimation techniques employed by Nowman (1997) to estimate the South African short-term interest rate using South afrcan Treasury bill data. A range of single-factor continuous-time models of the short-term interest rate are estimated using a discrete-time model and compared to a discrete approximation used by Chan, Karolyi, Lonstaff and Sanders (1992a). We find that the process followed by the South African short-term interest rate is best explained by the Constant Elasticity of Variance (CEV) model and that the conditional volatility depends to some extent on the level of the interest rate. In addition we find evidence of a structural break in the mid-1980s, confirming our suspicions that the financial liberalisation of that period affected the short rate process.

In this thesis we study three different, but interconnected low-factor market models: LIBOR market model, Markov-functional model, and two-currency Markov-functional model. The LIBOR market model (LMM) is one of the most popular term structure models. However, it suffers from a major drawback, it is high-dimensional. The problem of highdimensionality can be in part solved imposing a separability condition. We will be interested how the separability condition interacts with time-homogeneity, a desirable property of an LMM. We address this question by parametrising two- and three-factor separable and time-homogeneous LMMs and show that they are of practical interest. Markov-functional models (MFMs) are a computationally efficient alternative to the LMMs. We consider two aspects of the MFMs, implementation and specification. First we provide two new algorithms that can be used to implement the one-dimensional MFM under the terminal and the spot measure driven by a general diffusion process. Since the existing literature has been focused exclusively on the Gaussian driving processes our algorithms open the scope for new parameterisations. We then prove that the dynamics of the onedimensional MFM are only affected by the time dependence of the driving process, described by a copula, and not by its marginal distributions. We then shift our focus and show that the one-dimensional MFM under the terminal measure is closely related to the one-factor separable local-volatility LMM. Finally, we move our attention to the models of a two-currency economy. We propose a new three-factor model that we calibrate to the domestic and foreign caplet prices and the foreign exchange call options. To maintain the no-arbitrage condition while calibrating to foreign exchange market we propose a predictor-corrector type step. It is our conjecture that the predictor-corrector step converges, thus the model is well defined.

This paper estimates rates of return across the gross wealth distribution in eight European countries. Like differential saving rates, differential rates of return matter for Post Keynesian theory, because they impact the income and wealth distribution and add an explosive element to growth models. We show that differential rates of return matter empirically by merging data on household balance sheets with long-run returns for individual asset categories. We find that (1) the composition of wealth differentiates between three socioeconomic groups: 30% are asset-poor, 65% are middle-class home owners, and the top 5% are business-owning capitalists; (2) rates of return rise across all groups; and (3) rates of return broadly follow a log-shaped function across the distribution, where inequality in the lower half of the distribution is higher than in the upper half. If socioeconomic groups are collapsed into the bottom 95% workers and top 5% capitalists, then rates of return are 5.6% for the former and 7.2% for the latter.
Series: Ecological Economic Papers

In this thesis we use Markov chain Monte Carlo (MCMC) simulation to calibrate a two-factor arbitrage-free model for the term structure of interest rates which is proposed by Cairns (2004a) based on the positive-interest framework (Flesaker and Hughston, 1996). The model is a time-homogeneous model driven by latent state variables which follow a two-dimensional Ornstein-Uhlenbeck process. A number of MCMC algorithms are developed and employed for estimating both model parameters and latent variables where simulated data are used in the first place in order to validate the algorithms and ensure that they can result in reasonable and reliable estimates before using UK market data. Once the posterior estimates are obtained, we next investigate goodness of fit of the model and eventually assess the impact of parameter uncertainty on the forecasting of yield curves in which the achieved MCMC output can be used directly. Additionally, the developed algorithm is also applied for estimating the two-factor Vasicek term structure model for comparison. We conclude that our algorithms work reasonably well for estimating the Cairns term structure model. The model is then fitted to UK Strips data, and it found to produce reasonable fits for medium- and long-term yields, but we also conclude that some improvement may be required for the short-end of the yield curves.

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O objetivo do presente trabalho é verificar se o modelo que combina correção de erros e fatores extraídos de grandes conjuntos de dados macroeconômicos produz previsões mais precisas das taxas de juros do Brasil em relação aos modelos VAR, VECM e FAVAR. Para realizar esta análise, foi utilizado o modelo sugerido por Banerjee e Marcellino (2009), o FAVECM, que consiste em agregar o mecanismo de correção de erros ao modelo proposto por Bernanke, Boivin e Eliasz (2005), o FAVAR. A hipótese é que o FAVECM possuiu uma formulação teórica mais geral. Os resultados mostram que para o mercado brasileiro o FAVECM apresentou ganhos significativos de previsão para as taxas mais longas e horizontes de previsão maiores.
The objective of the present work is to examine if the model that combines error correction and factors extracted from large macoeconomic data sets offers a higher forecasting accuracy of the interest rate in Brazil when compared to VAR, VECM and FAVAR. In order to conduct this analysis it was used the econometric methodology introduced by Banerjee and Marcellino (2009), the FAVECM, which allows for the inclusion of error correction terms in the model introduced by Bernanke, Boivin and Eliasz (2005), the FAVAR. The hypothesis is that the FAVECM has several conceptual advantages given it is a nesting (or has a more general) specification. The results show that, for the Brazilian market, the FAVECM presented significant gains in forecasts for longer maturity rates and for longer prevision horizons.

The scope of this study is to estimate the zero-coupon yield curve of tomorrow by using Vasicek yield curve model with the zero-coupon bond yield data of today. The raw data of this study is the yearly simple spot rates of the Turkish zero-coupon bonds with different maturities of each day from July 1, 1999 to March 17, 2004. We completed the missing data by using Nelson-Siegel yield curve model and we estimated tomorrow yield cuve with the discretized Vasicek yield curve model.

In the first part of this thesis, we introduce a new methodology for stress-test exercises. Our approach allows to consider richer stress-test exercises, which assess the impact of a modification of the whole distribution of asset prices' factors, rather than focusing as the common practices on a single realization of these factors, and take into account the potential reaction to the shock of the portfolio manager. The second part of the thesis is devoted to the pricing of bonds with very long-term time-to-maturity (more than ten years). Modeling the volatility of very long-term rates is a challenge, due to the constraints put by no-arbitrage assumption. As a consequence, most of the no-arbitrage term structure models assume a constant limiting rate (of infinite maturity). The second chapter investigates the compatibility of the so-called "level" factor, whose variations have a uniform impact on the modeled yield curve, with the no-arbitrage assumptions. We introduce in the third chapter a new class of arbitrage-free term structure factor models, which allows the limiting rate to be stochastic, and present its empirical properties on a dataset of US T-Bonds.

Diese Arbeit besteht aus vier Essays, die empirische und methodische Beiträge zu den Gebieten der Finanzmarktökonomik und der Makroökonomik liefern. Der erste Essay beschäftigt sich mit der Spezifikation der Investoren verfügbaren Informationsmenge in Tests bedingter Kapitalmarktmodelle. Im Speziellen schlägt es die Verwendung dynamischer Faktoren als Instrumente vor. Diese fassen per Konstruktion die Information in einer Vielzahl von Variablen zusammen und stellen daher intuitive Maße für die Investoren zur Verfügung stehenden Informationen dar. Es wird gezeigt, dass so die Schätzfehler bedingter Modelle im Vergleich zu traditionellen, auf einzelnen Indikatoren beruhenden Modellvarianten substantiell verringert werden. Ausgehend von Ergebnissen, dass die Zentralbank zur Festlegung des kurzfristigen Zinssatzes eine große Menge an Informationen berücksichtigt, wird im zweiten Essay im Rahmen eines affinen Zinsstrukturmodells eine ähnliche Idee verwandt. Speziell wird die Dynamik des kurzfristigen Zinses im Rahmen einer Faktor-Vektorautoregression modelliert. Aufbauend auf dieser dynamischen Charakterisierung der Geldpolitik wird dann die Zinsstruktur unter der Annahme fehlender Arbitragemöglichkeiten hergeleitet. Das resultierende Modell liefert bessere Vorhersagen US-amerikanischer Anleihenzinsen als eine Reihe von Vergleichsmodellen. Der dritte Essay analysiert die Vorhersagekraft der Zinsstrukturkomponenten "level", "slope", und "curvature" im Rahmen eines dynamischen Faktormodells für makroökonomische und Zinsdaten. Das Modell wird mit einem Metropolis-within-Gibbs Sampling Verfahren geschätzt, und Überraschungsänderungen der drei Komponenten werden mit Hilfe von Null- und Vorzeichenrestriktionen identifiziert. Die Analyse offenbart, dass der "curvature"-Faktor informativer in Bezug auf die zukünftige Entwicklung der Zinsstruktur und der gesamtwirtschaftlichen Aktivität ist als bislang vermutet. Der vierte Essay legt eine monatliche Chronologie der Konjunkturzyklen im Euro-Raum vor. Zunächst wird mit Hilfe einer verallgemeinerten Interpolationsmethode eine monatliche Zeitreihe des europäischen BIP konstruiert. Anschließend wird auf diese Zeitreihe ein Datierungsverfahren angewandt, das kurze und flache Konjunkturphasen ausschließt.
This thesis consists of four essays of independent interest which make empirical and methodological contributions to the fields of financial economics and macroeconomics. The first essay deals with the proper specification of investors’ information set in tests of conditional asset pricing models. In particular, it advances the use of dynamic factors as conditioning variables. By construction, dynamic factors summarize the information in a large number of variables and are therefore intuitively appealing proxies for the information set available to investors. The essay demonstrates that this approach substantially reduces the pricing errors implied by conditional models with respect to traditional approaches that use individual indicators as instruments. Following previous evidence that the central bank uses a large set of conditioning information when setting short-term interest rates, the second essay employs a similar insight in a model of the term structure of interest rates. Precisely, the dynamics of the short-term interest rate are modelled using a Factor-Augmented Vector-Autoregression. Based on this dynamic characterization of monetary policy, the term structure of interest rates is derived under the assumption of no-arbitrage. The resulting model is shown to provide superior out-of-sample forecasts of US government bond yields with respect to a number of benchmark models. The third essay analyzes the predictive information carried by the yield curve components level, slope, and curvature within a joint dynamic factor model of macroeconomic and interest rate data. The model is estimated using a Metropolis-within-Gibbs sampling approach and unexpected changes of the yield curve components are identified employing a combination of zero and sign restrictions. The analysis reveals that the curvature factor is more informative about the future evolution of the yield curve and of economic activity than has previously been acknowledged. The fourth essay provides a monthly business cycle chronology for the Euro area. A monthly series of Euro area real GDP is constructed using an interpolation routine that nests previously suggested approaches as special cases. Then, a dating routine is applied to the interpolated series which excludes business cycle phases that are short and flat.

碩士
東海大學
財務金融學系
98
This article uses Ritchken & Sankarasubramanian model(RS model；1995) which has state variables； the model like this has Markov process characteristic and the zero coupon bond price derived from RS model also owns the same state variables. It will makes the simulation efficient. In this article, we compare one factor RS model accuracy in simulating interest rate derivatives with two factor Inui & Kijima model(IK model；1998). Two models volatility are all the function of short rate；one factor RS model volatility is exponential dampened , and two factor IK model volatility are constant and exponential dampened.

This diploma thesis deals with short-term interest rate models. Many interest models have been developed in the last decades. They focus on accuracy of prediction. The pioneering one was developed by Vasicek in 1977 followed by the work of others. Nowadays these vary in their level of comprehensiveness and technical difficulty. The main aim of the thesis is to introduce not only a basic Vasicek's work but also more sophisticated models such as Brennan-Schwartz or Longstaff-Schwartz.

Tese de mestrado em Matemática Financeira, apresentada à Universidade de Lisboa, através da Faculdade de Ciências, 2010
The present work focuses on the pricing of European-style interest rate swaptions, using the Edgeworth expansion [Collin-Dufresne and Goldstein (2002)] and the Hyperplane approxima-tions [Singleton and Umantsev (2002)], under multi-factor exponentially-affine models of the term structure. In a market without arbitrage opportunities, it is shown that an interest rate swaption can be priced as an option on a coupon-bearing bond. While the Edgeworth approx-imation suggests a cumulant expansion of the probability density function of the price of the underlying coupon-bearing bond, the Hyperplane approximation proposes a linearization of the exercise region, so that the same methods used when under one-factor models can be applied. Both methods are analyzed in detailed, and then implemented considering a three-factor Gaussian model, and different maturities for the underlying interest rate swaps, as well as a range of strike prices for each swaption. While there are almost no differences between the results yielded by both approximations, the Edgeworth approximation proves to be significantly slower as the time-to-maturity of the underlying swap increases. Moreover, the Edgeworth approximation is less .flexible, because it requires a closed-form solution for the moments of the distribution of the underlying asset (i.e. a coupon-bearing bond), which are not so readily available for non-affine term structure models.

碩士
淡江大學
財務金融學系
92
It’s a long time to talk about one-factor and two-factor interest models accounting for interest rate behavior. The one factor interest rate model has lower explanatory power in empirical study. Most financial academics try to use two-factor interest rate model to explain the diffusion behavior. The BDT interest rate model is one of the no-arbitrage models which can fit the initial term structure automatically. It has two good points: no negative interest rate、capturing the yield curve. We use the Maximum likelihood method to measure the level effect and GARCH effect in one-factor interest rate model and level-GARCH effect in two-factor interest rate model and to compare the pricing and forecasting performance. Through the Monte Carlo Simulation，we can simulated the level and level-GARCH paths to compare with the real behavior. Then we can define the drift in four types: linear、quadratic、nonlinear、cubic and test which one performs best. We discover that the level-GARCH model always get Maximum likelihood value. The coefficient of determination from absolute value of the interest rates changes can be explained by the estimated conditional volatilities to test the predictive power. Two—factor level-GARCH model’s simulated path is closer to real interest path than one-factor level model’s simulated path. The conclusion is that level-GARCH model has good ability to capture the actual behavior of interest rate.

Mestrado em Finanças
Os modelos estruturais de avaliação de obrigações com risco de crédito modelam a possibilidade de incumprimento fazendo o preço das obrigações depender da evolução do valor da empresa emitente, que obedece a um processo de difusão. Adicionalmente, a incerteza na estrutura temporal de taxas de juro é introduzida fazendo o preço das obrigações depender de uma taxa de juro estocástica de curto prazo. Porém, a descrição da estrutura temporal de taxas de juro através de um único processo estocástico implica que os preços das obrigações sem risco são perfeitamente correlacionados ao longo de diferentes maturidades, o que é claramente irrealista. Neste trabalho estudou-se o impacto no preço de obrigações com risco da introdução num modelo estrutural de uma estrutura temporal de taxas de juro descrita por duas variáveis estocásticas: as taxas de juro de curto e de longo prazo. Foram obtidas soluções numéricas e verificou-se que a introdução de uma taxa de juro de longo prazo estocástico pode afectar significativamente tanto a forma como a magnitude da estrutura temporal de spreads de crédito.
Structural models of corporate bond pricing capture the possibility of default by allowing the price of risky bonds to be contingent upon the evolution of the issuing firm value, which follows some diffusion process. Furthermore, the uncertainty in the term structure of interest rates is usually introduced by making the bond price depend on a sthocastic short-term interest rate process. However, the description of the term structure of interest rates by a single stochastic factor implies that the prices of riskless bonds across different maturities are perfectly correlated, which is clearly unrealistic. In this work we investigate the impact on corporate bond prices of introducing in a structural model a term structure of interest rates described by two stochastic variables: the short-term and the long-term interest rates. Numerical solutions of bond prices are obtained. It is found that the introduction of a stochastic long-term interest rate process may affect significantly both the level and shape of the term structure of credit spreads.
N/A

碩士
國立高雄第一科技大學
金融營運系碩士班
89
The effect of a valuation of mortgage-backed security includes the uncertainly of the risk of default and prepayment. Previous researches on the valuation of mortgage-backed securities, have been focused on the one-factor security valuation framework, that the borrower will prepay when the mortgage’s coupon rate exceeds refinancing rate. This article provides two-factor security valuation framework, considering the fluctuation of interest rate（Hull-White）and mortgaged house values. The two factors are interest and mortgaged house values. Assuming that interest rate follows Hull and White model and the mortgaged house values follows lognormal model. We use the method of valuation procedures that Hilliard, Kau, and Slawson（1998）jointly developed and the equations of forward induction that Dharan（1991）introduced to value MBS in lattice. Finally, we summarize our valuation results as follow： 1.The higher the house values volatility emerges, the lower the value of MBS appears. 2.The higher the interest rate volatility emerges, the higher the value of MBS appears. 3.The higher the mean-reverting parameter emerges, the higher the value of MBS appears. 4.The larger the speed-of-prepayment parameter emerges, the lower the value of MBS appears.

碩士
中原大學
國際經營與貿易研究所
106
This study mainly carries out two modifications based on the three-factor model proposed by Fama-French (1993) (market factor, size factor, and book /market factor). First, we add the term of price-cost margin that represents market monopoly power into the Fama-French model as another factor to form a linear four-factor model. The price-cost margins are similar to the market monopoly indicators - Lerner index and Bain index. The larger the price set by the firm deviates from the marginal cost or average cost, the higher the firm''s monopoly power would be. Second, we apply the panel smooth transition regression (PSTR) model and rewrite the linear four-factor model as a four-factor PSTR framework. In the four-factor PSTR model, the deposit spread is used as the transition variable to estimate stock returns and four risk premiums (market, size, book-to-market, and monopoly power) that vary with companies and time. Empirically, a panel data set of 28 listed financial stocks in Taiwan during March 2008 to June 2017 is used. Thus, there are 1064 observations. Empirical results are summarized as follows: First, for the financial industry, the growth stocks have higher excess returns than value stocks; the big size stocks have higher excess returns than small size stocks. Second, the four risk premiums all vary with the deposit spreads of individual financial companies in different periods, which is quite different from the constant risk premiums obtained from the traditional Fama-French three-factor model and linear four-factor model. Third, when considering deposit spreads, the traditional linear model underestimates the positive impact of market factors on the stock returns. In addition, a high deposit spread would increase the contribution of market factors to stock prices, while a moderate deposit spread would minimize the contribution. Fourth, the impact of size factor on stock returns is significant, but the sign is ambiguous. In the case of moderate deposit spreads, there may be an increase in the non-performing loans, resulting in a decrease in the size premium. Fifth, the contribution of book-to-market ratio to share prices is insignificant and ambiguous. The value premium is maximum when the deposit spreads are high. Sixth, the effect of market monopoly power on stock returns is negative but not significant. However, the effect in the linear four-factor model is positive and insignificant. In other words, simply considering the factor of market monopoly power and ignoring different level of deposit spreads will misestimate its impact on the stock returns.

This dissertation: ANALYSIS OF THE BRAZILIAN YIELD CURVE: A NO-ARBITRAGE FACTOR-AUGMENTED VECTOR AUTOREGRESSION APPROACH, applies a parsimonious method to analyse the Brazilian term structure exploiting a vast number of macroeconomic variables. The procedure, developed in Moench (2008), combines the short-term interest rate with the principal components extracted from a large macroeconomic dataset. The short-term dynamics are described by a factor-augmented vector autoregression. Subsequently, the term structure is obtained by the no-arbitrage method. The results in-sample and out-of-sample of the so called No-arbitrage Factor Augmented Vector Autoregression (NAFAVAR) model is compared with the model in Diebold and Li (2006), since this model delivers both in-sample fitting and out-of-sample forecasts. The results of the NAFAVAR model outperforms the competitor model in some maturities of the term structure, which could be helpful for out-of-sample forecasts. The NA-FAVAR model seems to adapt well to the Brazilian interest rate market, which could help financial agents to evaluate and forecast securities using a model with macroeconomic interpretation.