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Gregorová, Jitka. "Návrh metodiky výběru pojišťovacích produktů pro fyzické osoby." Master's thesis, Vysoké učení technické v Brně. Ústav soudního inženýrství, 2012. http://www.nusl.cz/ntk/nusl-232639.
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Diploma Thesis called “Methodology Suggestion for the Choosing of Insurance Products for Individuals” deals with Procedure design of selected insurance products for natural persons with regard for their insurance needs and costs. In order to see the differences between clients' real needs and what insurance companies offer I have compared insurance companies statistics with question-forms' results. The question-forms were focused on the needs of clients in insurance. After that I have designed a procedure and algorithm of choice of suitable insurance products for cost optimization for each assurance
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Parker, Bobby I. Mr. "Assessment of the Sustained Financial Impact of Risk Engineering Service on Insurance Claims Costs." Digital Archive @ GSU, 2011. http://digitalarchive.gsu.edu/math_theses/100.
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This research paper creates a comprehensive statistical model, relating financial impact of risk engineering activity, and insurance claims costs. Specifically, the model shows important statistical relationships among six variables including: types of risk engineering activity, risk engineering dollar cost, duration of risk engineering service, and type of customer by industry classification, dollar premium amounts, and dollar claims costs.
We accomplish this by using a large data sample of approximately 15,000 customer-years of insurance coverage, and risk engineering activity. Data sample is from an international casualty/property insurance company and covers four years of operations, 2006-2009. The choice of statistical model is the linear mixed model, as presented in SAS 9.2 software. This method provides essential capabilities, including the flexibility to work with data having missing values, and the ability to reveal time-dependent statistical associations.
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Rasoul, Ryan. "Comparison of Forecasting Models Used by The Swedish Social Insurance Agency." Thesis, Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:mdh:diva-49107.
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We will compare two different forecasting models with the forecasting model that was used in March 2014 by The Swedish Social Insurance Agency ("Försäkringskassan" in Swedish or "FK") in this degree project. The models are used for forecasting the number of cases. The two models that will be compared with the model used by FK are the Seasonal Exponential Smoothing model (SES) and Auto-Regressive Integrated Moving Average (ARIMA) model. The models will be used to predict case volumes for two types of benefits: General Child Allowance “Barnbidrag” or (BB_ABB), and Pregnancy Benefit “Graviditetspenning” (GP_ANS). The results compare the forecast errors at the short time horizon (22) months and at the long-time horizon (70) months for the different types of models. Forecast error is the difference between the actual and the forecast value of case numbers received every month. The ARIMA model used in this degree project for GP_ANS had forecast errors on short and long horizons that are lower than the forecasting model that was used by FK in March 2014. However, the absolute forecast error is lower in the actual used model than in the ARIMA and SES models for pregnancy benefit cases. The results also show that for BB_ABB the forecast errors were large in all models, but it was the lowest in the actual used model (even the absolute forecast error). This shows that random error due to laws, rules, and community changes is almost impossible to predict. Therefore, it is not feasible to predict the time series with tested models in the long-term. However, that mainly depends on what FK considers as accepted forecast errors and how those forecasts will be used. It is important to mention that the implementation of ARIMA differs across different software. The best model in the used software in this degree project SAS (Statistical Analysis System) is not necessarily the best in other software.
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Guleroglu, Cigdem. "Portfolio Insurance Strategies." Master's thesis, METU, 2012. http://etd.lib.metu.edu.tr/upload/12614809/index.pdf.
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The selection of investment strategies and managing investment funds via employing portfolio
insurance methods play an important role in asset liability management. Insurance strategies
are designed to limit downside risk of portfolio while allowing some participation in potential
gain of upside markets. In this thesis, we provide an extensive overview and investigation,
particularly on the two most prominent portfolio insurance strategies: the Constant Proportion
Portfolio Insurance (CPPI) and the Option-Based Portfolio Insurance (OBPI).
The aim of the thesis is to examine, analyze and compare the portfolio insurance strategies in
terms of their performances at maturity, via some of their statistical and dynamical properties,
and of their optimality over the maximization of expected utility criterion.
This thesis presents the financial market model in continuous-time containing no arbitrage
opportunies, the CPPI and OBPI strategies with definitions and properties, and the analysis
of these strategies in terms of comparing their performances at maturity, of their statistical
properties and of their dynamical behaviour and sensitivities to the key parameters during the
investment period as well as at the terminal date, with both formulations and simulations.
Therefore, we investigate and compare optimal portfolio strategies which maximize the expected utility criterion. As a contribution on the optimality results existing in the literature,
an extended study is provided by proving the existence and uniqueness of the appropriate
number of shares invested in the unconstrained allocation in a wider interval.
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Assonken, Tonfack Patrick Armand. "Modeling in Finance and Insurance With Levy-It'o Driven Dynamic Processes under Semi Markov-type Switching Regimes and Time Domains." Scholar Commons, 2017. http://scholarcommons.usf.edu/etd/6675.
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Mathematical and statistical modeling have been at the forefront of many significant advances in many disciplines in both the academic and industry sectors. From behavioral sciences to hard core quantum mechanics in physics, mathematical modeling has made a compelling argument for its usefulness and its necessity in advancing the current state of knowledge in the 21rst century. In Finance and Insurance in particular, stochastic modeling has proven to be an effective approach in accomplishing a vast array of tasks: risk management, leveraging of investments, prediction, hedging, pricing, insurance, and so on. However, the magnitude of the damage incurred in recent market crisis of 1929 (the great depression), 1937 (recession triggered by lingering fears emanating from the great depression), 1990 (one year recession following a decade of steady expansion) and 2007 (the great recession triggered by the sub-prime mortgage crisis) has suggested that there are certain aspects of financial markets not accounted for in existing modeling. Explanations have abounded as to why the market underwent such deep crisis and how to account for regime change risk. One such explanation brought forth was the existence of regimes in the financial markets. The basic idea of market regimes underscored the principle that the market was intrinsically subjected to many different states and can switch from one state to another under unknown and uncertain internal and external perturbations. Implementation of such a theory has been done in the simplifying case of Markov regimes. The mathematical simplicity of the Markovian regime model allows for semi-closed or closed form solutions in most financial applications while it also allows for economically interpretable parameters. However, there is a hefty price to be paid for such practical conveniences as many assumptions made on the market behavior are quite unreasonable and restrictive. One assumes for instance that each market regime has a constant propensity of switching to any other state irrespective of the age of the current state. One also assumes that there are no intermediate states as regime changes occur in a discrete manner from one of the finite states to another. There is therefore no telling how meaningful or reliable interpretation of parameters in Markov regime models are. In this thesis, we introduced a sound theoretical and analytic framework for Levy driven linear stochastic models under a semi Markov market regime switching process and derived It\'o formula for a general linear semi Markov switching model generated by a class of Levy It'o processes (1). It'o formula results in two important byproducts, namely semi closed form formulas for the characteristic function of log prices and a linear combination of duration times (2). Unlike Markov markets, the introduction of semi Markov markets allows a time varying propensity of regime change through the conditional intensity matrix. This is more in line with the notion that the market's chances of recovery (respectively, of crisis) are affected by the recession's age (respectively, recovery's age). Such a change is consistent with the notion that for instance, the longer the market is mired into a recession, the more improbable a fast recovery as the the market is more likely to either worsens or undergo a slow recovery. Another interesting consequence of the time dependence of the conditional intensity matrix is the interpretation of semi Markov regimes as a pseudo-infinite market regimes models. Although semi Markov regime assume a finite number of states, we note that while in any give regime, the market does not stay the same but goes through an infinite number of changes through its propensity of switching to other regimes. Each of those separate intermediate states endows the market with a structure of pseudo-infinite regimes which is an answer to the long standing problem of modeling market regime with infinitely many regimes.
We developed a version of Girsanov theorem specific to semi Markov regime switching stochastic models, and this is a crucial contribution in relating the risk neutral parameters to the historical parameters (3). Given that Levy driven markets and regime switching markets are incomplete, there are more than one risk neutral measures that one can use for pricing derivative contracts. Although much work has been done about optimal choice of the pricing measure, two of them jump out of the current literature: the minimal martingale measure and the minimum entropy martingale measure. We first presented a general version of Girsanov theorem explicitly accounting for semi Markov regime. Then we presented Siu and Yang pricing kernel. In addition, we developed the conditional and unconditional minimum entropy martingale measure which minimized the dissimilarity between the historical and risk neutral probability measures through a version of Kulbach Leibler distance (4).
Estimation of a European option price in a semi Markov market has been attempted before in the restricted case of the Black Scholes model. The problems encountered then were twofold: First, the author employed a Markov chain Monte Carlo methods which relied much on the tractability of the likelihood function of the normal random sequences. This tractability is unavailable for most Levy processes, hence the necessity of alternative pricing methods is essential. Second, the accuracy of the parameter estimates required tens of thousands of simulations as it is often the case with Metropolis Hasting algorithms with considerable CPU time demand. Both above outlined issues are resolved by the development of a semi-closed form expression of the characteristic function of log asset prices, and it opened the door to a Fourier transform method which is derived on the heels of Carr and Madan algorithm and the Fourier time stepping algorithm (5).
A round of simulations and calibrations is performed to better capture the performance of the semi Markov model as opposed to Markov regime models. We establish through simulations that semi Markov parameters and the backward recurrence time have a substantial effect on option prices ( 6). Differences between Markov and Semi Markov market calibrations are quantified and the CPU times are reported. More importantly, interpretation of risk neutral semi Markov parameters offer more insight into the dynamic of market regimes than Markov market regime models ( 7). This has been systematically exhibited in this work as calibration results obtained from a set of European vanilla call options led to estimates of the shape and scale parameters of the Weibull distribution considered, offering a deeper view of the current market state as they determine the in-regime dynamic crucial to determining where the market is headed.
After introducing semi Markov models through linear Levy driven models, we consider semi Markov markets with nonlinear multidimensional coupled asset price processes (8). We establish that the tractability of linear semi Markov market models carries over to multidimensional nonlinear asset price models. Estimating equations and pricing formula are derived for historical parameters and risk neutral parameters respectively (9). The particular case of basket of commodities is explored and we provide calibration formula of the model parameters to observed historical commodity prices through the LLGMM method. We also study the case of Heston model in a semi Markov switching market where only one parameter is subjected to semi Markov regime changes. Heston model is one the most popular model in option pricing as it reproduces many more stylized facts than Black Scholes model while retaining tractability. However, in addition to having a faster deceasing smiles than observed, one of the most damning shortcomings of most diffusion models such as Heston model, is their inability to accurately reproduce short term options prices. An avenue for solving these issues consists in generalizing Heston to account for semi Markov market regimes. Such a solution is implemented and a semi analytic formula for options is obtained.
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Yan, Yuxing. "Three essays on financial intermediation." Thesis, McGill University, 1998. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=35654.
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This dissertation consists of three essays: (I) Double Liability, Moral Hazard and Deposit Insurance Schemes, (II) Contract Costs, Lender Identity and Bank Loan Pricing, and (III) Bank Capital Structure and Differential Lending Behaviour. The first essay proposes to add double liability to a deposit insurance scheme to induce insurees (depository financial institutions) to reveal their true risk types. The second essay looks at the differential lending patterns of American banks versus Japanese banks. The third essay discusses the relationship between the characteristics of a lender and those of the borrower.
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Li, Jiang. "Financial Mathematics Project." Digital WPI, 2012. https://digitalcommons.wpi.edu/etd-theses/263.
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This project describes the underlying principles of Modern Portfolio Theory, the Capital Asset Pricing Model (CAPM), and multi-factor models in detail, explores the process of constructing optimal portfolios using the Modern Portfolio Theory, estimates the expected return and covariance matrix of assets using CAPM and multi-factor models, and finally, applies these models in real markets to analyze our portfolios and compare their performances.
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Dang, Zhe. "Financial Mathematics Project." Digital WPI, 2012. https://digitalcommons.wpi.edu/etd-theses/262.
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This project describes the underlying principles of Modern Portfolio Theory (MPT), the Capital Asset Pricing Model (CAPM), and multi-factor models in detail. It also explores the process of constructing optimal portfolios using Modern Portfolio Theory, as well as estimates the expected return and covariance matrix of assets using the CAPM and multi-factor models. Finally, the project applies these models in real markets to analyze our portfolios and compare their performances.
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Zhou, Junhua, and 周俊华. "To survive and succeed in the risky financial world: applications of mathematical optimization in finance andinsurance." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2010. http://hub.hku.hk/bib/B44407579.
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Lindensjö, Kristoffer. "Essays in financial mathematics." Doctoral thesis, Handelshögskolan i Stockholm, Institutionen för Finansiell ekonomi, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:hhs:diva-2145.
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Ekström, Erik. "Selected Problems in Financial Mathematics." Doctoral thesis, Uppsala University, Department of Mathematics, 2004. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-4574.
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This thesis, consisting of six papers and a summary, studies the area of continuous time financial mathematics. A unifying theme for many of the problems studied is the implications of possible mis-specifications of models. Intimately connected with this question is, perhaps surprisingly, convexity properties of option prices. We also study qualitative behavior of different optimal stopping boundaries appearing in option pricing.
In Paper I a new condition on the contract function of an American option is provided under which the option price increases monotonically in the volatility. It is also shown that American option prices are continuous in the volatility.
In Paper II an explicit pricing formula for the perpetual American put option in the Constant Elasticity of Variance model is derived. Moreover, different properties of this price are studied.
Paper III deals with the Russian option with a finite time horizon. It is shown that the value of the Russian option solves a certain free boundary problem. This information is used to analyze the optimal stopping boundary.
A study of perpetual game options is performed in Paper IV. One of the main results provides a condition under which the value of the option is increasing in the volatility.
In Paper V options written on several underlying assets are considered. It is shown that, within a large class of models, the only model for the stock prices that assigns convex option prices to all convex contract functions is geometric Brownian motion.
Finally, in Paper VI it is shown that the optimal stopping boundary for the American put option is convex in the standard Black-Scholes model.
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Lu, Bing. "Calibration, Optimality and Financial Mathematics." Doctoral thesis, Uppsala universitet, Matematiska institutionen, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-209235.
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This thesis consists of a summary and five papers, dealing with financial applications of optimal stopping, optimal control and volatility. In Paper I, we present a method to recover a time-independent piecewise constant volatility from a finite set of perpetual American put option prices. In Paper II, we study the optimal liquidation problem under the assumption that the asset price follows a geometric Brownian motion with unknown drift, which takes one of two given values. The optimal strategy is to liquidate the first time the asset price falls below a monotonically increasing, continuous time-dependent boundary. In Paper III, we investigate the optimal liquidation problem under the assumption that the asset price follows a jump-diffusion with unknown intensity, which takes one of two given values. The best liquidation strategy is to sell the asset the first time the jump process falls below or goes above a monotone time-dependent boundary. Paper IV treats the optimal dividend problem in a model allowing for positive jumps of the underlying firm value. The optimal dividend strategy is of barrier type, i.e. to pay out all surplus above a certain level as dividends, and then pay nothing as long as the firm value is below this level. Finally, in Paper V it is shown that a necessary and sufficient condition for the explosion of implied volatility near expiry in exponential Lévy models is the existence of jumps towards the strike price in the underlying process.
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Ekström, Erik. "Selected problems in financial mathematics /." Uppsala : Matematiska institutionen, Univ. [distributör], 2004. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-4574.
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SOUZA, GEIZI FERNANDES DE. "FINANCIAL LITERACY AND BASIC FINANCIAL MATHEMATICS IN MIDDLE SCHOOL." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2016. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=27574@1.
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PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIROO letramento financeiro do indivíduo é condição fundamental para seu planejamento financeiro e para a tomada de decisões financeiras conscientes. O conhecimento de Matemática Financeira é uma das plataformas necessárias ao letramento financeiro. Nesse sentido, consideramos que o ensino de Matemática Financeira deve ser iniciado o mais cedo possível, de forma contextualizada e adequada à faixa etária do educando. Neste trabalho apresentaremos propostas pedagógicas e metodológicas para o efetivo ensino de Matemática Financeira Básica no segundo segmento do Ensino Fundamental, baseadas em nossa experiência de trabalho nesta etapa, há mais de dez anos.
The person s financial literacy is a prerequisite for their financial planning and for making conscious financial decisions. The Financial Mathematics knowledge is one of the platforms necessary for financial literacy. In this sense, we consider that the Financial Mathematics teaching should be started as soon as possible, in context and appropriate to the student s age. In this work we present pedagogical and methodological proposals for effective teaching of basic knowledge of Financial Mathematics in Middle School, based on our experience working with this segment for more than ten years.
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Rowley, Jordan M. "The Martingale Approach to Financial Mathematics." DigitalCommons@CalPoly, 2019. https://digitalcommons.calpoly.edu/theses/2014.
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In this thesis, we will develop the fundamental properties of financial mathematics, with a focus on establishing meaningful connections between martingale theory, stochastic calculus, and measure-theoretic probability. We first consider a simple binomial model in discrete time, and assume the impossibility of earning a riskless profit, known as arbitrage. Under this no-arbitrage assumption alone, we stumble upon a strange new probability measure Q, according to which every risky asset is expected to grow as though it were a bond. As it turns out, this measure Q also gives the arbitrage-free pricing formula for every asset on our market. In considering a slightly more complicated model over a finite probability space, we see that Q once again makes its appearance. Finally, in the context of continuous time, we build a framework of stochastic calculus to model the trajectories of asset prices on a finite time interval. Under the absence of arbitrage once more, we see that Q makes its return as a Radon-Nikodym derivative of our initial probability measure. Finally, we use the properties of Q and a stochastic differential equation that models the dynamics of the assets of our market, known as the Ito formula, in order to derive the classic Black-Scholes Equation.
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lin, zhipeng. "Computational Methods in Financial Mathematics Course Project." Digital WPI, 2009. https://digitalcommons.wpi.edu/etd-theses/1192.
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This course project is made up of two parts. Part one is an investigation and implementation of pricing of financial derivatives using numerical methods for the solution of partial differential equations. Part two is an introduction of Monte Carlo methods in financial engineering. The name of course is MA573:Computational Methods in Financial Mathematics, spring 2009, given by Professor Marcel Blais.
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Taptagaporn, Pongphat. "Algorithmic learning from financial predictions." Thesis, London School of Economics and Political Science (University of London), 2017. http://etheses.lse.ac.uk/3514/.
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We study how financial predictions can be used in learning algorithms for problems such as portfolio selection and derivatives pricing, from the perspective of minimizing regret; the worst-case loss (across all possible price paths) against some optimal benchmark model with superior information. Unlike most studies in financial mathematics, we do not make any underlying assumptions beyond the existence of such predictions, so our results are robust in the model-free sense. This thesis consists of three main ideas: 1. Study a portfolio selection model that competes with an optimal static trading strategy (the best fixed strategy in hindsight) using predictions of the optimal portfolio allocation. 2. Study a portfolio selection model that competes (in probability) with an optimal dynamic trading strategy (the best greedy strategy in hindsight) using price predictions of each asset in the portfolio. 3. Derive robust derivative pricing bounds for vanilla options and various exotic derivatives based on price predictions of the underlying asset(s). This work is focused on the mathematical analysis of these models, using techniques from theoretical algorithmic and statistical learning.
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Zhou, Jianping. "On Multinomial Models of Some Financial Instruments /." The Ohio State University, 1996. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487935573770337.
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Scalfano, Denise. "Pricing Financial Derivatives Using Stochastic Calculus." Ohio University Honors Tutorial College / OhioLINK, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=ouhonors1492772147858348.
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Liu, Fangda, and 刘芳达. "Two results in financial mathematics and bio-statistics." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2011. http://hub.hku.hk/bib/B46976437.
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Copp, Jessica L. "Course Summary of Computational Methods of Financial Mathematics." Digital WPI, 2009. https://digitalcommons.wpi.edu/etd-theses/745.
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Most realistic financial derivatives models are too complex to allow explicit analytic solutions. The computational techniques used to implement those models fall into two broad categories: finite difference methods for the solution of partial differential equations (PDEs) and Monte Carlo simulation. Accordingly, the course consists of two sections.
The first half of the course focuses on finite difference methods. The following topics are discussed; Parabolic PDEs, Black-Scholes PDE for European and American options; binomial and trinomial trees; explicit, implicit and Crank- Nicholson finite difference methods; far boundary conditions, convergence, stability, variance bias; early exercise and free boundary conditions; parabolic PDEs arising from fixed income derivatives; implied trees for exotic derivatives, adapted trees for interest rate derivatives.
The second half of the course focuses on Monte Carlo. The following topics are discussed; Random number generation and testing; evaluation of expected payoff by Monte Carlo simulation; variance reduction techniques�antithetic variables, importance sampling, martingale control variables; stratification, low-discrepancy sequences and quasi-Monte Carlo methods; efficient evaluation of sensitivity measures; methods suitable for multifactor and term-structure dependent models.
Computational Methods of Financial Mathematics is taught by Marcel Blais, a professor at Worcester Polytechnic Institute.
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Wang, Chengbo. "Financial Applications of Algorithmic Differentiation." Thesis, Uppsala universitet, Tillämpad matematik och statistik, 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-412943.
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Govender, Kieran. "Statistical arbitrage in South African financial markets." Master's thesis, University of Cape Town, 2011. http://hdl.handle.net/11427/12241.
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Includes abstract.Includes bibliographic references (leaves 34-35).
Engle and Granger’s (1987) co-integrating framework provides a useful method of analyzing the dynamics of non-stationary data in both the short and long run. However, despite its popularity in various areas of research, the application of co-integration to financial data has been limited. This paper provides an example of the application of co-integration in a pairs trading strategy to identify mean reverting spreads. The strategy is implemented with an algorithmic trading setup that models the spread in a state-space form...
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Hugo, Thoursie, and Lucas Fageräng. "Financial Metrics Effect on Companies Performance During COVID19." Thesis, KTH, Skolan för teknikvetenskap (SCI), 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-298075.
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Financial metrics are important tools for managers and investors to assess performance of companies. At the start of 2020, a global pandemic COVID-19 broke out, resulting in bearish markets when mandatory lockdowns were announced. On the 16th of March the Dow Jones Industrial average dropped 13% and the S&P500 north of 12%. The lockdowns all over the world have had massive impact on businesses with layoffs required to stay afloat together with closing of factories. This study aims to establish which, if any, economic metrics have given companies the edge during the pandemic. Through the use of Multiple Linear Regression, models were created for three sectors in the Swedish market, Healthcare, Industry and Consumers Discretionary. From the models there were four different variables found to have correlation to how well companies performed during the pandemic, with different combinations for each sector. These were current ratio for Healthcare and Industry, as well as D/E and ROE for Consumers Discretionary. The study also contains a qualitative study of the models and an evaluation. The evaluation and results did indicate that certain financial metrics had some type of correlation with the Net Income change of a company. Most important on the other hand was that other factors did probably influence the results of a company more than previously mentioned financial metrics.
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Sedman, Robin. "Online Outlier Detection in Financial Time Series." Thesis, KTH, Matematisk statistik, 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-228069.
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In this Master’s thesis, different models for outlier detection in financial time series are examined. The financial time series are price series such as index prices or asset prices. Outliers are, in this thesis, defined as extreme and false points, but this definition is also investigated and revised. Two different time series models are examined: an autoregressive (AR) and a generalized autoregressive conditional heteroskedastic (GARCH) time series model, as well as one test statistic method based on the GARCH model. Additionally, a nonparametric model is examined, which utilizes kernel density estimation in order to detect outliers. The models are evaluated by how well they detect outliers and how often they misclassify inliers as well as the run time of the models. It is found that all the models performs approximately equally good, on the data sets used in thesis and the simulations done, in terms of how well the methods find outliers, apart from the test static method which performs worse than the others. Furthermore it is found that definition of an outlier is very crucial to how well a model detects the outliers. For the application of this thesis, the run time is an important aspect, and with this in mind an autoregressive model with a Student’s t-noise distribution is found to be the best one, both with respect to how well it detects outliers, misclassify inliers and run time of the model.I detta examensarbete undersöks olika modeller för outlierdetektering i finansiella tidsserier. De finansiella tidsserierna är prisserier som indexpriser eller tillgångspriser. Outliers är i detta examensarbete definierade som extrema och falska punkter, men denna definition undersöks och revideras också. Två olika tidsseriemodeller undersöks: en autoregressiv (AR) och en generel au-toregressiv betingad heteroskedasticitet1 (GARCH) tidsseriemodell, samt en hypotesprövning2 baserad på GARCH-modellen. Dessutom undersöks en icke-parametrisk modell, vilken använder sig utav uppskattning av täthetsfunktionen med hjälp av kärnfunktioner3 för att detektera out-liers. Modellerna utvärderas utifrån hur väl de upptäcker outliers, hur ofta de kategoriserar icke-outliers som outliers samt modellens körtid. Det är konstaterat att alla modeller ungefär presterar lika bra, baserat på den data som används och de simuleringar som gjorts, i form av hur väl outliers är detekterade, förutom metoden baserad på hypotesprövning som fungerar sämre än de andra. Vidare är det uppenbart att definitionen av en outlier är väldigt avgörande för hur bra en modell detekterar outliers. För tillämpningen av detta examensarbete, så är körtid en viktig faktor, och med detta i åtanke är en autoregressiv modell med Students t-brusfördelning funnen att vara den bästa modellen, både med avseende på hur väl den detekterar outliers, felaktigt detekterar inliers som outliers och modellens körtid.
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Tegnér, Gustaf. "Recurrent neural networks for financial asset forecasting." Thesis, KTH, Matematisk statistik, 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-229924.
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The application of neural networks in finance has found renewed interest in the past few years. Neural networks have a proven capability of modeling non-linear relationships and have been proven widely successful in domains such as image and speech recognition. These favorable properties of the Neural Network make them an alluring choice of model when studying the financial markets. This thesis is concerned with investigating the use of recurrent neural networks for predicting future financial asset price movements on a set of futures contracts. To aid our research, we compare them to a set of simple feed-forward networks. We conduct further research into the various networks by considering different objective loss functions and how they affect our networks performance. This discussion is extended by considering multi-loss networks as well. The use of different loss functions sheds light on the importance of feature selection. We study a set of simple and complex features and how they affect our model. This aids us in further examining the difference between our networks. Lastly, we analyze of the gradients of our model to provide additional insight into the properties of our features. Our results show that recurrent networks provide superior predictive performance compared to feed-forward networks both when evaluating the Sharpe ratio and accuracy. The simple features show better results when optimizing for accuracy. When the network aims to maximize Sharpe, the complex features are preferred. The use of multi-loss networks proved successful when we consider achieving a high Sharpe ratio as our main objective. Our results show significant improved performance compared to a set of simple benchmarks. Through ensemble methods, we achieve a Sharpe ratio of 1.44 and an accuracy of 52.77% on the test setTillämpningen av neurala nätverk i finans har fått förnyat intresse under de senaste åren. Neurala nätverk har en erkänd förmåga att kunna modellera icke-linjära förhållanden och har bevisligen visat sig användbara inom områden som bild och taligenkänning. Dessa egenskaper gör neurala nätverk till ett attraktivt val av model för att studera finansmarknaden Denna uppsats studerar användandet av rekurrenta neurala nätverk för pre-diktering av framtida prisrörelser av ett antal futures kontrakt. För att underlätta får analys jämför vi dessa nätverk med en uppsättning av enkla framåtkopplade nätverk. Vi dyker sedan djupare in i vår analys genom att jämföra olika målfunktioner för nätverken och hur de påverkar våra nätverks prestation. Vi utökar sedan den här diskussionen genom att också undersöka multi-förlust nätverk. Användandet av flera förlust funktioner visar på betydelsen av vårt urval av attribut från indatan. Vi studerar ett par simpla och komplexa attribut och hur de påverkar vår modell. Det hjälper oss att göra en ytterligare jämförelse mellan våra nätverk. Avslutningsvis så undersöker vi vår modells gradienter för att få en utökad förståelse över hur vår modell agerar med olika attribut. Resultaten visar på att rekurrenta nätverk utpresterar framåtkopplade nät-verk, både i uppgiften att maximera sharpe ration och precision. De enkla attributen visar på bättre resultat när nätverket optimeras för precision. När vi optimerar för att maximera Sharpe ration fungerar de komplexa attributen bättre. Tillämpningen av multi-förlust nätverk visade sig framgångsrik när vårt huvudmål var at maximera sharpe ration. Våra resultat visar på en signifikant ökad prestation av våra nätverk jämfört med ett par enkla benchmarks. Genom ensemble metoder uppnår vi en Sharpe ratio på 1.44 samt en precision på 52.77% på test datan.
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Widegren, Philip. "Deep learning-based forecasting of financial assets." Thesis, KTH, Matematisk statistik, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-208308.
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Deep learning and neural networks has recently become a powerful tool to solve complex problem due to improvements in training algorithms. Examples of successful application can be found in speech recognition and machine translation. There exist relative few finance articles were deep learning have been applied, but existing articles indicate that deep learning can be successfully applied to problems in finance. This thesis studies forecasting of financial price movements using two types of neural networks, namely; feedforward and recurrent networks. For the feedforward neural networks we considered non-deep networks with more neurons and deep networks with fewer neurons. In addition to the comparison between feedforward and recurrent networks, a comparison between deep and non-deep networks will be made. The recurrent architecture consists of a recurrent layer mapping into a feedforward layer followed by an output layer. The networks are trained with two different feature setups, one less complex and one more complex. The findings for non-deep vs. deep feedforward neural networks imply that there does not exist any general pattern whether deep or non-deep networks are preferable. The findings for recurrent neural networks vs. feedforward neural networks imply that recurrent neural networks do not necessarily outperform feedforward neural networks even though financial data in general are time-dependent. In some cases, adding batch normalization can improve the accuracy for the feedforward neural networks. This can be preferable instead of using more complex models, such as a recurrent neural networks. Moreover, there are significant differences in accuracies between using the two different feature setups. The highest accuracy for all networks are 52.82%, which is significantly better than the simple benchmark.Djupa neuronnät har under det senaste årtiondet blivit ett väldigt användarbart verktyg för att lösa komplexa problem, tack vare förbättringar i träningsalgoritmer. Två områden där djupinlärning visat sig väldigt användbart är inom taligenkänning och maskinöversättning. Det finns relativt få artiklar där djupinlärning används inom finans men i de få som existerar finns det tydliga tecken på att djupinlärning skulle kunna appliceras framgångsrikt på finansiella problem. Denna uppsats studerar prediktering av finansiella prisrörelser med framåtkopplade nätverk och rekurrenta nätverk. För de framåtkopplade nätverken kommer vi använda oss av djupa nätverk med färre neuroner per lager och mindre djupa nätverk med fler neuroner per lager. Förutom en jämförelse mellan framåtkopplade nätverk och rekurrenta nätverk kommer även en jämförelse mellan de djupa och mindre djupa framåtkopplade nätverken att göras. De rekurrenta nätverket består av ett rekurrent lager som sedan projicerar på ett framåtkopplande lager följt av ett outputlager. Nätverken är tränade med två olika uppsättningar av insignaler, ett mindre komplext och ett mer komplext. Resultaten för jämförelsen mellan de olika framåtkopplade nätverken indikerar att det inte med säkerhet går att säga om man vill använda sig av ett djupare nätverk eller inte, då det beror på många olika faktorer som tex. variabeluppsättning. Resultaten för jämförelsen mellan de rekurrent nätverken och framåtkopplade nätverken indikerar att rekurrenta nätverk nödvändigtvis inte presterar bättre än framåtkopplade nätverk trots att finansiell data vanligtvis är tidsberoende. Det finns signifikanta resultat där den mer komplexa variabeluppsättningen presterar bättre än den mindre komplexa. Den högsta träffsäkerheten för att prediktera rätt tecken på nästkommande prisrörelse är 52.82% vilket är signifikant bättre än ett enkelt benchmark.
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Sidahmed, Abdelmgid Osman Mohammed. "Mesh free methods for differential models in financial mathematics." Thesis, University of the Western Cape, 2011. http://etd.uwc.ac.za/index.php?module=etd&action=viewtitle&id=gen8Srv25Nme4_3917_1319185202.
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Many problems in financial world are being modeled by means of differential equation. These problems are time dependent, highly nonlinear, stochastic and heavily depend on the previous history of time. A variety of financial products exists in the market, such as forwards, futures, swaps and options. Our main focus in this thesis is to use the numerical analysis tools to solve some option pricing problems. Depending upon the inter-relationship of the financial derivatives, the dimension of the associated problem increases drastically and hence conventional methods (for example, the finite difference methods or finite element methods) for solving them do not provide satisfactory results. To resolve this issue, we use a special class of numerical methods, namely, the mesh free methods. These methods are often better suited to cope with changes in the geometry of the domain of interest than classical discretization techniques. In this thesis, we apply these methods to solve problems that price standard and non-standard options. We then extend the proposed approach to solve Heston' volatility model. The methods in each of these cases are analyzed for stability and thorough comparative numerical results are provided.
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Arnarson, Teitur. "PDE methods for free boundary problems in financial mathematics." Doctoral thesis, KTH, Matematik (Inst.), 2008. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-4777.
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We consider different aspects of free boundary problems that have financial applications. Papers I–III deal with American option pricing, in which case the boundary is called the early exercise boundary and separates the region where to hold the option from the region where to exercise it. In Papers I–II we obtain boundary regularity results by local analysis of the PDEs involved and in Paper III we perform local analysis of the corresponding stochastic representation. The last paper is different in its character as we are dealing with an optimal switching problem, where a switching of state occurs when the underlying process crosses a free boundary. Here we obtain existence and regularity results of the viscosity solutions to the involved system of variational inequalities.QC 20100630
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Huang, Jennifer 1973. "A model of efficiency and trading opportunities in financial markets." Thesis, Massachusetts Institute of Technology, 1996. http://hdl.handle.net/1721.1/39765.
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Savka, Andriy. "Wavelet Transform in Financial Time Series Analysis: Denoising and Forecast." Kent State University / OhioLINK, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=kent1543573160243739.
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Hultquist, Martin. "Examples of Multiscale Aspects of Volatility in Financial Markets." Thesis, Uppsala University, Department of Mathematics, 2007. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-121213.
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Hällman, Ludvig. "The Rolling Window Method: Precisions of Financial Forecasting." Thesis, KTH, Matematisk statistik, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-205595.
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In this thesis we set out to study the prediction accuracy of statistical quantities related to portfolio analysis and risk management implied by a given set of historical data. The considered forecasting procedure rely on rolling-window estimates over varying horizons where the resulting empirical return distributions can be considered the corresponding stationary distributions. By using scenarios generated from a joint interest rate-equity framework the rolling-window method allows to, empirically, study the uncertainty of return statistics as well as risk measures related to market risk. The study shows that, given the chosen models, the method is valid in predicting future statistical quantities related to portfolio return of up to one year. For risk measures, the forecasting uncertainty is found to be too significant and highlights the difficulty in foreseeing extremities of future market movements.I detta examensarbete ämnar vi oss att studera precisionen av predikterade statistiska storheter relaterade till portföljanalys och riskhantering givet en mängd historisk data. Den använda prediktionsmetoden använder sig av rullande fönster estimeringar över varierande horisonter där de resulterande empiriska avkastningsfördelningarna kan ses som de motsvarande stationära fördelningarna. Genom att använda scenarier generade från ett ramverk för räntor och aktier, möjliggör rullande fönster metoden att, empiriskt, studera osäkerheter i skattade avkastnings statistikor och riskmått relaterade till marknads risk. Studien visar, givet de ingående modellerna, att metoden är giltig att använda för prediktering av statistiska storheter relaterade till portföljavkastningar upp till ett år. För riskmått visar sig skattningsosäkerhet vara för stor och belyser svårigheten att förutse extremiteter i framtida marknadsutfall.
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Birch, Jenna. "Modelling financial markets using methods from network theory." Thesis, University of Liverpool, 2015. http://livrepository.liverpool.ac.uk/2028739/.
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This thesis discusses how properties of complex network theory can be used to study financial time series, in particular time series for stocks on the DAX 30. First, we make a comparison between three correlation-based networks: minimum spanning trees; assets graphs and planar maximally filtered graphs. A series of each of these network types is created for the same dataset of time series' of DAX 30 stocks and we consider what information each network can provide about the relationship between the stock prices from the underlying time series. We also analyse two specific time periods in further detail - a period of crisis and a period of recovery for the German economy. Next, we look at the structure and representations of planar maximally filtered graphs and in particular we consider the vertices that form the 3-cliques and 4-cliques [Tumminello et al. (2005)] state '... normalizing quantities are n_s - 3 for 4-cliques and 3n_s - 8 for 3-cliques. Although we lack a formal proof, our investigations suggest that these numbers are the maximal number of 4-cliques and 3-cliques, respectively, that can be observed in a PMFG of n_s elements.' Within this thesis we provide a proof for these quantities and a different construction algorithm. Finally, rather than correlation-based networks, we discuss two relatively new types of networks: visibility graphs and the geometrically simpler horizontal visibility graphs. We review the field's that these networks have already been applied to and consider if this is an appropriate method to apply to financial time series - specifically stock prices. We also consider using horizontal visibility graphs as a method for distinguishing between random and chaotic series within stock price time series.
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Pang, Hong Kui. "New numerical methods and analysis for Toeplitz matrices with financial applications." Thesis, University of Macau, 2011. http://umaclib3.umac.mo/record=b2492157.
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Zhou, Sen Lin. "Geometric Asian option: Geometric Ornstein-Uhlenbeck process." Master's thesis, University of Cape Town, 2013. http://hdl.handle.net/11427/22062.
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Asian options, also known as average value options, are exotic options whose payoffs are dependent on the average prices of the underlying assets over the life of the options. The Asian options are very popular among the market participants when dealing with thinly traded commodities because the average property of the Asian options makes it very difficult to manipulate the payoffs of the options. Another reason for the popularity of Asian options is that they are cheaper than the corresponding portfolio of standard options to hedge the same exposure. The pricing of Asian options has been the subject of continuous studies. In previous studies, Asian options have been priced based on the assumption that the underlying asset follows a geometric Brownian motion. This dissertation, however, assumes that the underlying asset follows a geometric Ornstein-Uhlenbeck process and provides an explicit formula for the geometric Asian options. The geometric Ornstein-Uhlenbeck process is more economically appropriate than the geometric Brownian motion for modelling commodity prices, exchange rates and interest rates due to its mean-reverting property.
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Clur, John-Craig. "Nonparametric smoothing in extreme value theory." Master's thesis, University of Cape Town, 2010. http://hdl.handle.net/11427/10285.
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Includes bibliographical references (leaves 137-138).This work investigates the modelling of non-stationary sample extremes using a roughness penalty approach, in which smoothed natural cubic splines are fitted to the location and scale parameters of the generalized extreme value distribution and the distribution of the r largest order statistics. Estimation is performed by implementing a Fisher scoring algorithm to maximize the penalized log-likelihood function. The approach provides a flexible framework for exploring smooth trends in sample extremes, with the benefit of balancing the trade-off between 'smoothness' and adherence to the underlying data by simply changing the smoothing parameter. To evaluate the overall performance of the extreme value theory methodology in smoothing extremes a simulation study was performed.
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Steyn, Dirk. "Portfolio construction using index regression models." Master's thesis, University of Cape Town, 2008. http://hdl.handle.net/11427/4933.
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Includes bibliographical references (leaves 130-130).In this dissertation we review the Sharpe Index Model and an innovation on this model introduced by Hossain, Troskie and Guo (2005b). These models are extended to the multi index framework. We then empirically investigate the impact of the models on portfolio creation over an extensive data set. Next we extend these models by modelling the regression residuals as ARMA and GARCH(l, 1) processes and investigate the effect on the resulting portfolios. We then introduce the topic of bounded influence regression and apply it to financial data by down weighting extreme returns prior to regression. A new weighting function is introduced in this dissertation and the effects on the efficient frontiers and resulting market portfolios for the chosen set of shares are investigated.
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Munhumwe, Blessing. "The Bates model : Fourier Transform for option pricing under jump-diffusions in the South African market." Master's thesis, University of Cape Town, 2011. http://hdl.handle.net/11427/13042.
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Includes bibliographical references (leaves [51] - 55).The purpose of this study is to price options under jump diffusions using Fourier Transforms and obtain the implied volatility surface from these option prices.
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Van, Straaten Conrad. "Modern portfolio optimization using robust estimation techniques." Master's thesis, University of Cape Town, 2005. http://hdl.handle.net/11427/4943.
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Includes bibliographical references.Rather than following a normal distribution, share returns and market proxies have been shown to follow skewed distributions, with long tails in some cases. In this dissertation various robust estimation techniques are investigated in an attempt to minimise the influence that outliers may have on the estimation and to better estimate the input parameters for the Markowitz and Sharpe portfolio models. The main goal is to ascertain whether or not the input parameters determined, using the robust procedures, yield better results than the Ordinary Least Squares (OLS) procedure.
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Linley, Christopher. "Modelling dependance in collateralied debt obligations with copulas." Master's thesis, University of Cape Town, 2010. http://hdl.handle.net/11427/4903.
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In this paper we provide a review of credit derivatives, and some of the tools used to model them. We give a basic introduction to copulas and how they are used to model the depedence between single name credit derivatives. We then investigate various features of Gaussian and t copula dependence using numerical results obtained from Monte-Carlo simulation.
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Sihlobo, Odwa. "Stochastic time-changed Lévy processes with their implementation." Master's thesis, University of Cape Town, 2014. http://hdl.handle.net/11427/13156.
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Includes bibliographical references.We focus on the implementation details for Lévy processes and their extension to stochastic volatility models for pricing European vanilla options and exotic options. We calibrated five models to European options on the S&P500 and used the calibrated models to price a cliquet option using Monte Carlo simulation. We provide the algorithms required to value the options when using Lévy processes. We found that these models were able to closely reproduce the market option prices for many strikes and maturities. We also found that the models we studied produced different prices for the cliquet option even though all the models produced the same prices for vanilla options. This highlighted a feature of model uncertainty when valuing a cliquet option. Further research is required to develop tools to understand and manage this model uncertainty. We make a recommendation on how to proceed with this research by studying the cliquet option’s sensitivity to the model parameters.
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Knox, Sean D. "Pricing 2-colour rainbows : nonparametric methods using copulae." Master's thesis, University of Cape Town, 2005. http://hdl.handle.net/11427/11778.
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Includes bibliographical references.This paper investigates the use of copulae for non parametric pricing of multivariate contingent claims. Price estimates and no-arbitrage bounds for various types of two-colour rainbow options on the South African equity and bond markets were calculated. Implied marginal risk-neutral distributions were derived nonparametrically from each assets option price spread. This was achieved in a very simple manner by assuming that, for each of the underlying assets in question, a continuum of option prices exist. Cubic splines were used to fit this continuum to the implied volatilities of the actual options available. Two nonparametric copulae were considered: an empirical copula based directly upon the data and a kernel copula derived from a smooth two-dimensional kernel approximation of the historic density function. In addition, various parametric copulae were considered for comparison purposes. The differences between each of these approaches was found to vary from one type of rainbow to another.
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Ramsden, Bevan. "Pricing options in a fuzzy environment." Master's thesis, University of Cape Town, 2008. http://hdl.handle.net/11427/4924.
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Includes abstract.Includes bibliographical references (leaves 114-116).
Although Fuzzy Logic is not new, it is however only since 2004 that an axiomatic theory has been created that has all the desirable effects of Fuzzy Logic. This theory, named Credibility theory was proposed by Dr. Liu. Within this thesis we aim to utilize credibility theory to model the psychological impacts of market participants on European options. Specifically this is done by modifying the approach that was originally taken by Black and Scholes. The Hew model, which is known as the fuzzy drift parameter model, begins by replacing the deterministic drift within Brownian motion with a fuzzy parameter. This fuzzy parameter models the psychological impacts of market participants. Naturally as we are dealing in Chance theory 1 the risk neutral dynamics change from that of Black and Scholes and thus so does the price of European call options.
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Hagspihl, Christoph. "A comparison of three analytical approximations for basket option valuation." Master's thesis, University of Cape Town, 2013. http://hdl.handle.net/11427/18690.
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Three prominent analytical approximations for pricing basket options,by Levy (1992), Ju (2002) and Deelstra et aI. (2004), are tested for performance and accuracy. Sensitivity analysis shows that all three have greater errors in high volatility and long maturity environments, while Deelstra has weaknesses with small correlation and baskets with few stocks. Deelstra and Levy show tendencies to underprice and overprice respectively, while Ju's errors are more consistently around the true price. A mathematical understanding of the three techniques is also developed.
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Damaseb, W. B. "Investigation on the efficient frontier based on CVaR under copula dependence structure with applications to South African JSE stocks." Master's thesis, University of Cape Town, 2005. http://hdl.handle.net/11427/4877.
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Includes bibliographical references.We study the feasihility of using a coherent monetary risk measure, Conditional Value at Risk (CVaR) also known as Expected Shortfall (ES), to optimise a portfolio of South African stocks. Value at Risk (VaR) is not a sub-additive risk measure and therefore does not possess one of the four properties that all coherent risk measures must satisfy. Using copula to describe the dependence structure between the instruments in our portfolio, we implement and backtest a CVaR optimization algorithm and compare the backtested results to those obtained using parametric and non-parametric/Monte Carlo VaR. Finally we optimise the portfolio of stocks and generate an efficient frontier specifying CVaR as the risk measure instead of the portfolio variance traditionally used in Markowitz and CAPM models.
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Ndebele, Ndumiso. "3-month bond option strategies: an analysis of performance from 1998 to 2010 in the South African market." Master's thesis, University of Cape Town, 2011. http://hdl.handle.net/11427/11468.
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Includes abstract.Includes bibliographical references (leaves 35-36).
Due to the 2008 financial crisis, investors have become more risk averse in investing in equities and have increased their holdings in bonds as they are believed to be less risky. However, South African interest rates have been volatile over the past decade due to changes in the inflation rate. This has caused the returns of bond portfolios to be uncertain since bond prices are inversely related to interest rates. It is thus imperative to manage the interest rate risk inherent in bond portfolios so that institutional investors can achieve their mandates and targeted returns.
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Mtemeri, Tinotenda. "Modelling of volatility of stock prices using GARCH models & its importance in portfolio construction." Master's thesis, University of Cape Town, 2009. http://hdl.handle.net/11427/8958.
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Includes bibliographical references (leaves 93-96).This thesis is aimed at investigating the possibility to model the risk of stocks in financial markets and evaluating the adequacy and effectiveness of univariate GARCH models such as the symmetric GARCH and a few other variations such as the EGARCH, TARCH and PARCH in modelling volatility in monthly returns of stocks traded on the Johannesburg Stock Exchange. This is further used to investigate the importance of GARCH modelling in portfolio construction using Improved Sharpe Single Index Models. The data used for model estimation has been randomly selected from different sectors of the South African economy. GARCH models are estimated and validated for the data series of the randomly selected 15 JSE stocks. Conclusions are drawn regarding the different GARCH models, best lag structure and best error distributions for modelling. The GARCH (1,1) model demonstrates a relatively good forecasting performance as far as the short term forecasting horizon is concerned. However, the use of alternatives to the more common GARCH (1,1) and use of non-normal distributions is not clearly supported. Also, the use of higher order GARCH models such as the GARCH (1,2), GARCH (2,1) and GARCH (2,2) is not clearly supported and the GARCH (1, 1) remains superior overall to these models. The results obtained from this thesis are of paramount importance in portfolio construction, option pricing and formulating hedging strategies. An illustration of the importance of the G ARCH (1,1) model in portfolio construction is given and conclusions are drawn regarding its usefulness in improving our volatility estimations for purposes of portfolio construction.
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Bhyat, Aneez. "An examination of liquidity risk and liquidity risk measures." Master's thesis, University of Cape Town, 2010. http://hdl.handle.net/11427/10113.
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Includes bibliographical references (leaves 199-205).Liquidity risk represents a vacuum of rigour in the otherwise well-researched area of risk management. In both practice and theory most of finance is silent regarding its scope and effect. This is principally due to a lack of consensus regarding its definition and measurement. Current liquidity risk measures differ fairly widely in both respects. This thesis attempts at addressing this by consolidating and examining the principle liquidity risk measures used in financial literature.
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Kirk, Richard. "Modelling seasonality in South African agricultural futures." Master's thesis, University of Cape Town, 2007. http://hdl.handle.net/11427/11710.
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Includes bibliographical references (leaves 86-87).This study investigates the seasonality in agricultural commodity futures prices. Futures prices are modelled using the model developed by Sørensen (2002). The model defines the commodity spot price as the sum of a nonstationary state variable, a stationary state variable and a deterministic seasonal component. Standard no-arbitrage arguments are applied in order to derive futures and option prices. Model parameters are estimated using Kalman filter methodology and maximum likelihood estimation. Model parameters are estimated for white maize, yellow maize and wheat futures traded on the South African Futures Exchange (SAFEX). Furthermore, this research considers other models for commodity derivatives as well as pricing futures contracts in the presence of price limits.