### Browsing by Author "Polakow, Daniel"

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- ItemOpen AccessApplication of extreme value theory to the calculation of value-at-risk(2001) Seymour, Anthony; Polakow, DanielThe main aim of the study was to test the applicability of published EVT-based VaR calculation methods to the South African market. Two methods were tested on a hypothetical portolio of South African stocks, using the standard backtesting technique.
- ItemOpen AccessBounds on baskets option prices(2005) De Swardt, N C; Polakow, DanielThe celebrated Black-Scholes option pricing model is unable to produce closed-form solutions for arithmetic basket options. This problem stems from the lack of an analitical form for the distribution of a sum of lognormal random variables. lVlarket participants commonly price basket options by assuming the basket follows lognormal dynamics, although it is known that this approximation performs poorly in some cicumstances. The problem of finding an analytical approximation to the sum of lognormally distributed random variables has been widely studied. In this dissertation we seek to draw these studies together and apply them in an option pricing setting. We propose some new option pricing formulae based on these approximations. In order to examine the utility of these new formulae and compare them to commonly used market approximations we present rigorous analytical bounds for the price of arithmetic basket options using the theory of comonotonicity. In this we follow the ideas in Deelstra et al. [7]. Additionally we provide an interval of hedge parameters (the Greeks). We carry out a numerical sensitivity analysis and identify circumstances under which the market approximation misprices basket options.
- ItemOpen AccessCurrency trios - using geometric concepts to visualise and interpret relationships between currencies(2016) Davidson, Abby; Mahomed, Obeid; Polakow, Daniel; Van de Linde, GideonA currency trio is a set of three currencies and their respective exchange rates, which have a relationship fixed by a triangular arbitrage condition. This condition forms the basis for the derivation of a geometric interpretation of the relationships between the exchange rates. In the geometric framework, the three currencies in a currency trio are represented by a triangle, where each of the vertices represents a currency. The volatilities of the exchange rates are represented by the lengths of the sides joining the respective currencies and the cosine of each angle represents the correlation between the two exchange rates depicted by the angle's adjacent sides. The geometric approach is particularly useful when dealing with implied data as it allows the calculation of implied correlation using implied volatility. This is valuable as implied volatility is frequently quoted in the foreign exchange market; whereas, implied correlation is not directly quoted and is more difficult to extract from market data. This dissertation aims to thoroughly investigate the geometric framework and use it to visualise and interpret the relationships between currencies in a currency trio. The analysis will initially look at currency trios with realised spot data before moving on to implied data. In the implied data context, the framework will be used to extract and evaluate implied correlation estimates using implied volatility data extracted from the foreign exchange market. The framework will be extended to investigate whether an illiquid option can be proxy hedged using options on the two other currencies in a currency trio. Finally, the findings will be discussed and the feasibility of the applications of the framework will be considered.
- ItemOpen AccessThe effect of security return dispersion on performance measurement in a South African context(2014) Gething, Bryce A; Polakow, DanielThis work replicates a similar study performed by de Silva et al. (2001). Our study was performed on the South African market. De Silva et al. (2001) studied the effect of cross-sectional volatility (CSV) on fund managerial skill measurement. This lead to the conjecture that increased fund performance dispersion was primarily due to higher CSV, and not changes in informational efficiency or ranges in managerial talent. In this dissertation we firstly critique the CSV-adjusted alpha as a measure of fund performance and show that it can only be used as a means of normalising fund performance, yet reveals very little with regard to managerial talent. Since fund performance is intrinsically linked to CSV, we find it difficult to disentangle the effects of CSV and managerial talent dispersion. Adjusting for CSV therefore also implies adjustment for managerial talent, and we conclude with ideas for how a CSV-adjusted alpha may be used to assess manager talent.
- ItemOpen AccessMaking cents of yesterday, today and tomorrow : trading rules for volatility arbitrage(2003) De Araujo, Mark; Polakow, DanielThis study is intended to be a rigorous examination of a valid and attractive practical problem in financial mathematics in the real world rather than a theoretical contribution. It has foci in statistical modelling of derivative (Black-Scholes) mechanics. The impetus for this research was initially gleaned while working with an active South African derivatives brokerage house (Cadiz Holdings) as an intern. It was immediately evident that there was a pressing need for an investigation into volatility trading rules to recommend trades (from the sell-side brokers) as well as to trigger trades (from the institutional investors point of view). The rules that both parties typically used appeared too simple to be useful or profitable.
- ItemOpen AccessNew perspectives in the modelling of alpha(2012) Flint, Emlyn James; Polakow, DanielThis dissertation presents an eclectic mix around a central theme of alpha, or value-add. It comprises four essays that are concerned with various theoretical and empirical aspects of alpha. The primary objective is to provide new perspectives in the major areas of modelling alpha; namely, performance measurement, opportunity forecasting and tradability.
- ItemOpen AccessThe Impact of the Carry Trade on Global Currency Markets(2019) Smit, Steven; Pienaar, Etienne; Polakow, DanielThis work analyses the effect of the carry trade factor, statistically derived from a comprehensive basket of currencies, on currencies in various heuristically defined global risk appetite regimes. Findings of a heightened (lessened) impact of this factor for Emerging/Commodity (Developed/European) currencies in the presence of high risk are presented. The risk appetite process is additionally analysed by modelling it as a Markov-switching model, providing evidence of three inherent regimes, with properties roughly consistent with findings in the literature.