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.

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.

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.

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.

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.

Includes bibliographical references (leaves 97-100). / This study examines two approaches to modelling the volatility skew that is used to price options on the Johannesburg Stock Exchange (JSE) TOP40 index. The first approach involves using historical prices of the underlying index to obtain a model of the skew. Two models that use this approach, namely the Edgeworth and Normal Mixture AGARCH models were implemented.

Includes abstract. Includes bibliographical references (leaves 223-230).

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.

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.

Includes bibliographical references (leaves 110-111).