Displaying theses 110 of 396 total
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W. Wang 
Master programme: Stochastics and Financial Mathematics  January 15th, 2018  
Institute: KdVI  Research group: Stochastics and Financial Mathematics  Graduation thesis  Supervisor: dr. B.J.K. Kleijn; dr. R.G. de Vilder 
Do stock prices react fast to the market information? This thesis studies how the financial information is absorbed into stock price after a corporate makes a profit warning public. We use novel estimators to measure the volatility, volume, and spread revealed in the high frequency stock prices. The observed highly volatile prices with small trading volumes upon the market opening implies market opening prices do not fully absorb the information. We also find that small cap stocks with positive profit warning have a persistent upgrade trend, such trend, however, disappears when the profit warning is negative. Moreover, large cap stocks do not exhibit such trend. The last contribution of this thesis is the introduction of the consecutive low volatility period defined as equilibrium, which serves as a general description of information absorbing process. There is moderate variation among small cap and large cap stocks: information needs more time to be absorbed into small cap stock price than large cap stock price. 

Scientific abstract (pdf 1K) Full text (pdf 803K) 
D. Wei 
Master programme: Stochastics and Financial Mathematics  October 30th, 2017  
Institute: KdVI  Research group: Stochastics and Financial Mathematics  Graduation thesis  Supervisor: A.V. (Arnoud) den Boer 

Decision based model selection for the newsvendor problem In this thesis, the performance of a decision based model selection method is studied when it is applied to the newsvendor problem. The DBMS is a model selection method that selects models based on the performance of the decisions derived by the models rather than the goodnessoffit of the underlying demand distribution. The expressions of the expected regret caused by DBMS are derived in the scenario cases where two models are available. The expressions are obtained by firstly computing the distributions of the decision and then calculating the regrets of the two decisions. The robustness measured by the maximum regret of a given decision, is discussed knowing partial information of the underlying model, and the maximum regret is shown to be achieved by a twopoint distribution. The performance of DBMS is illustrated numerically when the underlying model assumes a twopoint distribution. It is shown that DBMS performs better than the purely datadriven approach, based on the empirical distribution of the demands, when the performance is measured in terms of the expected cost. 

Scientific abstract (pdf 1K) For more info or full text, mail to: A.V.denBoer@uva.nl 
N. Disveld 
Master programme: Mathematics  October 25th, 2017  
Institute: UvA / Other  Research group: Kortewegde Vries Institute for Mathematics  Graduation thesis  Supervisor: Jasper Stokman 

Nonsymmetric Interpolation Okounkov Polynomials There exist (non)symmetric interpolation polynomials that are connected to the famous (non)symmetric Macdonald polynomials. With Laurent polynomials, the role of the (non)symmetric Macdonald polynomials is being played by the (non)symmetric Koornwinder polynomials. There exist symmetric interpolation Laurent polynomials that are connected to the symmetric Koornwinder polynomials, we give a new proof of this existence. Also, we give a definition of the nonsymmetric interpolation Laurent polynomials that are connected to the nonsymmetric Koornwinder polynomials and prove their existence. 

Scientific abstract (pdf 1K) For more info or full text, mail to: j.v.stokman@uva.nl 
P. Bongers 
Master programme: Mathematics  October 6th, 2017  
Institute: KdVI  Research group: Stochastics  Graduation thesis  Supervisor: prof. dr. R. Nunez Queija 
Queuing on a continuous circle, a mathematical analysis of a voidavoiding optical fiberloop In this thesis, we consider a node where data packets arrive and have to be processed. A node can only process one job at the time, therefore excess jobs have to be placed in a buffer. For this purpose, an optical fiberloop can be used. This fiberloop creates a small time delay. When the job emerges from the fiberloop, it can be transmitted or transferred into the fiber loop again. We begin our research by showing the relations between the fibermodel and queueing models. We describe the distribution of the queue content, the number of jobs that are in the system in steady state. In earlier literature, the mean and variance of the queue content were obtained. The goal of this master project is to understand this distribution better. We proceed by proving some properties of the model. Because direct analysis of the model is difficult, we present an approximation that makes the analysis of the model considerably easier. We show that the distribution of the number of jobs in the fiberloop for the approximation is very similar to that of the original model, but is much easier to obtain. 

Scientific abstract (pdf 1K) Full text (pdf 752K) 
D. Mitkidou 
Master programme: Stochastics and Financial Mathematics  September 26th, 2017  
Institute: KdVI  Research group: Stochastics and Financial Mathematics  Graduation thesis  Supervisor: Asma Khedher 

Quadratic hedging strategies in affine models This master thesis studies the problem of hedging European style options in incomplete markets. The most celebrated model which is often used for option pricing and hedging is the BlackScholes model. This model imposes certain assumptions which allow to form perfect hedging strategies and therefore the risk involved in trading options is eliminated. The most significant assumption is that volatility is constant over time. However, if we would like to take a more realistic view of the financial world, the latter assumption needs to be relaxed. In the context of this thesis, we consider stochastic volatility models, where the volatility is modelled as a stochastic process. In this class of models perfect hedging strategies do not exist. Our goal is to form such strategies that reduce the risk as much as possible. To approach this problem we use a method called quadratic hedging. Affine stochastic volatility models constitute one subclass of stochastic volatility models. They are of special interest due to their computational tractability which often allows to obtain closedform solutions for pricing several options. This thesis uses the rich structural properties of affine models to obtain semiexplicit formulas for quadratic hedging strategies. 

Scientific abstract (pdf 1K) Full text (pdf 568K) 
P.A. van Reeuwijk 
Master programme: Mathematics  September 15th, 2017  
Institute: KdVI  Research group: Algebraic Geometry  Graduation thesis  Supervisor: Arno Kret 
The LanglandsKottwitz method for the modular curve A moduli space is a space parametrising geometric objects; these are objects of primary interest in algebraic geometry. These spaces, however, are often very complicated. From a moduli space a zeta function can be construced, a complex function that, being an anayltic object, is supposed to be much easier to handle while still containing valuable information on the geometry and arithmetic of the moduli space. For this to work, the zeta function needs to satisfy a number of anaylic properties. We use the approach of Langlands and Kottwitz to work towards understanding the zeta fuction of moduli spaces of elliptic curves: we can use the special properties of these elliptic curves to explicitly count the number of points on their moduli spaces, leading to a better understanding of the properties of the zeta function. 

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I.C. Bodin 
Master programme: Stochastics and Financial Mathematics  August 31st, 2017  
Institute: UvA / Other  Research group: Kortewegde Vries Institute for Mathematics  Graduation thesis  Supervisor: Peter Spreij 
Pricing and Hedging of Mortgage Option This thesis provides different pricing methods for four mortgage options, namely the pipelineoption, the meeneemoption,the LtVoption and rentemiddeling. A theoretical approach is present for each option and also the results of numerical experiments are presented. Common techniques are Monte Carlo, trinomial trees and Lévy theory. Real data is used to calibrate the models to guarantee the most relevant results. These turn out to be in line with the result of the currently used behaviour models in case of European options. American options are differently priced and the bank should be aware of the possible consequences. 

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M.J.M. Derksen 
Master programme: Stochastics and Financial Mathematics  August 29th, 2017  
Institute: KdVI  Research group: Stochastics and Financial Mathematics  Graduation thesis  Supervisor: Peter Spreij 
Pricing of Contingent Convertible Bonds In this thesis different pricing models are studied for the pricing of Contingent Convertible bonds (CoCos). These are special type of bonds, which convert into equity or are written down, when the capital of the issuing bank becomes too low. In this way, outstanding debt is reduced and capital is raised, to strengthen the capital position of the bank. In practice, this conversion is typically triggered by the capital ratio of the issuing bank falling below some threshold or by a regulator calling for conversion. However, in all of the existing pricing models the conversion of CoCos is triggered by a market value, like a stock price, falling below some threshold. In this thesis a model is proposed, in which the market cannot observe the true asset value process, but it only has access to noisy accounting reports, which are only published at discrete moments in time. In this way, the price of CoCos can only be based on the information from the accounting reports, not on the true asset process. 

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I.S. Liesker 
Master programme: Stochastics and Financial Mathematics  August 22nd, 2017  
Institute: KdVI  Research group: Stochastics and Financial Mathematics  Graduation thesis  Supervisor: Peter Spreij 

Affine and quadratic interest rate models: A theoretical and empirical comparison In the financial world people try to speculate about the financial market. There are many variables that are unknown and that one wants to describe by, for example, stochastic models. These models help to get insight in the financial variables and are sometimes even used to predict the future development of the variable in order to do proper investments or protect themselves against risk. The latter, in form of interest rate risk modeling, is studied in this thesis. One of the popular interest rates models is the affine model. Affine models are becoming increasingly popular due to their analytical and computational tractability. Affine processes have a nice pricing formula for multiple financial products. Quadratic processes are, to some extent, an extension of affine models and have similar properties as affine models. This thesis compares these affine and quadratic models on a theoretical and an empirical level. For the theoretical level, the mathematics of affine and quadratic interest rate models is explained. For both affine and quadratic models analytical ('nice') formulas for some financial products are provided using admissible parameters and Riccati equations. Also, using the analytical bond prices, a small empirical comparison is performed where some computational examples are discussed. 

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R.Q. Riksen 
Master programme: Stochastics and Financial Mathematics  August 22nd, 2017  
Institute: KdVI  Research group: Stochastics and Financial Mathematics  Graduation thesis  Supervisor: Peter Spreij 

Using Artificial Neural Networks in the Calculation of Mortgage Prepayment Risk A client with a mortgage loan has the possibility to pay back part of his mortgage before the end of the contract. Because this poses a risk to the bank due to the loss of future interest payments, it is very important to predict the probability that a client will prepay on his mortgage. There are many parameters that can influence these mortgage prepayments in a complicated way. Artificial neural networks are used as approximators. A network consists of many connected nodes, that are grouped into layers. Each node takes a weighted sum of all the input it receives, applies a certain function to it and sends it on to all neurons in the next layer. The key to making a neural network approximate the target function, is to make it `learn' the correct weights. It gets to see a lot of input values and makes predictions. If the prediction was incorrect, all weights are changed a little in the direction that will make the network give a better prediction next time. This way, the network learns by making mistakes. In this thesis at ABN AMRO, we explore how we can use artificial neural networks to predict prepayment behaviour. 

Scientific abstract (pdf 1K) Full text (pdf 1396K) 
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