Uygulamalı Matematik Enstitüsü

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.

CAN (controller area network) için güvenli haberleşme protokolü

The widespread communication of vehicles with each other and road infrastructure has raised concerns about how to ensure network security of the electronic control units (ECUs) in the vehicle. The fact that networks such as the Controller Area Network (CAN), which is commonly used in in-vehicle communications, will also be connected to external networks (e.g. 3G / 4G mobile networks) will allow malicious adversaries to benefit from the vulnerability of the CAN. The authentication of messages of ECUs in the vehicle is required to ensure that in-vehicle communications are secured. However, the cryptographic algorithms and protocols that can be used for this message verification process should be selected considering the real-time communication requirement in the vehicle.

Kriptografide yüksek performanslı sayı kuramsal dönüşümler

Theoretical advances in physics opened up a new window into quantum computation. This window rendered a number of mathematically hard problems unusable for cryptographic applications. For instance, Shor showed that it is possible factor integers by a quantum algorithm efficiently thus rendering the standard public-key encryption scheme RSA insecure. In February 2016, NIST launched a standardization process for post-quantum cryptography algorithms to study the effect of quantum computing on the current generation of cryptographic algorithms and to build the next generation cryptosystems that are resistant to quantum attacks. One type of quantum safe cryptographic systems is based on lattices. In order to improve the performance in lattice based systems, Number Theoretic Transforms (NTT) are used. In this thesis, the performance of NTT in cryptography is studied. First, Peikert's Scheme and its realization BCNS Algorithm and NewHope key encapsulation method is discussed. Next, SWIFFTX hash function that uses NTT as a building block is presented. Finally, an efficient GPU implementation of SWIFFTX hash function is provided. Experimental results indicate almost 10x improvement in speed and 5 Watts decrease in power consumption per 2 16 hashes.

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.

Gerçekleme ataklarına karsı matematıksel tedbırler

Parola tabanlı kimliği doğrulanmış anahtar değişim protokolleri üzerine

Authentication and key agreement protocols play an important role in today's digital world. Key agreement methods mostly mimic Diffie-Hellman key exchange protocol, but unfortunately they are susceptible to man-in-the-middle attacks. Password based authenticated key exchange (PAKE) protocols promise to handle these key agreement and authentication without requiring existence of certificate authorities or trusted third parties. More importantly, PAKE protocols enable agreement on low-entropy passwords rather than high-entropy cryptographic keys shared by only involved parties. Even if PAKE protocols are not widely used in practice, they are already included in IEFT (RFC), ISO security standards and TLS cryptographic suite. In this thesis, by following these recent developments, we first present these PAKE protocols in three forms, namely balanced PAKE protocols, augmented PAKE protocols and password authenticated key retrieval (PAKR) protocols and within both single and multi server settings. Particularly, we revisit EKE, SPEKE, PAK, PPK, J-PAKE, SPAKE, SESPAKE balanced, and SRP, AugPAKE, OPAQUE, B-SPEKE augmented protocols. Then, we summarize security attacks to these protocols. Afterwards, detailed explanations of the attacks against these protocols are given. We further present current state of the art for PAKE protocols. Finally, we draw attention to possible extensions for PAKE protocols and state currently open questions about the subject.

Hafif siklet kriptografi üzerine bir çalışma

Technology is evolving rapidly and with technology, the internet is also changing. People used to use internet to connect to each other. But with the changes in recent years, the internet is starting to be used more to connect devices to each other. These devices can range from powerful computing devices, such as desktop computers and tablets, to resource contrained devices, such as RFID tags and sensor networks. When it comes to these constrained devices, conventional cryptographic algorithms fail to provide necessary security and performance. Therefore, specific algorithms, designed with the limitations of constrained devices in mind, called lightweight algorithms are needed. For this reason, NIST has started a Lightweight Cryptography Project to standardize lightweight algorithms. In this thesis, we first explain what lightweight cryptography is, along with its target devices and performance metrics and give two examples of lightweight algorithms, block cipher PRESENT and stream cipher TRIVIUM . After that, we summarize the Lightweight Cryptography Project and give its timeline. Lastly, we talk about ASCON , one of the second round algorithms of the Lightweight Cryptography Project.

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.

Simetrik olmayan matrisler için spektral bölümlemeyi yeniden değerlendirme

Parallel solutions to scientific problems having graph representation require efficient tasks and partitioning data. In this thesis, various parallel graph partitioning algorithms are studied. While these algorithms are applicable to both directed and undirected graphs, we focus on the directed case whose matrix representations are sparse and unsymmetric arising in linear system of equations representing various application domains such as computational fluid dynamics and thermal problems. Strategies inspected in this study are ParMETIS with the Multilevel Kernighan-Lin algorithm and the spectral partitioning algorithm with k-means clustering (SPEC) as well as the recursive spectral partitioning algorithm in CHACO. We have implemented SPEC in C programming language using PETSc and SLEPc libraries, whereas CHACO and ParMETIS are called from PETSc. Weighted partitioning is done under the consideration of the edge weights of the graph. SPEC is compared with the libraries only when the unweighted partitioning is made due to the limitations of the libraries for weighted partitioning. Hence, for weighted partitioning, only various eigensolver tolerances in SLEPc are studied in terms of the edge-cut and partitioning time. Another study is performed for the spectral partitioning algorithm based on eigensolver tolerance used with the k-means algorithm in MATLAB. The comparison is based on the quality of the partitioning (edge-cut and partition imbalance) and the number of iterations. The quality of partitioning is determined by the edge-cut and the load imbalance, which could be based on the edge and vertex imbalance ratios of partitions depending on the application. Since the adjacency matrix of a graph is structurally symmetric, the eigenvalue problem can only be solved approximately when the matrix is unsymmetric. Thus, only approximate results are provided in this study. It is deduced that using SPEC performs better than the existing software libraries when the number of cut edges is compared in unweighted partitioning of unsymmetric matrices.