Contributions published at Quantitative Finance (Erich Walter Farkas)

This thesis investigates the pricing of single-asset autocallable barrier reverse convertibles in the Heston local-stochastic volatility (LSV) model. Autocallable structured notes are the most traded equity-linked exotic derivatives. However, their complexity is responsible for recent hedging-related losses at investment banks. The autocallable pay-off embeds an early-redemption feature generating strong path- and model-dependency. In this regard, the local volatility (LV) model is overly simplified for pricing and risk management. Given its ability to match the implied volatility smile and reproduce its realistic dynamics, the LSV model is, in contrast, better suited for exotic derivatives such as autocallables. We use quasi-Monte Carlo methods to study the pricing results of the Heston LSV model and compare it with the LV model. In particular, we establish the sensitivity of the valuation differences of autocallables between the two models with respect to payoff features, model parameters, underlying characteristics, and volatility regimes. We find that the improved spot-volatility dynamics captured by the Heston LSV model typically result in higher prices, thus demonstrating the dependence of autocallables on the forward-skew. Moreover, we show that the parameters of the stochastic component of LSV models allow controlling for the autocallables price while leaving the fit to European options unaffected.

This paper focuses on portfolio optimization with respect to cryptocurrencies and shows that they significantly differ from each other in their technological attributes but also value proposition. Additionally, it is illustrated that cryptocurrencies are extremely volatile assets with leptokurtic, skewed and heavy tailed return distributions. The correlation amongst different coins is extremely large, whereas the correlation strongly depends on the state of the market. Moreover, a semi-parametric bootstrapping framework for portfolio optimization with respect to the Value-at-Risk (VaR) and Expected Shortfall (ES) is introduced and compared to the classical multiperiod mean-variance optimization. The three optimizations are executed for constant and non-rebalancing portfolios that are restricted to stocks, bonds and cash exclusively and portfolios that additionally contain cryptocurrencies. Overall, the results did not clearly indicate the existence of a portfolio rebalancing bonus for the analyzed investment horizon. However, they showed that including cryptocurrencies in a portfolio can significantly increase the return to risk ratio, independent of the optimization technique. Furthermore, the mean-ES optimization delivers the best performance compared to optimizations with other risk measures.

This master's thesis aims to analyse whether the sentiment expressed on Twitter has an impact on the returns of individual assets. A dataset of approximately 17 million tweets on five technology stocks and five cryptocurrencies is studied over a period of 26 months. The sentiment is assessed daily based on four different models. Among them are the two lexicon-based approaches VADER and Loughran-McDonald as well as a Naive Bayes classifier and finBERT, both of which are based on machine learning techniques. Granger causality tests are conducted to investigate whether the sentiment indices can improve the forecast of returns. Furthermore, a sentiment based trading strategy is implemented and compared to a buy-and-hold strategy as a benchmark. The main findings of the analysis are that a sentiment analysis can be beneficial for the stocks of Facebook and Tesla, as well as for the cryptocurrencies Bictoin and Binance Coin in some scenarios. Overall, however, a stronger Granger causal relationship is found in the opposite direction for most of the assets. The VADER and finBERT models perform better than the other two methods in sentiment analysis. A minor outperformance against the benchmark can be achieved in one case each for Bitcoin and Ethereum. However, in general the buy-and-hold strategy outperforms the implemented trading strategy considerably due to the large number of trading signals, resulting in high transaction costs, and the significant positive developments after the price drops caused by the Corona pandemic.

We construct a derivative that depends on the SPY and VIX and, in this way, incorporates both the market risk premium and the variance risk premium. We show that the product’s Sharpe ratio is higher than the SPY Sharpe ratio. If we had invested $10,000 into the product, the product’s payoff would have been about $60,000 at the end of 2018. In comparison, if we invested $10,000 into the SPY, the SPY payoff would be only about $30,000

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Innovation demonstrates powerful influence as we evaluating corporate performance. Firms that engage intensively in innovation development or invest heavily in Research and Development activities earn higher risk-adjusted returns. Combing the insights and conclusions from existing researches, we propose a set of meaningful variables measuring innovation. The innovation factor is then composed based on the significant variables, which rationalize this special risk premium. In order to test the contribution of our factors under the established asset pricing system, we form an evaluating process for newly proposed factors, from the extra alpha for the Fama-French model to a more rigorous test based on the loading on stochastic discount factor. While we apply different mechanisms to the variable pool to set up the factor or the portfolios, data envelopment analysis (DEA) method is shown to give the best performance.

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This thesis is about the pricing performance and strategy development based on pricing deviation of the machine learning algorithms of European options and convertible bonds. The classical models such as the Black-Scholes model and the Heston model usually make some unrealistic economical and statistical assumptions, and suffer from huge computational power required for parametric calibration. Regarding the inevitable flaws of traditional models, this article attempts to break out of the constraints of formula models and explore the issue of derivative pricing from the perspective of non-parametric models. The empirical analysis is based on data sets of China's 50ETF options and convertible bonds. A least squared error fitness function is used to calibrate the parameters for the Heston model. It shows that machine learning algorithms, especially the XGBoost method, not only has higher pricing accuracy and less calibration time, but also has some pricing power for abnormal prices in the market. In order to prove that the results obtained are not just products of over-fitting, this thesis back-tests the corresponding arbitrage strategy based on pricing deviation. The result shows that the XGBoost method has better annualized returns and risk control.

Renewable energy sources are becoming increasingly important for power generation. Production capacities for solar energy and wind power have been extending over the last two decades in Germany with the intention to substitute electricity generated by coal, natural gas and nuclear power plants. In contrast to thermal power plants, the production capacity of wind and solar plants depends on weather. The increasing share of electricity production through renewable energies therefore also leads to greater fluctuations in electricity generation, which are influenced by the weather and are therefore difficult to control. Since the electricity price is based on the classic rules of supply and demand, an excessively large supply of electricity can meanwhile also lead to negative electricity prices, i.e. the provider pays the consumer for receiving the electricity. This thesis aims to assess the joint impact of wind on production volumes, and electricity prices on sales revenues. The insights gained in this analysis shall be used to develop a pricing model for an illustrative, combined wind / electricity price derivative, which a market participant might want to use to mitigate its financial risks.

The present article deals with intra-horizon risk in models with jumps. Our general understanding of intra-horizon risk is along the lines of the approach taken in Boudoukh et al. (2004); Rossello (2008); Bhattacharyya et al. (2009); Bakshi and Panayotov (2010); and Leippold and Vasiljević (2020). In particular, we believe that quantifying market risk by strictly relying on point-in-time measures cannot be deemed a satisfactory approach in general. Instead, we argue that complementing this approach by studying measures of risk that capture the magnitude of losses potentially incurred at any time of a trading horizon is necessary when dealing with (m)any financial position(s). To address this issue, we propose an intra-horizon analogue of the expected shortfall for general profit and loss processes and discuss its key properties. Our intra-horizon expected shortfall is well-defined for (m)any popular class(es) of Lévy processes encountered when modeling market dynamics and constitutes a coherent measure of risk, as introduced in Cheridito et al. (2004). On the computational side, we provide a simple method to derive the intra-horizon risk inherent to popular Lévy dynamics. Our general technique relies on results for maturity-randomized first-passage probabilities and allows for a derivation of diffusion and single jump risk contributions. These theoretical results are complemented with an empirical analysis, where popular Lévy dynamics are calibrated to the S&P 500 index and Brent crude oil data, and an analysis of the resulting intra-horizon risk is presented.

Our paper adds to the vast literature of electricity price forecasting of day-ahead markets. The transformation of electricity markets from state-owned monopolies to competitive actors dominated recently by the rapid development of renewable energy has made the market increasingly unpredictable. To manage the volatility of prices and the risks to the transmission system operators, an accurate model of the day-ahead market is very important. Power producers and traders are also exposed to financial risk. The research aims to develop a short term electricity price forecasting tool useful for trading and managing positions. We propose a LASSO regression using parameters such as fuel prices and physical network inputs. On top of these parameters, we develop a new variable from the stack curves of the daily day-ahead auction process. We believe this variable can enhance the prediction of the non-linear behaviour of electricity price spikes. The lasso regression performs better in terms of fitness compared to an OLS regression. We test our assumption using a trading algorithm with real market data consisting of reconstructed bids and offers. We describe the mechanism of market functioning and test the suggested model with data from the day-ahead EPEX auction for Germany. We find that this algorithm can outperform a naive benchmark in terms of profit and loss and risk measures, even when we include transaction costs.

According to Lakonishok et al. (1994), the Value Investing strategy outperformed the Growth Investing Strategy in the past. However, Growth companies in the Information Technology sector are becoming more important in recent years, especially during the pandemic. In this thesis, we use S&P 500 stocks to sort them into portfolios based on multiples to differentiate between Value and Growth stocks during and before the pandemic. Similarly, we form portfolios based on other factors such as financials, sectors, and industries. As expected, the Growth portfolios outperform the Value portfolios during and before the pandemic. In addition, we also conclude that the Value portfolios are riskier during rare disaster using Maximum Drawdown, Sharpe Ratio, and Annual Standard Deviation as risk measurements. The sector Information Technology outperforms the market in general, where as the sector Energy in terms of both earnings and stock market performance suffered tremendously during the pandemic. Lastly, using second quarter earnings from 2020, we measure if new all-time highs of certain stocks are justified.

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In this thesis, we systematically implemented the pretest-based approach proposed by Kazak and Pohlmeier (2019a) and applied it to do parameter selection for momentum strategies. We first showed the necessity and difficulty of optimal strategy selection via naive examples and then use the pretest-based method in Kazak and Pohlmeier (2019a) to choose optimal strategy. To verify the effectiveness of the proposed method, especially in terms of out-of-sample performance for momentum strategy, we conducted extensive experiment with various settings. Results showed that although the meta strategy selected by the statistical learning and testing approach performs worse than the benchmark occasionally, for most of the time it can outperform the benchmark strategy, indicating that the algorithm can successfully identify and choose the winning strategy. In terms of the failure cases, we hypothesis that this is due to market regime change, which is not predictable from the momentum information only.

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