The aim of this study is to compare the performance of the four interest rate models (Vasicek Model, Cox Ingersoll Ross Model, Ho Lee Model and Black Der- man Toy Model) that are commonly used in pricing zero coupon bond options. In this study, 1{5 years US Treasury Bond daily data between the dates June 1, 1976 and December 31, 2007 are used. By using the four interest rate models, estimated option prices are compared with the real observed prices for the begin- ing work days of each months of the years 2004 and 2005. The models are then evaluated according to the sum of squared errors. Option prices are found by constructing interest rate trees for the binomial models based on Ho Lee Model and Black Derman Toy Model and by estimating the parameters for the Vasicek and the Cox Ingersoll Ross Models.

Submitted by Andre Akamine (andre_akamine@yahoo.com.br) on 2014-02-25T19:51:22Z No. of bitstreams: 1 dissertacao-andre_akamine -versao final.pdf: 1090370 bytes, checksum: 2cc992eb83cbdbf42457a77eeb02dffa (MD5) / Approved for entry into archive by Vera Lúcia Mourão (vera.mourao@fgv.br) on 2014-02-25T20:48:28Z (GMT) No. of bitstreams: 1 dissertacao-andre_akamine -versao final.pdf: 1090370 bytes, checksum: 2cc992eb83cbdbf42457a77eeb02dffa (MD5) / Made available in DSpace on 2014-02-26T12:20:22Z (GMT). No. of bitstreams: 1 dissertacao-andre_akamine -versao final.pdf: 1090370 bytes, checksum: 2cc992eb83cbdbf42457a77eeb02dffa (MD5) Previous issue date: 2014-01-29 / Com o objetivo de analisar o impacto na Estrutura a Termos de Volatilidade (ETV) das taxas de juros utilizando dois diferentes modelos na estimação da Estrutura a Termo das Taxas de Juros (ETTJ) e a suposição em relação a estrutura heterocedástica dos erros (MQO e MQG ponderado pela duration), a técnica procede em estimar a ETV utilizando-se da volatilidade histórica por desvio padrão e pelo modelo auto-regressivo Exponentially Weighted Moving Average (EWMA). Por meio do teste de backtesting proposto por Kupiec para o VaR paramétrico obtido com as volatilidades das ETV´s estimadas, concluí-se que há uma grande diferença na aderência que dependem da combinação dos modelos utilizados para as ETV´s. Além disso, há diferenças estatisticamente significantes entre as ETV´s estimadas em todo os pontos da curva, particularmente maiores no curto prazo (até 1 ano) e nos prazos mais longos (acima de 10 anos). / For the purpose of analyzing the impact in Volatility Term Structure (VTS) of interest rate using two different models in the estimation of the Term Structure of Interest Rates (TSIR) and the assumption regarding the heterocedastic structure of errors (OLS and GLS weighted by duration), the technique proceeds in estimating the VTS using the historical volatility by the standard deviation and autoregressive model Exponentially Weighted Moving Average (EWMA). Through the backtesting test proposed by Kupiec for parametric VaR obtained with the volatilities of VTS’s estimate, conclude that there is a big difference in adherence that depend on the combination of the models used for VTS’s. In addition, there is statistically significant differences between the VTS’s estimated around the points of the curve, specially higher in the short term (less than 1 year) and long term (over 10 years).

This study applies the Vasicek stochastic interest rate model in order to determine optimal capital structures for listed firms. A Swedish interest rate data set is used to estimate Vasicek model parameter that are reliable and independent of initial start values. These interest rate parameters are then used in a capital structure model which is evaluated through a sensitivity analysis and a firm-specific analysis which is applied to listed Swedish firms. The tax benefits of debt must be balanced against transaction costs and bankruptcy costs when determining optimal leverage ratio and optimal debt maturity. The results imply that firms should primarily focus on the long-term mean parameter of the interest rate process, the volatility of its firm value, the transaction cost of issuing debt and the effective corporate tax rate when choosing a capital structure. The capital structure model is well-founded in previous research and yields results which align with empirical data quite well. The conclusions of this study has implications for corporate finance, as the Vasicek model provides a better understanding of the stochastic nature of interest rates and its influence in determining optimal capital structures. / Denna studie tillämpar Vasiceks stokastiska räntemodell för att bestämma optimala kapitalstrukturer för noterade företag. Vasicekmodellen anpassas till ett Svensk dataset över räntor för att estimera parametrar. Dessa parametrar används sedan i en kapitalstruktursmodell för att analysera modellens känslighet för variationer i parametrar samt för att härleda optimala kapitalstrukturer för en rad Svenska noterade bolag. Skattefördelarna av skuld måste balanseras mot transaktionskostnader av skuldemissioner och konkurskostnader vid bestämning av optimal skuldsättningsgrad och optimal skuldlöptid. Resultaten antyder att företag bör primärt fokusera på det långsiktiga medelvärdet av den stokastiska ränteprocessen, volatiliteten av bolagsvärdet, transaktionskostnaden av skuldemissioner och effektiva bolagsskatten när de väljer en kapitalstruktur. Denna studie har implikationer för finansieringsteori då Vasiceks modell närmare modellerar räntors stokastiska dynamiker och dess påverkan på bestämning av bolags kapitalstrukturer.

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))

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))