Affine term structure models (ATSMs) are one set of popular models for yield curve modeling. Given that the models forecast yields based on the speed of mean reversion, under what circumstances can we distinguish one ATSM from another? The objective of my dissertation is to quantify the benefit of knowing the “true” model as well as the cost of being wrong when choosing between ATSMs. In particular, I detail the power of out-of-sample forecasts to statistically distinguish one ATSM from another given that we only know the data are generated from an ATSM and are observed without errors. My study analyzes the power and size of affine term structure models (ATSMs) by evaluating their relative out-of-sample performance. Essay one focuses on the study of the oneactor ATSMs. I find that the model’s predictive ability is closely related to the bias of mean reversion estimates no matter what the true model is. The smaller the bias of the estimate of the mean reversion speed, the better the out-of-sample forecasts. In addition, my finding shows that the models' forecasting accuracy can be improved, in contrast, the power to distinguish between different ATSMs will be reduced if the data are simulated from a high mean reversion process with a large sample size and with a high sampling frequency. In the second essay, I extend the question of interest to the multiactor ATSMs. My finding shows that adding more factors in the ATSMs does not improve models' predictive ability. But it increases the models' power to distinguish between each other. The multiactor ATSMs with larger sample size and longer time span will have more predictive ability and stronger power to differentiate between models.

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.

This thesis applies the concept of cost e ciency to the design of executive compensation. In a classical Black-Scholes framework, we are able to express the cost e cient counterpart of the Asian Executive Option explicitly, and design a payo that has the same distribution as the Asian Executive Indexed Option but comes at a cheaper price. The cost e cient counterpart of the latter option is not analytically tractable, but we are able to simulate its price. Furthermore, we extend the study of these two types of options in the presence of stochastic interest rates modeled by a Vasicek process. We are able to derive new closedform pricing formulas for these options. A framework for crafting the state price process is introduced. From here, an explicit expression for the state process is given and its distribution is derived. Using the pricing formulas and the state price process, we are then able to simulate the prices of the corresponding cost e cient counterparts in a stochastic interest rate environment. We conclude with some avenues for future research.

Inflation-indexed instruments provide a real return and protect investors from the erosion of the purchasing power of money. Hence, inflation-indexed markets grow very fast day by day. In this thesis, we focus on pricing of the inflation-indexed swaps and swaptions which are the most liquid derivative products traded in the inflation-indexed markets. Firstly, we review the Hull-White extended Vasicek model in the HJM framework. Then, we use this model to price inflation-indexed swaps. Also, pricing of inflation-indexed swaptions is given using Black&rsquo / s market model.

This thesis applies the concept of cost e ciency to the design of executive compensation. In a classical Black-Scholes framework, we are able to express the cost e cient counterpart of the Asian Executive Option explicitly, and design a payo that has the same distribution as the Asian Executive Indexed Option but comes at a cheaper price. The cost e cient counterpart of the latter option is not analytically tractable, but we are able to simulate its price. Furthermore, we extend the study of these two types of options in the presence of stochastic interest rates modeled by a Vasicek process. We are able to derive new closedform pricing formulas for these options. A framework for crafting the state price process is introduced. From here, an explicit expression for the state process is given and its distribution is derived. Using the pricing formulas and the state price process, we are then able to simulate the prices of the corresponding cost e cient counterparts in a stochastic interest rate environment. We conclude with some avenues for future research.

In the original Vasicek model interest rates are calculated assuming that volatility remains constant over the period of analysis. In this study, we constructed a stochastic volatility model for interest rates. In our model we assumed not only that interest rate process but also the volatility process for interest rates follows the mean-reverting Vasicek model. We derived the density function for the stochastic element of the interest rate process and reduced this density function to a series form. The parameters of our model were estimated by using the method of moments. Finally, we tested the performance of our model using the data of interest rates in Turkey.

In this dissertation, we investigate the spread option pricing problem with stochastic interest rate. First, we will review the basic concept and theories of stochastic calculus, give an introduction of spread options and provide some examples of spread options in different markets. We will also review the market efficiency theory, arbitrage and assumptions that are commonly used in mathematical finance. In Chapter 3, we will review existing spread pricing models and term-structure models such as Vasicek Mode, and the Heath-Jarrow-Morton framework. In Chapter 4, we will use the martingale approach to derive a partial differential equation for the price of the spread option with stochastic interest rate. In Chapter 5, we will study the spread option numerically. We will conclude this dissertation with ideas for future research.

This thesis deals with the management of the fund of alternative investments with an emphasis on photovoltaic projects in the Czech Republic. The main objective is to evaluate whether, after numerous legislative changes, these projects continue to be an attractive investment alternative. The impact of legislative changes on the economy and efficiency of the projects were analyzed for fictitious projects using static and dynamic methods of investment evaluation. The analysis showed that if there was knowledge of the additional cost burden resulting from changes in legislation, then none of the evaluated projects would have been implemented. In general, changes have had the most significant impact on projects that initially appeared to be most effective. In terms of size, restrictions affected mainly smaller projects. Overall, there was a relative alignment of return. For projects with higher levels of debt, an additional cost burden could be liquidational. Then the portfolio of alternative investment fund was created, which consists of assets of two alternative projects evaluated before. This led to evaluation, whether, despite charged fees but a lower tax rate, the investment through the fund is more favorable compared to an own special purpose company. Due to the small size of the fund the hypothesis of fund being more effective mean of administration, was not confirmed.

The subject of this thesis are selected interest rate models and valuation of interest rate derivatives, especially interest rate options. Time-homogeneous one-factor short rate models, Vasicek and Cox-Ingersoll-Ross, and time-inhomogeneous short rate model, Hull{White, are treated. Heath-Jarrow-Morton framework is introduced as an alternative to short rate models, evolving the entire term structure of interest rates. The short rate models are shown to be special cases of models within the framework. The models are derived using the risk-neutral pricing methodology.

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.