### Browsing by Author "Becker, Ronald"

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- ItemOpen AccessAlternative distributions in the Black-Litterman model of asset allocation(2011) Mbofana, Stewart; Becker, RonaldIn this thesis we replace the normal distribution assumption in the calculation of the prior equilibrium returns used in the model with a more general distribution which captures the skewness and fat tails exhibited by stock data. We consider the á stable distributions as an alternative distribution to the normal distribution. Consequently we also consider alternative measures of risk, the Value at Risk and the Conditional Value at Risk other than the variance used in the normal case.
- ItemOpen AccessAnalysis of CDO tranche valuation and the 2008 credit crisis(2013) Muzenda, Nevison; Becker, RonaldThe causes of the 2008 financial crisis were wide ranging. Some financial commentators have suggested there were significant inadequacies in the models used to price complex derivatives such as synthetic Collaterilised Debt Obligations (CDOs). We discuss the technical properties of CDOs and the modeling approaches used by CDO traders and the watchdog credit rating agencies. We look at how the pricing models fared before and during the financial crisis. Comparing our model prices to market synthetic CDO prices, we investigate how well these pricing models captured the underlying financial risks of trading in CDOs.
- ItemOpen AccessApproximations to the Lévy LIBOR Model(2014) Al-Hassan, Hassana; Becker, Ronald; Mataramvura, SureIn this thesis, we study the LIBOR Market Model and the Lévy-LIBOR. We first look at the construction of LIBOR Market Model (LMM) and address the major problems associated with specifically the drift component of LMM. Due to the complexity of the drift for LMM, the Monte Carlo method seems to be the ideal tool to use. However, the Monte Carlo method is time consuming and therefore an expensive tool to use. To improve on the process we look beyond the dynamics of the lognormal distribution, where Brownian motion (the only Lévy process with continuous paths), is the driving process and apply other Lévy processes with jumps as the driving process in the dynamics of LIBOR. The resulting process is called Lévy LIBOR Model constructed in the framework of Eberlein and Özkan (2005). The Lévy LIBOR model is a very flexible and a general process to use but has a complicated drift part in the terminal measure. The complicated drift term has random terms in the drift part as a result of change of measure. We employ Picard approximation and cumulant expansions in the resulting drift component to make the processes tractable in the framework of Papapantoleon and Skovmand (2010).
- ItemOpen AccessThe Bates model : Fourier Transform for option pricing under jump-diffusions in the South African market(2011) Munhumwe, Blessing; Becker, RonaldThe purpose of this study is to price options under jump diffusions using Fourier Transforms and obtain the implied volatility surface from these option prices.
- ItemOpen AccessBayesian estimation of stochastic volatility models with fat tails and correlated errors applied to the South African financial market(2011) Savanhu, Richard; Becker, RonaldIn this study we apply Markov Chain Monte Carlo methods in the Bayesian framework to estimate Stochastic Volatility models using South African financial market data. A single move Gibbs sampler is used to sample parameters from the posterior distribution. Volatility is used as measure of an asset's risk. It is particularly important in risk management, derivatives pricing, and portfolio selection. When pricing derivatives it is important to quote the correct volatility trading in the market, hence there is need for good estimates of volatility. To capture the stylised facts about asset returns we used the model extended for fat tails and correlated errors. To support this model against the basic model of Taylor (1986), we computed Bayes Factors of Jacquier, Polson and Ross (2004). The extended model was found to be far superior to the basic model.
- ItemOpen AccessBoundary value problems for semilinear evolution equations of compact type(1982) Sager, Herbert Casper; Becker, Ronald
- ItemOpen AccessChoice of one factor interest rate term structure models for pricing and hedging Bermudan swaptions(2011) Holilal, Amiel; Becker, RonaldThis paper revisits pricing and hedging differences presented by Z. Guan, et. al., 2008 from a South African context. The Asset Liabilities Management (ALM) departments in large financial institutions are plagued by a number of problems. Among them is the choice of interest rate model for managing the risks associated with mortgage (home loan) repay-ments. This paper will address these problems by comparing various one-factor models, including Hull-White, Black-Karasinski and CIR models for the pricing and hedging of long-term Bermudan Swaptions which resembles mortgage loans in banks' books.
- ItemOpen AccessCompound Lévy random bridges and credit risky asset pricing(2016) Ikpe, Dennis Chinemerem; Künzi, Hans-Peter A; Becker, Ronald; Mataramvura, SureIn this thesis, we study random bridges of a certain class of Lévy processes and their applications to credit risky asset pricing. In the first part, we construct the compound random bridges(CLRBs) and analyze some tools and properties that make them suitable models for information processes. We focus on the Markov property, dynamic consistency, measure changes and increment distributions. Thereafter, we consider applications in credit risky asset pricing. We generalize the information based credit risky asset pricing framework to incorporate prematurity default possibilities. Lastly we derive closed-form expressions for default trends and intensities for credit risky bonds with CLRB as the background partial information process. We obtain analytical expressions for specific CLRBs. The second part looks at application of stochastic filtering in the current information based asset pricing framework. First, we formulate credit risky asset pricing in the information-based framework as a filtering problem under incomplete information. We derive the Kalman-Bucy filter in one dimension for bridges of Lévy processes with a given finite variance.
- ItemOpen AccessA comprehensive view of Markov-Functional models and their application(2006) Lapere, Michael; Becker, RonaldMarkov-Functional models are a very powerful class of market models which calibrate and compute prices and Greeks quickly. This dissertation explains, in detail, how Markov-Functional models work as well as discussing all of the specific models developed in the literature. It contains the key points that can be found in the present literature. We explain, in detail, all of the concepts, from the theoretical framework down to the numerical implementation of the specific models. This involves explaining the framework for Markov-Functional models, describing specific models, obtaining a deeper understanding of how the model parameters affect the results, discussing the issues involved in the implementation, implementing various models and investigating the effect of numerical and market parameters on the outcome. Various concepts, not discussed in the present literature, such as considerations for selecting a discretization grid for the numerical implementation, are developed. The practical application of Markov-Functional models is considered as well as alternative fields, such as Actuarial science, where the model can be applied. In summary, this dissertation embodies a complete discussion of the current class of Markov-Functional models.
- ItemOpen AccessEfficient Monte Carlo simulations of pricing captions using Libor market models(2013) Mkhwanazi, MA (Mpendulo Armstrong); Becker, RonaldThe cap option (caption) is one of common European exotic options discussed in literature. This (interest rates) exotic option has no closed form solution and its accurate pricing and hedging in a volatile market is a challenge for traders. The reason for this is that, comparatively, the behaviour on an individual interest rate is more complex than that of a stock price. To price any interest rate product, it is essential to develop an interest rates model describing the behaviour of the entire zero coupon yield curve. The equity and yield curve, respectively, relate to the difference in the dynamics of a scalar variable and vector variable. Moreover, captions are second order with respect to the discount bonds in that they are options on caps (which are also options on bonds). These reasons make it of particular interest to study efﬁcient numerical solutions to price captions. Monte Carlo simulation provides a simple method for pricing this option, and a suitable interest rate model to use is the Libor market model. The approach of describing the behaviour of the entire zero coupon yield curve, in the era post the 2007 credit crunch crisis, is what is called a standard single-curve market practice, and Part l of this work is based on it. . After introducing the framework for option pricing in the interest rate market, the theory and implementation procedure for Monte Carlo simulation using Libor market models is described. A detailed analysis of the results is presented together with a sensitivity analysis, and finally suggestions for efﬁcient pricing of captions are given. In Part II we review the recent financial market evolution, triggered by the credit crunch crisis towards double-curve approach. Unfortunately, such a methodology is not easy to build. In practice an empirical approach to price and hedge interest rate derivatives has prevailed in the market. Future cash flows are generated through multiple forwarding yield curves associated to the underlying rate tenors, and their net present value is calculated through discount factors front a single discounting yield curve.
- ItemOpen AccessAn examination and implementation of the libor market model(2006) Jardine, James; Becker, RonaldThe relatively young field of quantitative finance has grown over the past thirty years with the cherry-picking of a wide variety of techniques from the disciplines of finance, mathematics and computer science. The Libor Market Model, a model for pricing and risk-managing interest rate derivatives, is a prime example of this cherry-picking, requiring an understanding of the interest rate markets to understand the problem to be modelled, requiring some deep mathematics from probability theory and stochastic calculus to build the model, and requiring a level of computer expertise to efficiently implement the computationally demanding requirments of the model. This dissertation intends to draw from a wide literature to bring into one body of work a treatment of the Libor Market Model from start to finish.
- ItemOpen AccessAn examination of liquidity risk and liquidity risk measures(2010) Bhyat, Aneez; Becker, RonaldLiquidity 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.
- ItemOpen AccessFinite activity jump models for option pricing(2011) Koimburi, Mercy Muthoni; Becker, RonaldThis thesis aims to look at option pricing under affine jump diffusion processes, with particular emphasis on using Fourier transforms. The focus of the thesis is on using Fourier transform to price European options and Barrier options under the Heston stochastic volatility model and the Bates model. Bates model combines Merton's jump diffusion model and Heston's stochastic volatility model. We look at the calibration problem and use Matlab functions to model the DAX options volatility surface. Finally, using the parameters generated, we use the two stated models to price barrier options.
- ItemOpen AccessAn investigation of short rate models and the pricing of contigent claims in a South African setting(2010) Jones, Chris; Becker, RonaldThis dissertation investigates the dynamics of interest rates through the modelling of the short rate { the spot interest rate that applies for an in-infinitesimally short period of time. By modelling such a rate via a diffusion process, one is able to characterize the entire yield curve and price plain vanilla options. The aim is to investigate which of the more popular short rate models is best suited for pricing such options, which are actively traded in the market. Thus one can then use such models to price more exotic options, as such options are typically less frequently traded in the market.
- ItemOpen AccessMarkov-Switching models and resultant equity implied volatility surfaces: a South African application(2012) Fairbrother, Mark; Becker, RonaldStandard Geometric Brownian Motion is the stock model underlying Black-Scholes famous option pricing formula. There are however numerous problems with this stock model as certain features do not follow some empirical stylised facts we see from the observation of actual asset prices. In particular, the constant parameter idea behind Geometric Brownian Motion is flawed. It is argued that information flow dictates stock price movements and information is a function macro-economic regimes shifts. As such, we propose an alternative model, one in which the parameters in the Standard Geometric Brownian Motion change according to an underlying Hidden Markov Process. This new model, termed a Markov-Switching model, is presented in extensive detail. Parameter Estimation methods, Simulation Methods and Option Pricing Theory are explored. Summary algorithms are presented so that this dissertation may be used as a good reference guide for those wishing to apply Markov-Switching Models. The model is tested by fitting the model on South African data and using the discussed option theory to create various implied volatility surfaces. The surfaces produced appear to obey some of the empirical observations and theoretical ideas around expected implied volatility surfaces, indicating that the Markov-Switching model has some value for option pricing.
- ItemOpen AccessMethods of pricing convertible bonds(2010) Zadikov, Ariel; Becker, RonaldThe aim of this dissertation was to build a basic understanding of hybrid securities with a focus on convertible bonds. We look at various methods to price these complex instruments and learn of the many subtleties they exhibit when traded in the market.
- ItemOpen AccessModelling credit spreads in an illiquid South African corporate debt market(2019) Jones, Samantha; Laurie, Henri; Fredericks, Ebrahim; Becker, Ronald; Dugmore, BrettThe South African debt market suffers from severe illiquidity, as is common in most emerging markets. Infrequent trading leads to out-of-date market prices and stale, unreliable credit spreads. Since the coverage of the South African debt market by credit ratings agencies is poor, meaningful credit spreads become even more important in gauging credit worth. The illiquidity of corporate vanilla bonds traded on the Johannesburg Stock Exchange and the ensuing adverse effects on their credit spreads are rigourously illustrated. Lack of data poses a serious problem when modelling any system and this analysis provides motivation for the necessity of a framework that addresses the statistical complications that incomplete data sets present. A new model, which is a distinctive modification of the well-known mean-reverting Ornstein-Uhlenbeck or Vasicek process, is introduced. This innovative approach creates a mathematically and intuitively sound relationship between the credit spread process and that of the stock price of the bond issuer. This key feature is used in a Bayesian methodology to impute missing credit spread data for calibration, for more meaningful inference. On sparse simulated data and market observed credit spread time series, the model proves to deliver an improved quality of the estimations, with probabilities that are now statistically founded. Even on complete credit spread time series, the model is shown to have some merit over the traditional model in terms of goodness of fit, giving further credence to its validity and explanatory power.
- ItemOpen AccessModelling dependance in collateralied debt obligations with copulas(2010) Linley, Christopher; Becker, RonaldIn 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.
- ItemOpen AccessMonte Carlo methods for the estimation of value-at-risk and related risk measures(2011) Marks, Dean; Becker, RonaldNested Monte Carlo is a computationally expensive exercise. The main contributions we present in this thesis are the formulation of efficient algorithms to perform nested Monte Carlo for the estimation of Value-at-Risk and Expected-Tail-Loss. The algorithms are designed to take advantage of multiprocessing computer architecture by performing computational tasks in parallel. Through numerical experiments we show that our algorithms can improve efficiency in the sense of reducing mean-squared error.
- ItemOpen AccessPricing inflation-linked derivatives using the Jarrow-Yildirim model(2009) Selamolela, Selebelo I; Becker, RonaldIn this thesis we price inflation linked swaps, Caplet, Floorlet and Option on real zero coupon bond on foreign-currency analogy, as Hughston (1998) [20]. The nominal assets are thought of as domestic assets, real assets as foreign assets and the consumer price index is interpreted as the exchange rate between the nominal and real assets. We price the inflation linked derivatives using Jarrow and Yildirim (2003) [23] three factor HJM model. We assume that volatilities of all asset price, including consumer price index, are deterministic.