Contributions published at Quantitative Finance (Erich Walter Farkas)

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Marcos Lopez de Prado introduced meta-labeling, a unique machine-learning technique for improving algorithmic trading tactics, in 2018. Meta-labeling is a term that refers to the process of assigning a binary label to past trades of a trading system based on their outcome (win or loss), constructing a set of time series features that are temporally aligned with the labels, and fitting a machine learning classification model to the features and labels. The learned classifier is then used to evaluate the probability of profitability for each new, unopened trade. Before the trade is opened, the position size for each new transaction is computed using the corresponding probability estimate. The objective is to increase the position size of trades with a high projected probability of profitability. This thesis aims to determine whether or not meta-labeling improves trading performance by adjusting the bet size for each trade based on the probability of profitability predicted by secondary meta-labeled machine learning layers when applied to real-world trading systems and to draw critical conclusions about the concept’s practical implementation. Three different meta-labeled machine learning layers are built on top of three existing investment expertise, which could be fundamental or systematically driven. As a result, the three systems’ performance is enhanced. The findings indicate that meta-labeling really improves trading system performance and thus should be considered by all traders.

The Variance Risk Premium (VRP) is defined as the difference between implied and realized volatility. Recent literature suggests that the VRP has a statistically significant predictive power on future returns. We define rigorously the VRP and investigate this predictive relation throw various models. We develop a trading strategy based on the VRP only and achieve a Sharpe ratio of 0.6.

The present article studies geometric step options in exponential Lévy markets. Our contribution is manifold and extends several aspects of the geometric step option pricing literature. First, we provide symmetry and duality relations and derive various characterizations for both European-type and American-type geometric double barrier step options. In particular, we are able to obtain a jump-diffusion disentanglement for the early exercise premium of American-type geometric double barrier step contracts and its maturity-randomized equivalent as well as to characterize the diffusion and jump contributions to these early exercise premiums separately by means of partial integro-differential equations and ordinary integro-differential equations. As an application of our characterizations, we derive semi-analytical pricing results for (regular) European-type and American-type geometric down-and-out step call options under hyper-exponential jump-diffusion models. Lastly, we use the latter results to discuss the early exercise structure of geometric step options once jumps are added and to subsequently provide an analysis of the impact of jumps on the price and hedging parameters of (European-type and American-type) geometric step contracts.

This thesis analyses stock return predictability on a sector level using machine learning techniques. The two main goals are investigating whether returns exhibit any predictability and using predictive models to construct simple sorted portfolios that rotate between the sectors. Specifically we are interested in seeing whether non-linear deep learning techniques can improve the performance of standard linear models. For this purpose, US sector aggregated data is used, for the period 1990-2021. We first show the potential added value of machine learning models in a regime switching simulation study. Next, for the market data, state-of-the-art RNN and CNN models are able to achieve slightly positive out-sample R2 values. Moreover, portfolios built based on these predictions are able to outperform benchmark portfolios on cumulative returns and Sharpe ratio. Given that similar predictive power is found in the European market, this research supports the conclusion that returns exhibit slight predictability.

This paper introduces a sparse and stable optimization approach for a multi-currency asset allocation problem. We study the benefits of joint optimization of assets and currencies as opposed to the standard industry practice of managing currency risk via so-called currency overlay strategies. In our setting, a classical mean-variance problem in an international framework is augmented by several extensions that aim at reducing parameter uncertainty related to the input parameters and induce sparsity and stability of the asset and currency weights. These extensions integrate maximal net exposure to foreign currencies, shrinkage of the input parameters, and constraints on the norms of the asset- and currency-weight vectors. The empirical performance of the portfolio optimization strategies based on the proposed regularization techniques and the joint (i.e., asset and currency) optimization is tested out of sample. We demonstrate that the sparse and stable joint optimization approach consistently outperforms the standard currency overlay as well as the equally-weighted and the non-regularized global portfolio benchmarks net of transaction costs. This result shows that the common industry practice of employing currency overlay strategies is suboptimal and can be improved by a joint optimization over assets and currencies.

Given the competitiveness of a market-making environment, the ability to speedily quote option prices consistent with an ever-changing market environment is essential. Thus, the smallest acceleration or improvement over traditional pricing methods is crucial to avoid arbitrage. We propose a novel method for accelerating the pricing of American options to near-instantaneous using a feed-forward neural network. This neural network is trained over the chosen (e.g., Heston) stochastic volatility specification. Such an approach facilitates parameter interpretability, as generally required by the regulators, and establishes our method in the area of eXplainable Artificial Intelligence (XAI) for finance. We show that the proposed deep explainable pricer induces a speed accuracy trade-off compared to the typical Monte Carlo or Partial Differential Equation-based pricing methods. Moreover, the proposed approach allows for pricing derivatives with path dependent and more complex payoffs and is, given the sufficient accuracy of computation and its tractable nature, applicable in a market-making environment.

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Pensionskassen sind gefordert, wenn es darum geht, im Tiefzinsumfeld höhere Renditen zu erzielen. Wie es gelingen kann, und was Schweden damit zu tun hat, erörtert Prof. Dr. Erich Walter Farkas, Professor for Quantitative Finance, Program Director "MSc UZH ETH in Quantitative Finance", entlang von drei brisanten Fragen.

There is an established approach for pricing swing (also called take-or-pay) option contracts in academia and industry alike, which consists of using the Longstaff-Schwarz method, which was introduced by the authors in 2001 and only moderately evolved since then. In this thesis, different ways to modify and extend this approach are explored, especially the use of neural networks among other machine learning methods for enhancement. The goal of this thesis is to find whether those techniques, made more available and economically viable to use by current progress in hardware, can deliver better results compared to established approaches. In particular, swing contract pricing on the gas market is researched. First, an overview of the market is given, then classic and other approaches are introduced. Finally, introduced approaches are compared on the basis of computational resources needed and overall performance. In conclusion, original Longstaff-Schwarz procedure is shown to be still relevant for swing option pricing. New approaches were faster in the real world situations, but due to data sourcing problem were unable to provide more accurate results. Novelty in the work is drawn from the extension of the existing techniques already tried for pricing of completely different financial assets or similar products, but in simpler cases to swing option pricing, where path-dependency and optimization of multiple exercise decisions schedule add considerable complexity.

Returns-based style analysis (RBSA) is a statistical method commonly used to investigate the exposure of investment funds. It involves identifying the combination of market factors that most closely reproduces a fund’s returns and attempts to characterize their investment styles. This thesis utilizes RBSA to explore the investment behaviours of the most relevant classes of Brazilian investments funds: foreign exchange (FX), fixed income, stocks, and multi-strategy funds. We demonstrate that RBSA is adequate for analysing funds that possess relatively stable asset allocations; however, its performance is not satisfactory for funds with time-varying exposures. To overcome this limitation, we adapt a state-space model and apply a Kalman filter to construct a dynamic style analysis model. Between January of 2010 and April of 2021, we studied 320 funds that were selected based on their asset values size. We found that FX and fixed income funds are generally passively managed, and, by applying a clustering algorithm to their style results, we demonstrated that these funds can be categorized into groups that track the same benchmarks. However, this study also suggests that several stock funds and most multi-strategy funds are actively managed. For these classes of funds, our empirical results indicate that the Kalman filter estimations improve style predictions and yield better and more interpretable outputs. Finally, we extend this proposed framework with the use of past disclosed fund information to identify actual portfolio constituents over time. Our analysis shows that this innovative approach achieves accurate results only when applied to funds with a small number of assets.

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Machine Learning (ML) is gaining prominence in financial risk management application studies by providing improved modelling flexibility compared to the current state-of-theart parametric approaches. Under the supervised learning framework, various classifiers may contribute to a more accurate estimation of risk parameters in Internal Rating-Based models developed by financial institutions. The main objective of this thesis is to construct and compare various classification models used in credit scoring applications and estimation of Probability of Default (PD). In particular, this study compares the performances of Random Forest (RF), k-Nearest Neighbors (k-NN), XGBoost, and AdaBoost on a realworld credit scoring portfolio made available by Credit Suisse. The portfolio considered in the analysis ranges from 2000 to 2014 and includes all counterparties in Credit Suisse’s corporate portfolio consisting of Swiss corporate small-medium enterprises (SME) and large enterprises (LE). Common issues in credit scoring portfolios such as the low default problem and feature selection are addressed in the analysis by employing oversampling techniques and hybrid feature selection procedures. Models specifically for SMEs and for both SMEs and LEs simultaneously are constructed and compared using AUROC and Brier Score performance metrics. The performance of these models is also compared to the logistic regression, which is the industry benchmark model for such applications. This study confirms the literature findings that ML models outperform traditional approaches (e.g., logistic regression) and supports the superior performance of these models on the Swiss corporate portfolio specifically. Out of the ML models, the best performing model in terms of AUROC is the RF, while the boosting models provide the most accurate probability predictions. k-NN performs worse than the rest of the ML models, but still outperforms the logistic regression. Finally, the effect of model averaging on model performance is assessed and compared to the performance of the single models. Averaging the three best ML models results in increased performance and reduced model risk. The results suggest that ML techniques prove to be important aids in credit risk modelling and should be considered as serious competitors of classical approaches.

This thesis investigates the application of generative adversarial networks to asset return time series. We analyze the performance of different network architectures in the unconditional and conditional frameworks. The analysis starts with univariate return time series and progresses to multivariate return time series of various asset classes. Training the model brings numerous challenges, such as mode collapse and vanishing gradients. Thereby, we apply Wasserstein generative adversarial network with gradient penalty (WGAN-GP) that overcomes those challenges. The most fundamental issue and open research problem is evaluating the performance of the trained generator. Thereby, we investigate computing the likelihood of the out-of-sample data arising from an empirical distribution estimated from the generated data. We use the best performing models in a practical application of backtesting Value-at-Risk estimates from the learned distribution. The ability to sample from the distribution enables us to observe more samples of unlikely events and gives us an upper hand over traditional methods. Value-at-Risk estimation using WGANGP applied to univariate time-series shows promising results. The application of WGAN-GP to multivariate data turns out to be more challenging. However, the performance is still competitive with classical methods. The application of generative adversarial networks to finance is a relatively recent topic that requires further research. Nevertheless, we believe it is a promising candidate for modelling financial time series in the future.

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The objective of the thesis is to investigate a one-paramenter family of risk measures called Conditional Drawdown at Risk (CDaR) and its application to Equal Risk Budgeting Portfolios and Machine Learning techniques for Asset Allocation. We first introduce and develop a theoretical framework for the Conditional Drawdown at Risk. The next step will be thorough study of the properties of Equal Risk Contribution and their drawbacks, that will lead to the formulation of an optimization problem based on the CDaR. The Hierarchical Clustering approach applied to portfolio allocation has been of interest for many years has it seemed to tackle what was commonly known as the Markowitz' curse. More recent studies implement techniques to improve the performance of this strategy by computing beforehand the optimal number of clusters and adopting different linkage methods. The use of a tail risk measure, like CDaR, instead of the volatility, defined as the standard deviation, will be tested in this context too. We produce a series of strategies based both Equal Risk Contribution and Hierarchical Clustering algorithms that we will backtest against traditional portfolios, namely Minimum Variance, Maximum Sharpe Ratio and Equally Weighted. The statistical significance of the risk adjusted performance of the proposed strategies will need to be evaluated in order to understand if outperfomances were produced by chance. Finally we will try to reconcile our finding within the modern portfolio theory framework.

By adding two factors to their profound three factor model, Eugene F. Fama and Kenneth R. French built a new five factor model with the intent to increase the explanatory power in variations of returns through the models. Ever since its introduction, the model itself was critically discussed and examined in different markets all around the globe. This thesis follows on this path and compares the two models for the German stock market over the last twenty years. In a first step, the comparison is based on linear regressions. The results indicate that the five factor model can explain the variations in return significantly better than its three factor competitor. In a second step, different forecasts are formed under the influence of the two models, on the basis of which the forecasting power of the two models is to be examined. Here too, in a direct comparison between the three and five factor models, it is concluded that the five factor model performs better. However, the results of the regressions and the forecasts should be treated with caution, as the performance of the models is only partially satisfying in absolute terms.