Thesis (Ph. D.)--University of Washington, 2006. / Vita. Includes bibliographical references (leaves 50-52).

This thesis uses Spline-based model, which was developed by McCulloch, and parsimonious model, which was developed by Nelson-Siegel, to estimate the yield curves of zero-coupon bonds in Turkey. In this thesis, we construct the data by using Turkish secondary government zero-coupon bond data, which contain the data from January 2005 to June 2005. After that, relative performances of models are compared using in-sample goodness of fit. As a result, we see that performance of McCulloch model in fitting yield is better than that of Nelson-Siegel model.

This report investigates the relationship between the yield volatility and the price volatility in the Swedish market. The method given in our report can be used to analyze any market with appropriate data set. We have used a time-series data of interest rate yield curves from Swedish government bonds. The curves are bootstrapped from the bills and bonds. The linear interpolation on these curves results in the nodes i.e. 1Y, 2Y,..., 10Y. We also need prices for instruments. A good choice is to use the synthetic government bonds namely SE GVB 2Y, SE GVB 5Y, and SE GVB 10Y. They are issued every day with maturity 2, 5, and 10 years. We also use the time-series of these bonds. These bonds have a yearly coupon of 6%. We can get zero-coupon values of these bonds by stripping their coupons using the interest rate yield curves. We have time-series data of zero-coupon prices with maturities 2, 5, and 10 years and time-series data of interest rates with the same tenors. We can use our data to calculate their respective volatilities to investigate how they are related to each other.

Forward rates and futures rates are conceptually identical in theory. In previous studies, the term structure has been used to demonstrate that there are synchronous changes among different maturities of coupon and zero-coupon bonds. Evidence has also been found that the magnitude of these synchronous changes is inversely related to the time to maturity. This study uses the Anderson-Leies synthetic zero-coupon yield curve from Caroline Leies' study of the Term Structure a/Zero-Coupon and Coupon Bonds. The term structure of the synthetic zero-coupon bonds is used to extract the "clean" implied forward rates embedded in its yield curve to be compared to the explicit futures rates of the Eurodollar. The evidence in this study suggests that the implied forward rates of the adjusted Anderson-Leies synthetic zero-coupon yield curve are not identical to the Eurodollar Futures rates. The adjusted forward rates were found, on average, to be less than the corresponding futures rates, suggesting that a risk premium is embodied in the Eurodollar futures rates. However, the adjusted forward rates are known to possess significant measurement errors that were unable to be corrected for, but whose possible sources are noted and explained. / Master of Arts

Empirical evidence indicates that the volatility in asset prices is not constant, but varies over time. However, many simple models for asset pricing rest on an assumption of constancy. In this thesis we analyse the zero-coupon bond price under a two-factor Vasicek model, where both the short rate and its volatility follow Ornstein-Uhlenbeck processes. Yield curves based on the two-factor model are then compared to those obtained from the standard Vasicek model with constant volatility. The simulated yield curves from the two-factor model exhibit "humps" that can be observed in the market, but which cannot be obtained from the standard model. / Det finns empiriska bevis som indikerar att volatiliteten i finansiella marknader inte är konstant, utan varierar över tiden. Dock så utgår många enkla modeller för tillgångsprisättning från ett antagande om konstans. I det här examensarbetet analyserar vi priset på nollkupongobligationer under en stokastisk Vasicekmodell, där både den korta räntan och dess volatilitet följer Ornstein-Uhlenbeck processer. De räntekurvor som tas fram genom två-faktormodellen jämförs sedan med de kurvor som erhålls genom den enkla Vasicekmodellen med konstant volatilitet. De simulerade räntekurvorna från två-faktormodellen uppvisar "pucklar" som kan urskiljas i marknaden, men som inte kan erhållas genom standardmodellen.

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.

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))

In this study, four frequently used yield curve construction methods are evaulated on a set of metrics with the aim of determining which method is the most suitable for estimating yield curves from European zero rates. The included curve construction methods are Nelson-Siegel, Nelson-Siegel-Svensson, cubic spline interpolation and forward monotone convex spline interpolation. We let the methods construct yield curves on multiple sets of zero yields with different origins. It is found that while the interpolation methods show greater ability to adapt to variable market conditions as well as hedge arbitrary fixed income claims, they are outperformed by the parametric methods regarding the smoothness of the resulting yield curve as well as their sensitivity to noise and perturbations in the input rates. This apart from the Nelson-Siegel method's problem of capturing the behavior of underlying rates with a high curvature. The Nelson-Siegel-Svensson method did also exhibit instability issues when exposed to perturbations in the input rates. The Nelson-Siegel method and the forward monotone convex spline interpolation method emerge as most favorable in their respective categories. The ultimate selection between the two methods must however take the application at hand into consideration due to their fundamentally different characteristics. / I denna studie utvärderas fyra välanvända metode för att konstruera yieldkurvor på ett antal punkter. Detta med syfte att utröna vilken metod som är bäst lämpad för att estimera yieldkurvor på Europeiska nollkupongräntor. Metoderna som utvärderas är Nelson-Siegel, Nelson-Siegel-Svensson, cubic spline-interpolering samt forward monotone convex spline-interpolering. Vi låter metoderna estimera yieldkurvor på flera sammansättningar nollkupongräntor med olika ursprung. Vi ser att interpoleringsmetoderna uppvisar en större flexibilitet vad gäller att anpassa sig till förändrade marknadsförutsättningar samt att replikera godtyckliga ränteportföljer. När det gäller jämnhet av yieldkurvan och känsligheten för brus och störningar i de marknadsräntor som kurvan konstrueras utifrån så presterar de parametiska metoderna däremot avsevärt bättre. Detta bortsett från att Nelson-Siegel-metoden hade problem att fånga beteendet hos nollkupongräntor med hög kurvatur. Vidare hade Nelson-Siegel-Svensson-metoden problem med instabilitet när de underliggande marknadsrentorna utsattes för störningar. Nelson-Siegen-metoden samt foward monotone convex spline-interpolering visade sig vara bäst lämpade för att konstruera yieldkurvor på de Europeiska marknaderna av de utvärderade metoderna. Vilken metod av de två som slutligen bör användas behöver bedömas från fall till fall grundat i vilken tillämpning som avses.