Contributions published at Quantitative Finance (Erich Walter Farkas)

In this thesis we extend well established statistical models on time-varying volatil- ity of financial returns with promising machine learning techniques. We work with models from the GARCH family as baseline and update their recursive volatility functions via more complicated estimators from the modern machine learning literature. The introduced models are fitted in financial datasets via optimization with respect to likelihood-based functions and as a result the ex- tended models inherit all the distributional assumptions of the baseline ones. The modelling methodology is additionally expanded to the multidimensional case, where we estimate the conditional correlation of a portfolio of assets over time. We perform an extensive comparison of the proposed models with the bench- marking ones and conclude to a not significant outperformance of the challenger models. At the second part, we work in two applications in the area of Lombard Lending. Under the assumption of time-varying volatility we use the described methodology of the first part to provide (i) a risk monitoring tool and (ii) an estimation of the lending value of a Lombard loan.

In this thesis we examine the performance of equal-weighted, size-weighted and value-weighted portfolios. In addition we test portfolios consisting of a value-weighted and a cash part. We find that the equal- and size-weighted portfolios outperform the value-weighted portfolio in terms of mean return, four-factor alpha and Sharpe Ratio. The best performance for every strategy was observed for the 13 week rebalancing frequency.

This thesis focuses on the question of the advantages in forecasting volatility of implied volatility indices in comparison to more dynamic models such as the ARCH and the GARCH model. The goal is statements about information content, bias, efficiency and better prediction. The existing literature is ambiguous about these statements, so this thesis further contributes to the discussion. First, a theoretical framework corresponding to the definition and history of the implied volatility indices and dynamic models is presented. Then the data of the time series of the implied volatility indices are assessed in terms of predictive power and compared to the dynamic models with an OLS regression. The results indicate that implied volatility contains additional information. However, the ARCH and the GARCH predict better.

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As many markets are not perfectly liquid, there is a necessity of adequate integration of market liquidity risk in risk measures. We discuss different approaches how liquidity risk can be incorporated into the value at risk and the expected shortfall and highlight their benefits and shortcomings. The theoretical discussion is then supplemented by an empirical study for the Swiss stock market. By performing various backtesting methods we check for the validity and performance of the different approaches. We conclude that there is a need of liquidity considerations in daily risk measures, especially in times of market turbulence and for smallcap stocks. As the relative importance of liquidity risk decreases for longer time horizons, we infer that liquidity risk can be incorporated roughly into risk measures by choosing long enough time horizons depending on the nature of the security.

This Thesis aims to confirm the relationship between option volume and abnormal re- turns in the context of insider trading, as it has already been investigated in various studies, and to test whether the effects are strong enough to develop a profitable invest- ment strategy based on them. For this purpose, I used various measurements based on the volume of traded call and put options prior to abnormal trading days and tested them statistically on a data set of 92 S&P500 companies. Based on the findings from the statistical analysis and the theoretical foundations, various investment strategies were developed. I conclude that although a relationship between option volume and abnormal returns prior to abnormal trading days, as shown in previous studies, can be confirmed, the effects are not strong enough to develop profitable investment strategies. I see the main reason for this as being the fact that increases in the options volume based parameters used do not occur exclusively before abnormal trading days, but also on normal trading days, as well as the fact that increases prior to abnormal trading days usually do not occur unilaterally, which makes prediction very difficult.

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Bitcoin was the overall best-performing asset in the last decade and the popularity of the most successful cryptocurrency seems unbroken with an average daily trading volume of more than 100 million US dollars since 2020. Despite the impressive past returns, the high volatility is widely seen as one of the most deterring factors for investors. Thus, for risk management and to optimise investor’s decision-making the analysis of volatility is crucial. This thesis uses adaptive machine learning models to forecast next day’s directional volatility movement with 21 features from five different categories: (1) two Bitcoin price features, (2) four technical indicator features, (3) four economic features, (4) six Bitcoin metric features, and (5) five financial market features. The primary objective is building a binary classification problem to predict an increase or decrease in daily volatility with boosting algorithms. Both the Adaptive Boosting classifier (AdaBoost) as well as the Extreme Gradient Boosting classifier (XGBoost) show promising results. XGBoost achieved the highest mean accuracy with 59.6%. The feature importance analysis suggests the advantage of selecting features from different categories. Furthermore, a multi-category model is built to separate the 10% biggest positive and negative volatility changes from minor increases or decreases. This model achieved a mean accuracy of 46.6%. The main conclusion of the analysis is that boosting algorithms show promising results for binary Bitcoin volatility forecasting but parameter tuning and potential overfitting are limits to the predictive power of the models. However, the results still indicate that a lean built machine learning model based on 21 features can make limited predictions of short-term Bitcoin volatility. This can be useful in terms of risk management and investment decisions.

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In this thesis, I introduce my crypto model, which is an application of the Fama-French Three-Factor model (FF3M) and its extension by Carhart for cryptocurrencies. We will find that the factors SMB (small minus big) and HML (high minus low) of the FF3M can be transferred to cryptocurrencies, whereby the SMB factor can be replaced by the market capitalization and the HML factor by the transaction-to-market ratio of a cryptocurrency. We will also discover that the PR1YR factor of Carhart’s model can be replaced by the momentum return on a cryptocurrency. I will conclude this thesis by providing evidence that small-size cryptocurrency portfolios do not have a significant higher return than big-size cryptocurrency portfolios and that high-value cryptocur- rency portfolios do not have a significant higher return than low-value cryptocurrency portfolios. This is not in line with the results of the Fama-French Three-Factor model. Another conclusion will be that high-momentum cryptocurrency portfolios do not have a significant higher return than low-momentum cryptocurrency portfolios, which is not in line with Carhart’s model.

Partner Reinsurance Europe SE (PRESE) is a European legal entity based in Dublin and a subsidiary of PartnerRe, a Bermuda-based composite reinsurer. PRESE holds an asset-liability portfolio with a net short-duration position where its long-duration liabilities are primarily in EUR and CHF while its shorter-duration invested assets are in USD. PRESE’s investment strategy reflects the view that USD assets yield higher returns than EUR or CHF assets and that the duration risk is not adequately compensated for in market pricing. The central question of the thesis is whether currency mismatch creates a substantial risk for which the entity is not sufficiently compensated. In other words, the thesis performs a formal validation of the current in- vestment strategy. In order to do so, the thesis constructs various investment portfolios by altering the currency composition of the existing investment portfolio and applies Group Capital Model (GCM), a stochastic model, to identify the investment portfolio with the best return-risk profile. Furthermore, the thesis explores the validity of res- ults by incorporating the cost of capital and examining the feasibility of hedging with forward agreements. In the last part, the thesis briefly discusses the limitations of the methodology used. The thesis concludes that the current investment strategy is close to optimal, and no significant gains can be obtained through currency reallocation.