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Stokastik volatilite altında, gecelik vadeye endeksli swap iskonto yöntemi ile kur opsiyonlarının modellenmesi
This study investigates the time contingent behavior of risk factor USDTRY. Option pricing models Black-Scholes and Heston has been utilized to estimate the behavior. The adjusted Black-Sholes model is the current market practice to model USDTRY risk factor. Market practitioners do not prefer to use constant volatility in the Black-Scholes Model, which violates the model assumption. They instead interpolate the volatility surface from market data of implied volatilities and use them in Black-Scholes Model. However, Heston model admits varying volatilities. The Heston Model adds a dimension to the Black-Scholes model by letting the volatility to be a stochastic process. In this thesis, we have used interpolated volatility surface as a benchmark for testing the results estimated by the Heston Model. Furthermore, while estimating option prices, Overnight-Indexed-Swap (OIS) discounting framework has been governed to achieve risk-free rates. The test results have indicated that Heston stochastic volatility model with OIS discounting offers arbitrage-free pricing with similar computation efficiency to the benchmark.
Faize dayalı türevlerde opsiyon fiyatlaması
The valuation of interest rate derivatives and embedded options in fixed-income securities is crucial for market practitioners. Although there have been many models to price interest rate derivatives, the inconsistency across the assumptions of the models creates difficulty in aggregating interest rate exposures. Besides, the models tend to be applicable to specific cases. In this regard, adaptation of a general methodology to price all interest rate derivatives without making additional assumptions has critical importance. This study is expected to contribute to the literature by providing a general approach that can be applied to any fixed-income security with regular or irregular cash flows using the Vasicek model. The methodology involves four main steps: (i) deriving the closed-form solution for the interest rate derivatives traded in the market, (ii) estimating the Vasicek model parameters, (iii) deriving the exhibit solution for the interest rate derivatives and (iv) plugging the estimated Vasicek model parameters to price the security. This methodology provides a general solution that is applicable to all interest rate derivatives with regular or irregular cash flows. Additionally, it allows aggregation of exposures to different interest rate derivatives and allows the derivation of sensitivities of the option values to the changes in model parameters. Although the study provides empirical evidence for European type of options, it also can be applied to price American or Bermudan type of options as well. Besides, the methodology can be implemented using other interest rate models with desirable properties.
Market mikro yapısının faktörlerinin analizi: Fiyat etkisi, likidite ve oynaklık
First chapter of this thesis is an attempt to model the price impact. It is assumed that the market is not perfectly efficient so that it takes to time to adjust new equilibrium price. Thus, in order to model the price impact, two new concepts are introduced which are market resiliency and speed of price informativeness. It is showed that market resiliency and price impact tend to raise as speed of price information increases which emphasizes the fact that speed of information matters in financial markets and market resiliency is not a phenomenon that can be neglected. In the second chapter, it is tried to stress the importance of the liquidity which is considered as the neglected dimension of the financial risk. To do that, a new approach called Liquidity Augmented Stochastic Volatility with Jump (LASVJ) model is introduced and it is compared with the Stochastic Volatility with Jump (SVJ) model in terms of stability and performance. This analysis includes both simulation and calibration analysis. The simulation results suggest that LASVJ model outperforms SVJ as it has lower bias and Root Mean Square Error. In the calibration part, ten companies listed in Dow-Jones 30 are used and it is found that the estimated probability of default and credit spread with LASVJ model are higher than those with SVJ model. In the third chapter, it is aimed to improve the volatility prediction which included in the financial risk management. As a well-performing volatility prediction sheds light on the uncertainty in the financial market, it is an important task to model it. To this end, GARCH-type models as well as SVR-GARCH. To this end, GARCH-type models as well as SVR-GARCH model are used to model the volatility and the results are compared based on the performance metrics. In part of empirical analysis, finding indicates that SVR-GARCH outperforms the traditional models in predicting volatility and also produce more reliable result in Value-at-Risk estimation.
Tekil Markov olmayan son değerlerli geriye doğru stokastik diferansiyel denklemlerin deterministik vadelerde çözümlerinin süreklilikleri
In this thesis we study a class of Backward Stochastic Differential Equations (BSDE) with superlinear driver process f adapted to a filtration F = fFt; t 2 [0; T]g supporting at least a d dimensional Brownian motion and a Poisson random measure on Rm n f0g in a deterministic time interval [0; T]. The superlinearity of f allows terminal conditions that can take the value +1 with positive probability. Such terminal conditions are called "singular." A terminal condition is said to be Markovian if it is a deterministic function of a Markov process.The first goal of the present thesis is to construct solutions to the class of BSDE we work with when they are coupled with singular non-Markovian terminal conditions. We consider the following class of terminal conditions: 1 = 1 1f 1 Tg + A 1f 1>Tg where 1 is any stopping time with a bounded density in a neighborhood of T and 2 = 1 1AT +A 1Ac T where At, t 2 [0; T] is a decreasing sequence of events adapted to the filtration F that is continuous in probability at T (equivalently, AT = f 2 > Tg where 2 is any stopping time such that P( 2 = T) = 0). In this setting we prove that the minimal supersolutions of the BSDE are in fact solutions, i.e., they are continuous at time T and attain almost surely their terminal values. Let X be a d-dimensional diffusion process driven by the Brownian motion and with strongly elliptic covariance matrix. The second goal of the present thesis is to derive density formulas for the first exit time of X from a time varying domain. The existence of these densities show that such exit times can be used as 1 and 2 to define the terminal conditions 1 and 2: We also discuss the implications of our results in stochastic optimal control.
Enflasyona endeksli tahvillerin ve gömülü deflasyon koruma opsiyonlarının fiyatlanması: Türk tahvil piyasası üzerine analiz
Fixed income securities are financial contracts that provide a stream of cash flows to the investors. Such cash flows are exposed to inflation risk. From the perspective of the lender, the purchasing power of provided cash flows might be subject to erosion in inflationary pressures. Inflation indexed bonds issued in a way that to hedge this risk and provide real return to the bond holder. UK issued first inflation indexed bonds as sovereign in 1981. Then, developed countries such as US, Canada, France, Germany, and emerging market countries such as Turkey, Brazil, Mexico had high interest in issuing these bonds. The principal and coupon payments of these bonds are linked to the changes in the reference price index. Inflation indexed bonds might be issued as plain, which excludes any protection against deflation. On the other hand, bonds might be issued with deflation protection (put) option embedded since bond cash flows will be less than the nominal value in a deflationary economic environment. Deflation protection might cover only principal value as in TIPS issued by US or both principal and coupon payments as inflation indexed bonds issued by Turkish Treasury. This thesis aims to price deflation protection option premium in Turkish bond market by decomposing bond structure into plain and option components. First, we review the Jarrow-Yildirim model under the HJM framework and the analytical formulas for derivative prices available in that model. Then, we use historical bond market data to estimate model parameters and the price of the embedded deflation protection option. Finally, we examine historical course of this premium for bonds with different characteristics and inflation expectations.
İkinci mertebeden market hacimli almgren-chriss modelinin özel fonksiyonlar yardımıyla çözümü
One of the current topics of research in mathematical finance is the scheduling of buy or sell orders to liquidate a position. A well-known framework for this problem is the one proposed by Almgren and Chriss that poses the problem as the maximization of the expected utility of the final terminal wealth. In the simplest formulation of the problem the market trading volume is taken as a constant. Under this and other assumptions an optimal trading curve can be computed in terms of the sinh function. This study aims to consider the same model under the assumptions that the market trading volume is an affine function of time, i.e, V_t = at+b and a quadratic function of time i.e, V_t = at^2+bt+c. A solution of the differential equations arising from the Almgren Chriss model under these assumptions is given in terms of the Modified Bessel function (for the affine volume curve) and the confluent hypergeometric function (for the quadratic volume curve). We also provide numerical examples on how the optimal trading curve varies with the model parameters a, b and c.
Hibrit makine öğrenme algoritmalarının finansal zaman serileri verileri üzerindeki performansı
Estimating stock indices that reflect the market has been an essential issue for a long time. Although various models have been studied in this direction, historically, statistical methods and then various machine learning methods have to introduced artificial intelligence into our lives. Related literature shows that neural networks and treebased models are mostly used. In this direction, in this thesis, four different models are examined. The first one is the most preferred neural network method for financial data called LSTM, and the second one is one of the most preferred tree-based models called XGBoost, and the third and the fourth models are the hybridizations of LSTM and XGBoost. Besides, these models have been applied to the total of nine stock market indexes, three from European markets, three from Asian and three from American markets, and the model that gives the best results is determined according to the Mean Absolute Scaled Error (MASE) evaluation criteria.
Yüksek frekanslı verilerle gün içi fiyat geri dönüşüm hareketleri: BIST100 endeksi üzerine bir uygulama
Investors are willing to exploit opportunities to earn abnormal profits. Event study methodology has received considerable attention to catch these opportunities. However, the literature dealing with short-term reactions to large price movements is quite small regarding emerging markets because of difficulties in collecting intraday dataset. In this thesis, we contribute to the literature by providing evidence about the existence of overreaction and intraday reversal effect over a 13-year period from an emerging market. The Istanbul Stock Exchange National 100 Index XU100 (BIST 100) is chosen for the analyses. The event set includes the days that experience price changes exceeding a prespecified threshold at the market open, and hypotheses of the results are tested using various statistical tests. The results document that overreaction in the market lasts only for a few minutes, and reversal happens after the second minute of the trading day. Additionally, our long-term investigation shows evidence in favor of major magnitudes of reversal as threshold levels rise, consistent with the previous findings in reversal literature.
Zaman serisi verileri için hibrit dalgacık-sinir ağı modelleri
The thesis aims to combine wavelet theory with nonlinear models, particularly neural networks, to find an appropriate time series model structure. Data like financial time series are nonstationary, noisy, and chaotic. Therefore using wavelet analysis helps better modeling in the sense of both frequency and time. S&P500 (^GSPC) and NASDAQ (^IXIC) data are divided into several components by using multiresolution analysis (MRA). Subsequently, each part is modeled by using a suitable neural network structure. In this step, the design of the model is formed according to the pattern of the subseries. Then predictions of each subseries are combined. The combined prediction result is compared to the original time series's prediction result using only a nonlinear model. Moreover, wavelets are used as an activation function for LSTM networks to form a hybrid LSTM-Wavenet model. Furthermore, the hybrid LSTM-Wavenet model is fused with MRA as a proposed method. In brief, it is studied whether using MRA and hybrid LSTM-Wavenet model decreases the loss or not for both S&P500 and NASDAQ data. Four different modeling methods are used: LSTM, LSTM+MRA, hybrid LSTM-Wavenet, hybrid LSTMWavenet+MRA (the proposed method). Results show that using MRA and wavelets as an activation function together decreases error values the most.
Yüksek frekanslı işlemlerde optimal piyasa yapıcılığı modelleri
In this thesis, we aim to develop optimal trading strategies in a limit order book for high-frequency trading by stochastic control theory. First, we address for evolving optimal prices where the underlying asset follows the Heston stochastic volatility model including jump components to explore the effect of the arrival of the orders. The goal of the market maker is to maximize her expected return while controlling the inventories where the remaining is charged with a liquidation cost. Two types of utility functions are considered: quadratic and exponential with a risk averse degree. Then, we study on a model considering an underlying asset with jumps in stochastic volatility. We derive the optimal quotes for both models under the assumptions. For numerical simulations, we apply finite differences and linear interpolation as well as extrapolation methods to obtain a solution of the related Hamilton-Jacobi-Bellman (HJB) equation. We demonstrate the risk metrics of the models including profit and loss distribution (PnL), standard deviation of PnL and Sharpe ratio which play important roles for the trader to make decisions on the strategies in high-frequency trading. Moreover, we provide the comparisons of the strategies with the existing ones. As a real data application, we conduct our simulations for the developed strategies in this thesis on a high-frequency data of Borsa Istanbul (BIST). For this purpose, we first estimate the parameters of each model and then perform the numerical experiments on the optimal quotes. Furthermore, we provide the applications on global stocks in order to see that the models are applicable, reasonable, and profitable also for the developed markets. Lastly, we take into account of the optimal market making models with stochastic latency impact. We contribute to this study by providing the numerical experiments with an artificial data. Finally, the thesis ends up with a conclusion and future research directions.
Yenilenebilir enerji kaynaklarına göre elektrik endüstrisinde optimum kapasite tahsisi: ABD örneği
Electricity generation cost and environmental effects of electricity generation continue to be among central themes in energy planning. The choice of electricity generation technology and energy source affect the environment through released greenhouse gases and other waste. United States is the worlds second-largest CO2 emitter and electricity consumer. This thesis aims to estimate the optimal capacity expansion of electric power sector in the United States for 2022-2050. We develop a fuzzy multi-objective linear program to minimize cost and environmental effects. In sensitivity analyses, we show how different policies and price evolution may alter the mix. Later on, we examine the effects of the new capacity mix and implied generation on the cost of electricity and emissions. We find that direct modeling of capacity factors give meaningful results. According to this thesis, renewable energy is expected to reach more than 1100 GW installed capacity by 2050. This reduces average cost of electricity generation by more than 70 percent and reduces CO2 emissions by more than 80 percent compared to expected end-2021 levels.
Odaklanma ya da çeşitlendirmenin banka performansı üzerindeki etkisi: Etik yapılanma etkili midir?
Financial institutions pursue a tradeoff model in order to reduce risk and maximize profitability and performance. Ethical practices, like those of any other profit-maximizing firm, must pursue profit. For banks that target sustainable practices, what matters is how they generate profits and whether their practices have harmful social or environmental consequences. The aim of this thesis is to investigate the impact of asset and liability diversification on bank performance by taking into consideration the bank's ethical status, which is measured by the bank's sustainability rating ESG. Fixed Effect Models, Random Effects Models, and Prais-Winsten Regressions are used to test the relationship between diversification and bank performance. The findings of the study suggest that having an asset-focused portfolio impacts a bank's profit performance and riskiness significantly. However, having a higher ESG score and an asset-focused portfolio decreases the impact of asset focus on return on assets and net interest margin. This finding implies that when a bank is rated higher on a compound sustainability measure, it has relatively lower profitability. On the other hand, liability focus has no significant impact on a bank's profitability or riskiness. However, if a bank has a higher ESG score and a liability-focused portfolio then the impact of liability focus on net interest margin and credit risk is increasing. This finding, in return, implies that the level of diversification on the liability side matters mostly for higher-ESG banks.
Markov olmayan tekil son değerli ve rastgele son zamanlı geriye doğru stokastik diferansiyel denklemler için süreklilik problemi
We study a class of nonlinear BSDEs with a superlinear driver process f adapted to a filtration F and over a random time interval [0, S] where S is a stopping time of F. The filtration is assumed to support at least a d-dimensional Brownian motion as well as a Poisson random measure. The terminal condition ξ is allowed to take the value +∞, i.e., singular. Our goal is to show existence of solutions to the BSDE in this setting. We will do so by proving that the minimal supersolution to the BSDE is a so lution, i.e., attains the terminal values with probability 1. We focus on non-Markovian terminal conditions of the following form: 1) ξ1 = ∞·1{τ≤S} and 2) ξ2 = ∞·1{τ>S} where τ is another stopping time. We call a stopping time S solvable with respect to a given BSDE and filtration if the BSDE has a minimal supersolution with terminal vii value ∞ at terminal time S. The concept of solvability plays a key role in many of the arguments. We also use the solvability concept to relax integribility conditions assumed in previous works for continuity results for BSDE with singular terminal conditions for terminal values of the form ∞ · 1{τ≤T} where T is deterministic. We provide numerical examples in cases where the solution is explicitly computable and a basic application in optimal liquidation.
Borsa istanbuldaki imalat firmaları için döviz kuru oynaklığının ve firmaya özgü özelliklerin getiri oranlarına etkisi: Bir CAPM yaklaşımı
This study examines the effects of the exchange rate volatility and the firm-specific features representing the liquidity, profitability, and leverage performance of firms on excess stock returns for the manufacturing firms listed in Borsa İstanbul (BIST) using dynamic panel data model. The exchange rate volatility is modeled by single-regime generalized autoregressive conditional heteroscedasticity (GARCH) models and Markov-switching GARCH (MSGARCH) models. The MSGARCH models show evidence that the evolution of the volatility process is heterogeneous across the different regimes. The principal component analysis method is employed to 8 financial ratios for the purpose of data reduction to identify the principal components that best represent firm-specific features. 4 components are identified and account for 83% of the total variance in the original dataset of 8 financial ratios. Empirical results from the dynamic panel data generalized method of moments (GMM) models imply that more volatile exchange rates are associated with much lower stock returns. The results also suggest that the excess stock returns of manufacturing firms increase with their liquidity, profitability, and leverage.