One of the financial risks an agent has to deal with is market risk. Market risk is caused by the uncertainty attached to asset values. There exit various measures trying to model market risk. The most widely accepted one is Value-at- Risk. However Value-at-Risk does not encourage portfolio diversification in general, whereas a consistent risk measure has to do so. In this work, risk measures satisfying these consistency conditions are examined within theoretical basis. Different types of coherent and convex risk measures are investigated. Moreover the extension of coherent risk measures to multiperiod settings is discussed.

In this thesis we mainly focused on the usage of the Conditional Value-at-Risk (CVaR) in risk management and on the pricing of the arithmetic average basket and Asian options in the Black-Scholes framework via a new log-normal sum approximation method. Firstly, we worked on the linearization procedure of the CVaR proposed by Rockafellar and Uryasev. We constructed an optimization problem with the objective of maximizing the expected return under a CVaR constraint. Due to possible intermediate payments we assumed, we had to deal with a re-investment problem which turned the originally one-period problem into a multiperiod one. For solving this multi-period problem, we used the linearization procedure of CVaR and developed an iterative scheme based on linear optimization. Our numerical results obtained from the solution of this problem uncovered some surprising weaknesses of the use of Value-at-Risk (VaR) and CVaR as a risk measure. In the next step, we extended the problem by including the liabilities and the quantile hedging to obtain a reasonable problem construction for managing the liquidity risk. In this problem construction the objective of the investor was assumed to be the maximization of the probability of liquid assets minus liabilities bigger than a threshold level, which is a type of quantile hedging. Since the quantile hedging is not a perfect hedge, a non-zero probability of having a liability value higher than the asset value exists. To control the amount of the probable deficient amount we used a CVaR constraint. In the Black-Scholes framework, the solution of this problem necessitates to deal with the sum of the log-normal distributions. It is known that sum of the log-normal distributions has no closed-form representation. We introduced a new, simple and highly efficient method to approximate the sum of the log-normal distributions using shifted log-normal distributions. The method is based on a limiting approximation of the arithmetic mean by the geometric mean. Using our new approximation method we reduced the quantile hedging problem to a simpler optimization problem. Our new log-normal sum approximation method could also be used to price some options in the Black-Scholes model. With the help of our approximation method we derived closed-form approximation formulas for the prices of the basket and Asian options based on the arithmetic averages. Using our approximation methodology combined with the new analytical pricing formulas for the arithmetic average options, we obtained a very efficient performance for Monte Carlo pricing in a control variate setting. Our numerical results show that our control variate method outperforms the well-known methods from the literature in some cases.

In this study, we show that realized bipower variation which is an extension of realized power variation is an alternative method that estimates integrated variance like realized variance. It is seen that realized bipower variation is robust to rare jumps. Robustness means that if we add rare jumps to a stochastic volatility process, realized bipower variation process continues to estimate integrated variance although realized variance estimates integrated variance plus the quadratic variation of the jump component. This robustness is crucial since it separates the discontinuous component of quadratic variation which comes from the jump part of the logarithmic price process. Thus, we demonstrate that if the logarithmic price process is in the class of stochastic volatility plus rare jumps processes then the difference between realized variance and realized bipower variation process estimates the discontinuous component of the quadratic variation. So, quadratic variation of the jump component can be estimated and jump detection can be achieved.

Exchange rate forecasting is hard issue for most of floating exchange rate economies. Studying exchange rate is very attractive matter since almost no model could beat random walk in short run yet. Relative yields and information in relative yield curves are contemporary topics in empirical literature and this study follows Chen and Tsang (2009) who model exchange rate changes with relative factors obtained from Nelson-Siegel (1987) yield curve model and find that relative factor model can forecast exchange rate change up to 2 years and perform better than random walk in short run. Analysis follows the methodology defined by Chen and Tsang (2009) and TL/USD, TL/EUR exchange rate changes are modeled by the relative factors namely relative level, relative slope and relative curvature. Basically, 162 weekly datasets from 09.01.2007 to 16.03.2010 are used and the relative factors for each week are estimated. Afterwards, regression analysis is made and results show that relative level and relative curvature factors are significant up to 4-6 weeks horizon but relative slope does not provide any valuable information for exchange rate prediction in Turkish financial market. Length of forecasting horizon of relative factor model is too short when compared to other exchange rate models. Since it is accepted that exchange rates follow random walk, we provided some tests to compare performance of the model. Similar to the literature, only short run performance of relative factor model is compared to random walk model and concluded that the relative factor model does not provide better forecasting performance in Turkish financial market

In this study, the effects of CBRT monetary policy decisions on the consumer, automobile, housing and commercial loans of the banks during the period from the early of 2004 to the middle of 2011 are examined. In order to perform this study, it is benefited from weekly weighted average loan interest rate data of the banks, which is the data having the highest frequency that could be obtained from the electronic data distribution system of CBRT. Monetary policy instruments of Central Bank may change in the course of time or monetary policy could be executed by more than one instrument. Therefore, as the political interest rate would be insufficient in the calculation of the effect of monetary policy on loan interest rates of the banks, Government Dept Securities&rsquo / premiums are used instead of the political interest rates in this study to make it reflect the policies of central bank more clearly as a whole. Among the Government Dept Securities that have different maturity structure, benchmark bonds that are adapted to the expected political interest rate changes and that react to the unexpected interest rate changes at the high rate (reaction coefficient 0.983) are used. In order to weight the cointegration relation between interest rates, unrestricted error correction model is established and it is determined by Bound Test that there is a long-term relation between each interest rate and interest rate of benchmark bond. After a cointegration relation is determined among the serials, autoregressive distributed lag model is used to determine the level of transitivity and it is determined that monetary policy decisions affect the banking interest rate at 77% level and by 13 weeks delay on average.

This study examines the relationship between the performances of US equity REITs and the market risk premium, SMB, HML, MOM as well as an industry index and a real estate index. The statistical significance of the abnormal returns and the beta coefficients of independent variables are examined. The REITs are categorized in seven groups according to their investment areas and the analysis results are compared. Daily return indexes of US equity REITs are collected for the period between 2005 and 2011. These data are then used to estimate the Capital Asset Pricing Model (CAPM) of Sharpe (1964) and Lintner (1965), the Fama and French&rsquo / s 3-Factor Model (1993) and Carhart&rsquo / s 4-Factor Model (1995). These models are re-estimated by adding an industry and a real estate index. The empirical results show that these added independent variables improve the available models. Additionally, no abnormal return is detected for REITs and their returns have a positive correlation with the SMB and HML factors and a negative correlation with the MOM factor. Therefore,, the REITs are relatively small and have high book-to-market ratios. The negative MOM coefficients indicate that the losers will win and the winners will lose.

There is a little doubt that, for a decade, risk measurement has become one of the most important topics in finance. Indeed, it is natural to observe such a development, since in the last ten years, huge amounts of financial transactions ended with severe losses due to severe convulsions in financial markets. Value at risk, as the most widely used risk measure, fails to quantify the risk of a position accurately in many situations. For this reason a number of consistent risk measures have been introduced in the literature. The main aim of this study is to present and compare coherent, convex, conditional convex and some other risk measures both in theoretical and practical settings.

In this thesis, modelling with L&eacute / vy processes is considered in three parts. In the first part, the general geometric L&eacute / vy market model is examined in detail. As such markets are generally incomplete, it is shown that the market can be completed by enlarging with a series of new artificial assets called &ldquo / power-jump assets&rdquo / based on the power-jump processes of the underlying L&eacute / vy process. The second part of the thesis presents two different methods for pricing European options: the martingale pricing approach and the Fourier-based characteristic formula method which is performed via fast Fourier transform (FFT). Performance comparison of the pricing methods led to the fact that the fast Fourier transform produces very small pricing errors so the results of both methods are nearly identical. Throughout the pricing section jump sizes are assumed to have a particular distribution. The third part contributes to the empirical applications of L&eacute / vy processes. In this part, the stochastic volatility extension of the jump diffusion model is considered and calibration on Standard&amp / Poors (S&amp / P) 500 options data is executed for the jump-diffusion model, stochastic volatility jump-diffusion model of Bates and the Black-Scholes model. The model parameters are estimated by using an optimization algorithm. Next, the effect of additional stochastic volatility extension on explaining the implied volatility smile phenomenon is investigated and it is found that both jumps and stochastic volatility are required. Moreover, the data fitting performances of three models are compared and it is shown that stochastic volatility jump-diffusion model gives relatively better results.