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Pair trading is a well-known strategy based on statistical arbitrage. This strategy uses a short-term deviation from the mean value of the price ratio of two highly correlated stocks from the same sector as the opportunity to open a position. When ratio returns to its mean value again, the position closes. This strategy has been used for many years and the main outcome of this thesis was to test whether this strategy can be profitable even in current market conditions. For that purpose, data ranging from 2010 to April 2017 on all stocks included in the S&P 500 index were used. It was subsequently found that a pair trading strategy generated 25x higher absolute profit in comparison to random agent. Thus, it can still be considered as a profitable strategy.

Diploma thesis is focused on analysis and comparison using financial derivatives to hedge currency risk. The first part of the thesis describes instruments used for hedging: forex forwards, futures contracts and currency options. Those instruments are used for back-testing in analytical part, currency crosses used for back-testing are EUR/USD, EUR/GBP and GBP/USD. The main goal of this thesis is to evaluate the posibility of using them to hedge currency risk, comparison of their efectivity and application.

We use an adversarial expert based online learning algorithm to learn the optimal parameters required to maximise wealth trading zero-cost portfolio strategies. The learning algorithm is used to determine the relative population dynamics of technical trading strategies that can survive historical back-testing as well as form an overall aggregated portfolio trading strategy from the set of underlying trading strategies implemented on daily and intraday Johannesburg Stock Exchange data. The resulting population time-series are investigated using unsupervised learning for dimensionality reduction and visualisation. A key contribution is that the overall aggregated trading strategies are tested for statistical arbitrage using a novel hypothesis test proposed by Jarrow et al. [31] on both daily sampled and intraday time-scales. The (low frequency) daily sampled strategies fail the arbitrage tests after costs, while the (high frequency) intraday sampled strategies are not falsified as statistical arbitrages after costs. The estimates of trading strategy success, cost of trading and slippage are considered along with an offline benchmark portfolio algorithm for performance comparison. In addition, the algorithms generalisation error is analysed by recovering a probability of back-test overfitting estimate using a nonparametric procedure introduced by Bailey et al. [19]. The work aims to explore and better understand the interplay between different technical trading strategies from a data-informed perspective.

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Since the introduction of derivatives to the financial markets, volatility trading has emerged as a method for investors to make money in every market condition. In parallel with introducing derivatives to the financial markets, hedging methods have emerged and are today essential instruments for the liquidity providers active in the markets. The most commonly used hedging method is delta hedging which cancels out the directional risk in the option. Hedging the vega risk with dispersion trading seems to be both a profitable and accurate hedging method. This thesis examines the effectiveness of dispersion trading for reducing the vega risk in OMXS30 options. This is investigated by backtesting a strategy based on going short OMXS30 index volatility and long volatility on a tracking portfolio with a zero net vega. This investigation aims to determine if the dispersion trading strategy can be a reliable risk management tool. It was found that vega could accurately be hedged using dispersion trading. However, when considering the bid-ask spread, the strategy did not show profitability over the simulated period. Weighting the portfolio more in favour of companies with smaller bid-ask spreads did not show improved profitability. / Sedan introduktionen av derivat på de finansiella marknaderna har volatilitetshandel dykt upp som en metod för investerare att tjäna pengar i alla marknadsförhållanden. Parallellt med introduktionen av derivat på de finansiella marknaderna har säkringsmetoder vuxit fram och är idag väsentliga instrument för de likviditetsgivare som är verksamma på marknaderna. Den vanligaste säkringsmetoden är delta säkring som tar bort den riktade risken i optionen. Att säkra vegarisken med spridningshandel tycks vara både en lönsam och pålitlig säkringsmetod. Detta examensarbete syftar till att undersöka effektiviteten av att använda en spridningshandel för att minska vegarisken i OMXS30-optioner. Metoden involverar att simulera en strategi baserad på att vara kort volatilitet i OMXS30 och lång volatilitet på en spårningsportfölj på historisk data. Genom denna undersökning strävas det efter att avgöra om strategin för spridningshandel kan vara ett tillförlitligt verktyg för riskhantering. Det visade sig att vega kunde säkras med hjälp av spridningshandel. Strategin visade sig vara lönsam under den simulerade perioden men när köp- och sälj-spreadarna i de enskilda aktieoptioner inkluderades var det inte längre lönsamt att utföra metoden. Att vikta portföljen mer till förmån för företag med mindre köp- och sälj-spread visade inte på förbättrad lönsamhet.

Since the introduction of derivatives into the modern financial market, volatility based tradingstrategies have emerged as important tools for asset managers. Since the financial crisis apopular trading strategy has been dispersion trading, however few published studies ofdispersion trading exist. This thesis aim to perform a study of how dispersion strategies performand their characteristics. This is achieved by finding basic common dispersion trading strategies,isolate and evaluate their attributes to then draw conclusions in general about dispersion trading.Three basic dispersion strategies are found based on vanilla option spreads and their performanceis back-tested. It was found that the strategies delivered positive return with low marketcorrelation and acceptable risk. It is also found that transaction costs is a key-factors tosuccessfully use dispersion trading. Thus it is a vital factor to consider when creating adispersion based trading strategy. An interesting topic for further research is how trading signalssuch as the implied correlation and the implied volatility spread can be used to increaseprofitability. As well to model market impact from dispersion trading.

本文以台灣股價加權指數，使用 AR(3)-GJR-GRACH(1,1) 模型，白噪音假設為 Normal 、 Skew-Normal 、 Student t 、 skew-t 、 EPD 、 SEPD 、與 AEPD 等七種分配。著重於兩個部份，(一) Student t 分配一族與 EPD 分配一族在模型配適與風險值估計的比較；(二) 預測風險值區分為低震盪與高震盪兩個區間，比較不同分配在兩區間預測風險值的差異。 實證分析顯示， t 分配一族與 EPD 分配一族配適的結果，無論是只考慮峰態 ( t 分配與 EPD 分配) ，或者加入影響偏態的參數 ( skew-t 分配與 SEPD 分配) ， t 分配一族的配適程度都較 EPD 分配一族為佳。更進一步考慮分配兩尾厚度不同的 AEPD 分配，配適結果為七種分配中最佳。 風險值的估計在低震盪的區間，常態分配與其他厚尾分配皆能通過回溯測試，採用厚尾分配效果不大；在高震盪的區間，左尾風險值回溯測試結果，常態分配與其他厚尾分配皆無法全數通過，但仍以 AEPD 分配為最佳。最後比較損失函數，左尾風險值估計以 AEPD 分配為最佳，右尾風險值則無一致的結果。因此我們認為 AEPD 分配可作為風險管理有用的工具。

The role of risk management has gained momentum in recent years most notably after the recent financial crisis. This thesis uses a quantitative approach to evaluate the theory of value at risk which is considered a benchmark to measure financial risk. The thesis makes use of both parametric and non parametric approaches to evaluate the effectiveness of VAR as a standard tool in measuring risk of stock portfolio. This study uses the normal distribution, student t-distribution, historical simulation and the exponential weighted moving average at 95% and 99% confidence levels on the stock returns of Sonny Ericsson, Three Months Swedish Treasury bill (STB3M) and Nordea Bank. The evaluations of the VAR models are based on the Kupiec (1995) Test. From a general perspective, the results of the study indicate that VAR as a proxy of risk measurement has some imprecision in its estimates. However, this imprecision is not all the same for all the approaches. The results indicate that models which assume normality of return distribution display poor performance at both confidence levels than models which assume fatter tails or have leptokurtic characteristics. Another finding from the study which may be interesting is the fact that during the period of high volatility such as the financial crisis of 2008, the imprecision of VAR estimates increases. For the parametric approaches, the t-distribution VAR estimates were accurate at 95% confidence level, while normal distribution approach produced inaccurate estimates at 95% confidence level. However both approaches were unable to provide accurate estimates at 99% confidence level. For the non parametric approaches the exponentially weighted moving average outperformed the historical simulation approach at 95% confidence level, while at the 99% confidence level both approaches tend to perform equally. The results of this study thus question the reliability on VAR as a standard tool in measuring risk on stock portfolio. It also suggest that more research should be done to improve on the accuracy of VAR approaches, given that the role of risk management in today’s business environment is increasing ever than before. The study suggest VAR should be complemented with other risk measures such as Extreme value theory and stress testing, and that more than one back testing techniques should be used to test the accuracy of VAR.

本文提出了一個新興風險衡量的工具的概念-期望尾端損失值(ETL)，其有別於風險值為百分位數且未考慮報酬分配的尾部風險(Tail Risk)，本研究期望能透過ETL的估計可以更完整表達投資組合所有可能面臨的風險，對於市場風險能更有效控管。 本文實證討論有關VaR與ETL穩定度的部分，VaR雖然在理論上證明無法滿足次可加性這個條件，但是在本研究實證中，即使在分配具厚尾狀況下，VaR仍滿足次加性的性質。這也表示，我們在現實生活中很難因VaR理論上缺乏次可加性，而捨棄VaR這個風險衡量工具，然ETL也有其貢獻性，其較VaR多考慮尾部資訊，可視為風險值外另一參考指標，此為本文貢獻一。 本文實證也探討移動窗口中歷史資料長度的不同，是否造成VaR與ETL估算準確性的差異，本文由實證結果發現：在歷史窗口的資料長度越長(1000日)下，並沒有正確預估VaR與ETL，而本研究中以移動窗口為500日下，使用內部模型較具正確性，故在使用風險值模型時，應謹慎選擇移動窗口之長度，此為本文貢獻二。