"uuid","repository link","title","author","contributor","publication year","abstract","subject topic","language","publication type","publisher","isbn","issn","patent","patent status","bibliographic note","access restriction","embargo date","faculty","department","research group","programme","project","coordinates"
"uuid:9b62374b-a95a-4e79-8464-c541e50f5bb6","http://resolver.tudelft.nl/uuid:9b62374b-a95a-4e79-8464-c541e50f5bb6","Een algoritme voor het prijzen van Amerikaanse opties met behulp van regressie- en variantie reductietechnieken","Roest, Raoul (TU Delft Electrical Engineering, Mathematics and Computer Science; TU Delft Delft Institute of Applied Mathematics)","Meester, Ludolf (mentor); Delft University of Technology (degree granting institution)","2017","In tegenstelling tot een Europese optie, is de prijs van een Amerikaanse optie vaak niet te berekenen met behulp van standaard analysemethoden. Om toch een optieprijs te kunnen bepalen, wordt er gebruik gemaakt van simulatiemethoden. In stochastische modellen, gebaseerd op zogenoemde arbitragevrije prijsbepalingen, is de optieprijs gelijk aan de verdisconteerde verwachtingswaarde van de maximale opbrengst over alle mogelijke uitoefenmomentenm van de optie onder de risico-neutrale maat. Het uitoefenmoment waarvoor de verdisconteerde verwachte opbrengst maximaal is, wordt gevonden door een optimale uitoefenstrategie te hanteren. Deze uitoefenstrategie kan worden bepaald met behulp van de continueringswaarden die horen bij de optie. Het bepalen van de prijs van een Amerikaanse optie draait om het vinden van de continueringswaarden. Longstaff & Schwartz [2001] veronderstellen dat de continueringswaarden kunnen worden beschreven door een functie. Het algoritme dat zij beschrijven, maakt gebruik van regressietechnieken voor het bepalen van een functiebenadering van de continueringswaardefunctie. Met behulp van deze functiebenadering kan een ondergrens voor de optieprijs benaderd worden. Omdat het evalueren van de optieprijs relatief veel rekentijd kost, willen we dat de gevonden ondergrens ook relatief nauwkeurig is. Dit motiveert het gebruik van variantie reductie methoden. Bolia et al. [2004] beschrijven in hun artikel een methode die gebruik maakt van importance sampling als techniek voor de reductie van de variantie. In een iteratief proces proberen zij een zogenoemde variantie-nul kansmaat te benaderen. Wanneer de optieprijs onder deze kansmaat wordt geëvalueerd, kan de optieprijs met variantie nul worden bepaald. Net als Longstaff & Schwartz [2001] veronderstellen Bolia, Glasserman en Juneja dat zowel de optiewaarde als de continueringswaarden kunnen worden benaderd met een functie. Net als in het algoritme van Longstaff & Schwartz [2001], worden deze functies benaderd aan de hand van regressiemethoden. De optiewaardefunctie kan vervolgens gebruikt worden bij het bepalen van een benadering van de eerder genoemde variantie-nul maat. Met de gevonden benaderde kansmaat kan een nieuwe optiewaardeen continueringswaardefunctie worden benaderd. Intuïtief volgt dat elke iteratie een nauwkeurigere benadering geeft van de continueringswaardefunctie. Wanneer er voldoende iteraties zijn uitgevoerd kan de optieprijs worden geëvalueerd onder de verbeterde strategie. Dit geeft een betere benadering voor de ondergrens van de optieprijs. In het verslag wordt het algoritme van Bolia et al. [2004] behandeld. Het project kent twee voornamelijke doelen. In de eerste plaats is het project gericht op het doorgronden van het algoritme. Hierbij is het de bedoeling dat het algoritme wordt beschreven voor derdejaars bachelor wiskundestudenten. Vanwege de hoeveelheid en ingewikkelde wiskunde achter het algoritme, is er gekozen om alleen de delen wiskunde te behandelen die noodzakelijk zijn voor het begrip van het algoritme. Het tweede doel binnen het project is het algoritme toepassen. Het verslag wordt dan ook afgesloten met een voorbeeld ter illustratie van het algoritme. In de gevonden resultaten treden discrepanties op met eerder gedaan onderzoek. Uit verschillende testen kan echter geen duidelijke fout in de implementatie van het algoritme worden aangewezen.","Option Pricing; American Options; Simulation; Importance Sampling","nl","bachelor thesis","","","","","","","","","","","","","",""
"uuid:12ccda1c-c642-400f-98fa-4b0975dcec98","http://resolver.tudelft.nl/uuid:12ccda1c-c642-400f-98fa-4b0975dcec98","Forecasting the implied volatility surface in risk-management applications","van Dijk, Marcel (TU Delft Electrical Engineering, Mathematics and Computer Science; TU Delft Delft Institute of Applied Mathematics)","Oosterlee, Kees (mentor); Delft University of Technology (degree granting institution)","2017","In risk-management, one typically simulates many states of the market using models that are in line with historical data, also known as real-world models. For example, new regulations require insurance companies to value their position on a 1-year horizon. Insurance companies issue guarantees that need to be valued according to market expectations, instead of historical data. By calibrating option pricing models to market prices or equivalently, the implied volatility surface, one obtains market consistent values for these guarantees. Currently, it is common practice to assume that the parameters of these option pricing models are constant, i.e. the calibrated parameters from time t = 0 are used, as the option prices at t = 1 are unknown. However, empirical data shows that the parameters are not constant and depend on the state of the market. In this research, we propose regression models that predict the calibrated parameters, given a set of market variables such as the VIX index and risk-free interest rates. When these market variables are included in the real-world simulation, one is able to predict the calibrated parameters and consequently the option prices which are in line with the simulated state of the market. By performing a regression we are able to predict the out-of-sample implied volatility surfaces accurately. Moreover, the impact on the Solvency Capital Requirement has been evaluated for different points in time. The impact depends on the initial state of the market and varies from -46% to +52%.","Option Pricing; risk-management; recalibration; implied volatility surface; Heston","en","master thesis","","","","","","","","","","","","Applied Mathematics","",""
"uuid:246714bf-fd09-4b04-90b9-b1a070b3c9a3","http://resolver.tudelft.nl/uuid:246714bf-fd09-4b04-90b9-b1a070b3c9a3","On the Application of Shannon Wavelet Inverse Fourier Techniques: An Extension to Asian Option Valuation and European Option Pricing under the SABR Model","Wagner, Emma (TU Delft Electrical Engineering, Mathematics and Computer Science)","Oosterlee, Kees (mentor); Ortiz Garcia, Antonio (mentor); Cirillo, Pasquale (graduation committee); Delft University of Technology (degree granting institution)","2017","This work is on the extension of the SWIFT method to option pricing problems where the sum of lognormals occurs. The SWIFT method (ShannonWavelet Inverse Fourier Technique) is extended to the valuation of geometric Asian options and arithmetic Asian options with a Lévy process as underlying price process and the valuation of European options under SABR dynamics. In both applications a sum of lognormals (or sum of increments) occurs. The main result in this thesis is the SWIFT-SIA method (SWIFT sinc integral approximation), which is applied to the valuation of arithmetic Asian options as well as to the valuation of European options under the SABRmodel. Within the SWIFT-SIA method the recovery of the probability density function is obtained by an approximation, instead of a numerical integration method, which results in a very fast method compared to an alternative method based on cosine expansions as well as high accuracy in the option values.","Shannon wavelets; Option Pricing; Asian Options; SABR model; Fourier Transform; Levy process","en","master thesis","","","","","","","","","","","","Applied Mathematics","",""
"uuid:a43d3aa4-e824-4145-aa18-3759be4f218a","http://resolver.tudelft.nl/uuid:a43d3aa4-e824-4145-aa18-3759be4f218a","Valuation and Hedging of Correlation Swaps","Draijer, Mats (TU Delft Electrical Engineering, Mathematics and Computer Science)","Oosterlee, Kees (mentor); Cirillo, Pasquale (mentor); van Elderen, Emiel (graduation committee); Ruszel, Wioletta (graduation committee); Delft University of Technology (degree granting institution)","2017","The aim of this thesis is to provide a formula for the value of a correlation swap. To get to this formula, a model from an article by Bossu is inspected and its resulting expression for fair the fair value of a correlation swap is simulated. The Jacobi process will be defined and two discretization schemes will be compared for it. Methods are discussed to make simulations of the Jacobi process as accurate as possible, making sure it crosses its boundaries -1 and 1 as little as possible. It will be shown that a correlation swap can be hedged by dynamically trading variance dispersion trades. The main result of the thesis is a partial differential equation for the fair value of a correlation swap. It will be shown that the expression for the value of a correlation swap obtained by Bossu's model satisfies this partial differential equation.","Correlation; Swaps; Hedging; Option Pricing; Correlation Swaps","en","bachelor thesis","","","","","","","","","","","","","",""
"uuid:029cbbc3-d4d4-4582-8be2-e0979e9f6bc3","http://resolver.tudelft.nl/uuid:029cbbc3-d4d4-4582-8be2-e0979e9f6bc3","Numerical Solutions for the Stochastic Local Volatility Model","van der Weijst, Roel (TU Delft Electrical Engineering, Mathematics and Computer Science; TU Delft Delft Institute of Applied Mathematics)","Oosterlee, Kees (mentor); Cirillo, Pasquale (graduation committee); Fokkink, Robbert (graduation committee); Delft University of Technology (degree granting institution)","2017","This thesis is about pricing European options and forward start options under the Heston LSV model. The impact of conditionally calibrating the Heston parameters on the satisfaction of the Feller condition and thereafter correcting with a local volatility surface is investigated here. The results show that this approach is computationally time efficient and accurate. Efficient numerical approaches for this LSV model, such as the multilevel Monte Carlo method, are also investigated. Furthermore, a comparison of several discretizations schemes for the SV part have been conducted. For the calibration of the local volatility surface, the efficiency of the Particle method and the Bin method are compared. An alternative numerical approach to this problem which builds on these two methods is developed and tested.","multilevel Monte Carlo; Local Stochastic Volatility; Forward Start Option; Option Pricing; Heston; Calibration","en","master thesis","","","","","","","","","","","","Applied Mathematics","",""
"uuid:eb4a8dd4-e024-48d7-9784-4bbecbebe1f1","http://resolver.tudelft.nl/uuid:eb4a8dd4-e024-48d7-9784-4bbecbebe1f1","The Heston model with Term Structure: Option Pricing and Calibration","van der Zwaard, T.","Oosterlee, C.W. (mentor); du Toit, J. (mentor)","2016","This thesis addresses the calibration of the Heston model with term structure (i.e. with piecewise constant parameters) to a set of European option prices from the FX market. Several option pricing methods are discussed and compared, among which the COS method, Lewis' method and the Andersen QE Monte Carlo scheme. Several modifications are proposed in order to improve the practical usability of the COS method in terms of speed, accuracy and robustness. The calibration of the Heston model with term structure is chosen as a benchmarking test-case for comparing several optimization techniques, that are both open-source as well as from licensed products. The performance the optimizers is measured in terms of speed of the calibration. In addition, a simple hedge test using the calibrated model is used as a secondary performance metric. The combined effort of finding the fastest optimization techniques and fastest pricing method has the potential of speeding up daily FX calibrations performed in many financial institutions.","option pricing; foreign exchange (FX) market; COS method; Heston model with term structure; calibration; optimization; benchmarking; hedging","en","master thesis","","","","","","","","2021-08-19","Electrical Engineering, Mathematics and Computer Science","Delft Institute of Applied Mathematics","","Numerical Analysis","",""
"uuid:6dcc68c9-f9f1-4449-8c69-f3b0af263cc4","http://resolver.tudelft.nl/uuid:6dcc68c9-f9f1-4449-8c69-f3b0af263cc4","Radial basis functions for option pricing in insurance liabilities","Schols, E.","Oosterlee, C.W. (mentor); Singor, S.N. (mentor)","2016","This thesis discusses the valuation of embedded options in insurance liabilities using radial basis functions. For insurance companies, the valuation of embedded options is an important topic within risk management. This valuation can become too computationally heavy when nested Monte Carlo simulations are used. To overcome this computational drawback, this thesis proposes an alternative method: the construction of an interpolation function based on radial basis functions. An overview of the interpolation method is presented, along with detailed looks into its features, exploring the topics accuracy, numerical stability, calibration of parameters and extrapolation. Furthermore, a new technique to sample data centers is presented. Starting with a small initial data set, new data centers are sampled iteratively. By doing so, in each iteration the current interpolation can be assessed; new data centers are based on this assessment. The use of such a data-dependent bottom-up sampling procedure is motivated by the computational costs related to constructing data centers; the number of data centers is preferably as low as possible.","numerical; interpolation; radial basis function; option pricing","en","master thesis","","","","","","","","","Electrical Engineering, Mathematics and Computer Science","Numerical Analysis","","Applied Mathematics","",""
"uuid:1bde7f59-a491-4f53-8ac7-ea49a0eff43f","http://resolver.tudelft.nl/uuid:1bde7f59-a491-4f53-8ac7-ea49a0eff43f","Reduction of Computing Time for Numerical Pricing of European Multi-dimensional Options based on the COS Method","Hazenoot, D.","Oosterlee, C.W. (mentor)","2016","Numerical integration methods such as the Fourier-based COS method can be used for effciently and accurately pricing financial products. The COS method can be applied to options on one underlying stock as well as on multiple underlying stocks. However, this method suffers from an exponential increase in computational complexity as the dimensions increase. In this thesis we research how to reduce the computational time, especially for multi-dimensional options. Firstly, we discuss the COS method. Secondly, we program this method in three different languages, namely MATLAB, C and CUDA. Thirdly, we perform numerical tests: MATLAB- and C-code on a CPU and CUDA-code on a GPU. Lastly, we compare some options for the different computing times of these codes.","option pricing; European options; multi-dimensional options; COS method; Fourier-cosine series; Fourier-cosine expansion; Fast Fourier Transform; discrete cosine transform; C; CPU computing; CUDA; GPU computing","en","master thesis","","","","","","","","","Electrical Engineering, Mathematics and Computer Science","Numerical Analysis","","Computational Finance","",""
"uuid:bdb4e885-91d9-431f-9657-d1c51cb270fb","http://resolver.tudelft.nl/uuid:bdb4e885-91d9-431f-9657-d1c51cb270fb","Pricing options on gas under a regime-switching model","Van Tol, L.J.M.","Oosterlee, C.W. (mentor); Vuik, C. (mentor); Fokkink, R.J. (mentor); Van Elderen, E.M. (mentor)","2015","This thesis deals with pricing options on natural gas under a regime-switching model. First of all, a regime-switching model for natural gas is considered. Hereafter, historical gasdata are examined to find a model which fits the data. Next, a system of PDE's is derived in order to price an option under the regime-switching model. Finally, option prices are determined through Monte Carlo simulation. The influence of various parameters on the option price is also investigated.","option pricing; regime-switching; natural gas","nl","bachelor thesis","","","","","","","","","Electrical Engineering, Mathematics and Computer Science","Applied mathematics","","","",""
"uuid:a080360d-9eeb-4b0d-9613-0c736f8769e5","http://resolver.tudelft.nl/uuid:a080360d-9eeb-4b0d-9613-0c736f8769e5","Numerical Pricing of Bermudan Options with Shannon Wavelet Expansions","Maree, S.C.","Oosterlee, C.W. (mentor); Ortiz-Gracia, L. (mentor)","2015","This thesis is about pricing Bermudan options with the SWIFT method (Shannon Wavelets Inverse Fourier Technique). We reformulate the SWIFT pricing formula for European options to improve robustness, which allows us to heuristically select - and test the goodness - of all of the parameters a priori. Furthermore, we propose a simplified version of the SWIFT method, based on the Whittaker-Shannon sampling theory, which is an easy to implement method that posses algebraic convergence in the pricing of European and Bermudan options. The main contribution of this thesis is a new pricing method for Bermudan options by the SWIFT method, for exponential Levy processes using the Fast Fourier Transform. We compare the results of the SWIFT method to those of the COS method.","option pricing; Bermudan options; exponential levy processes; wavelet series approximations; Shannon wavelets; Shannon-Whittaker sampling theory; Fourier transform inversion","en","master thesis","","","","","","","","","Electrical Engineering, Mathematics and Computer Science","Delft Institute of Applied Mathematics","","","",""
"uuid:ca07093c-44f1-40e6-8dc6-f01d9b7f61c8","http://resolver.tudelft.nl/uuid:ca07093c-44f1-40e6-8dc6-f01d9b7f61c8","Arbitrage-free methods to price European options under the SABR model","Van der Have, Z.","Oosterlee, C.W. (mentor); Dijkstra, T.P.T. (mentor)","2015","In this thesis we discuss several methods to price European options under the SABR model. In general, methods given in literature are not free of arbitrage and/or inaccurate for long maturities. This led to the development of a new pricing approach. We extend the BCOS method from one dimension to two dimensions. This extension is necessary for application of a simplification of the BCOS method, the DCOS method, to the SABR model. In this pricing method we use the characteristic function of the discrete forward process and the Fourier-based COS method. It is possible to price European options under the SABR model for multiple strikes in one computation with the DCOS method. Besides valuing European options, we can also price Bermudan and discretely monitored barrier options with this pricing approach.","option pricing; SABR; Fourier cosine expansion method; BCOS","en","master thesis","","","","","","","","","Electrical Engineering, Mathematics and Computer Science","Mathematics and Computer Science","","","",""
"uuid:ea39f04d-eec3-4957-a009-ab9a0a00a935","http://resolver.tudelft.nl/uuid:ea39f04d-eec3-4957-a009-ab9a0a00a935","Hardware Acceleration of Monte-Carlo Integration in Finance","De Jong, M.D.","Bertels, K. (mentor); Thomas, D. (mentor); Sima, V. (mentor)","2014","This thesis describes FPGA-accelerated Monte-Carlo integration using adaptive stratified sampling. Monte-Carlo integration can be used to determine the value of integrals that have no closed form solution. In this work, the FPGA-accelerated design is used to determine the price of different types of financial options. The considered options are a basket option, an Asian option and a barrier option. Stratified sampling is implemented with the recursive general purpose algorithm MISER. First, a parallel software implementation of MISER is developed. Next, the integrand independent part of the software is moved into reconfigurable hardware. Finally, the different options are priced in FPGAs by developing hardware implementations of the integrand for each option. The integrands are compiled into a deep pipeline, producing one function evaluation per cycle at 150 MHz. The FPGA-accelerated design requires up to 4200 times less execution time to achieve the same accuracy as a software implementation using the GSL library running on an Intel i7-4770 CPU at 3,40 GHz.","FPGA; option pricing; Monte-Carlo; stratified sampling; integration","en","master thesis","","","","","","","","","Electrical Engineering, Mathematics and Computer Science","Microelectronics & Computer Engineering","","Computer Engineering","",""
"uuid:84fe41f1-30f7-45d8-8612-873f25ca9057","http://resolver.tudelft.nl/uuid:84fe41f1-30f7-45d8-8612-873f25ca9057","A numerical method for backward stochastic differential equations with applications in finance.","Huijskens, T.P.","Oosterlee, C.W. (mentor); Ruijter, M.J. (mentor)","2013","This thesis starts by discussing the foundations of mathematical finance and some theoretical results on backward stochastic differential equations. We discuss some examples of these equations in mathematical finance (primarily option pricing) and develop a numerical method that can approximate solutions to these equations. Subsequently, we extend the framework to so called reflected backward stochastic differential equations and extend the numerical method to this new type of equation. This enables us to price a wide range of American options. Finally, we discuss a two-dimensional example and extend the numerical method to cope with this problem. This extension enables the pricing of options on two underlyings and we use the numerical method to price a spread option. In the final section we present the conclusions of this research.","bsde; finance; numerical method; options; backward stochastic differential equation; mathematical finance; options pricing","en","bachelor thesis","","","","","","","","","Electrical Engineering, Mathematics and Computer Science","Applied mathematics","","","",""
"uuid:adda4a26-55fa-4fa2-99b2-3f747a742be6","http://resolver.tudelft.nl/uuid:adda4a26-55fa-4fa2-99b2-3f747a742be6","Valuation of transmission capacity rights; an option pricing approach with volatility estimation using Garch models for the France Spain case","Tamayo Holguin, J.P.","Rodilla Rodríguez, P. (mentor)","2012","Transnational transmission presents a possible source of income for power producers and a way to decrease costs for consumers. The difference in neighboring countries' market prices encourages traders to profit from it by selling cheaper electricity in the market that has price it higher. Since the parties that own the transmission (TSOs) lines cannot generally participate in the market by regulation, they must allocate the Rights to transport electricity through transnational lines. Parties interested in these rights are usually power producers and other market agents seeking to exploit the rents that come from the price differences. Even though the auctioning of Transmission Rights (TRs) is not motivated by commercial interest, these rights have a commercial value. Then the issue becomes finding a way of valuing the asset according to benefits that it will generate in the future. One problem to deal with, consists in assessing how the agents in the system can hedge against the potential impact of transmission capacity constraints. Two simple ways to hedge against transmission congestion risk are the so-called Financial Transmission Right FTR one hand and the Physical Transmission Right PTR on the other. Both of them could be treated as financial instruments (options). In order to hedge the risk of a PTR an option pricing model can be used. Herein, for the particular case of France and Spain Interconnection was used the Margrabe formula for the exchange option with stochastic volatility by diagonal BEKK models. The model used here has a lot of properties that make it suitable for pricing it as a option, but also has some assumptions that usually don't hold in electricity prices. A more detailed study of the methodology could provide a tailored solution to this valuation problem. The model proposed by Cartea y González-Pedraz (2010), could be extended to the valuation of transmission rights and become able to price the option with zero strike price. This kind of model to derive a closed-form solution that allows for stochastic volatility has proven very difficult.","Transmission rights; Interconection Value; GARCH; Stochastic Volatility; Option Pricing","en","master thesis","","","","","","","Campus only","","Technology, Policy and Management","Policy Analysis","","Engineering and Policy Analysis EMIN","",""
"uuid:163347e5-15f1-43ad-a801-ab926b0a026b","http://resolver.tudelft.nl/uuid:163347e5-15f1-43ad-a801-ab926b0a026b","The Gibbs phenomenon in option pricing methods: Filtering and other techniques applied to the COS method","Versteegh, M.","Oosterlee, C.W. (mentor); Ruijter, M.J. (mentor)","2012","There are situations in which the COS method for option pricing has relatively slow convergence as a consequence of the Gibbs phenomenon. This thesis focusses on various methods to improve the convergence rate of the so called spectral methods. Note that we are not just interested in an accurate recovery, but that we also want to be able to perform fast option pricing, so the computational costs should remain relatively low. After a brief description of a wide range of possibilities some of the more promising methods for our subject are analyzed. After discussing the possible improvement methods, we test them in practical situations such as density recovery and option pricing for some popular financial models.","option pricing; cos method; gibbs phenomenon; filters; iprm; VG density; CIR; Heston; Gegenbauer","en","master thesis","","","","","","","","2012-10-11","Electrical Engineering, Mathematics and Computer Science","Applied mathematics","","Numerical analysis","",""
"uuid:7fed49fb-c6ae-4d12-8257-7e3de240e377","http://resolver.tudelft.nl/uuid:7fed49fb-c6ae-4d12-8257-7e3de240e377","Option pricing with perturbation methods","De Jong, L.","Van Horssen, W. (mentor)","2010","This thesis discusses the use of perturbation theory in the context of financial mathematics, in particular on the use of matched asymptotic expansions in option pricing. Our methods are applied to the ordinary Black-Scholes model for illustration. In this simple example of the Black-Scholes model an exact solution is available, so it is in fact not neccessary to apply the method of asymptotic expansions on this model. However, in case we do apply the method, two artificial layers have to be constructed. Making smart choices for the local variables leads to a transformation of the equations into a heat equation, which can easily be solved. Finally, the results are compared to a Taylor expansion of the exact solution to see that this method is very accurate. After this first instructive model, the method of matched asymptotic expansions is applied to two more advanced models based on papers by Sam Howison and Patrick Hagan et al.. Here, different choices for the scalings are made. The former discusses a fast mean-reverting stochastic volatility model that turns out to have many open ends. In Howison's paper quite a lot of assumptions and simplifications are made. Unfortunately, often the motivation for them is not explicitly given in the paper, and in some cases we even think these assumptions and simplifications are incorrect. The latter examines a new three-parameter stochastic volatility model that successfully prices back the volatility smile as observed in the market nowadays, and that is commonly used. The derivation of this model is the main focus of this thesis. The resulting expression for the implied volatility under the SABR model is obtained by considering the forward and backward Kol-mogorov equations per order in epsilon, making some smart choices for local variables and functions in order to transform them into an equation that looks like a heat equation, which is easier to solve. Recommendations for further investigation on these models would be to consider several different choices for the scalings and see which one works best.","European options; option price; perturbation theory; method of matched asymptotic expansions; implied volatility; financial models; financial derivatives","en","master thesis","","","","","","","","","Electrical Engineering, Mathematics and Computer Science","Applied mathematics","","Computational Science and Engineering (CSE)","",""