Search

The Greeks Delta and Gamma of plain vanilla options play a fundamental role in finance, e.g., in hedging or risk management. These Greeks are approximated in many models such as the widely used Variance Gamma model by Fourier techniques such as the Carr-Madan formula, the COS method or the Lewis formula. However, for some realistic market parameters, we show empirically that these three Fourier methods completely fail to approximate the Greeks. As an application we show that the Delta-Gamma VaR is severely underestimated in realistic market environments. As a solution, we propose to use finite differences instead to obtain the Greeks.

In this study, we predict next-day movements of stock end-of-day implied volatility using random forests. Through an ablation study, we examine the usefulness of different sources of predictors and expose the value of attention and sentiment features extracted from Twitter. We study the approach on a stock universe comprised of the 165 most liquid US stocks diversified across the 11 traditional market sectors using a sizeable out-of-sample period spanning over six years. In doing so, we uncover that stocks in certain sectors, such as Consumer Discretionary, Technology, Real Estate, and Utilities are easier to predict than others. Further analysis shows that possible reasons for these discrepancies might be caused by either excess social media attention or low option liquidity. Lastly, we explore how our proposed approach fares throughout time by identifying four underlying market regimes in implied volatility using hidden Markov models. We find that most added value is achieved in regimes associated with lower implied volatility, but optimal regimes vary per market sector.

Market makers play an essential role in financial markets. A successful market maker should control inventory and adverse selection risks and provide liquidity to the market. As an important methodology in control problems, Reinforcement Learning enjoys the advantage of data-driven and less rigid assumptions, receiving great attention in the market-making field since 2018. However, although the China Commodity market has the biggest trading volume on agricultural products, nonferrous metals, and some other sectors, the study of applying RL to Market Making in China market is still rare. In this thesis, we try to fill the gap. Our contribution is threefold: We develop the Automatic Trading System and verify the feasibility of applying Reinforcement Learning in the China Commodity market. Also, we probe the agent's behavior by analyzing how it reacts to different environmental conditions.

Using machine learning and alternative data for the prediction of financial markets has been a popular topic in recent years. Many financial variables such as stock price, historical volatility and trade volume have already been through extensive investigation. Remarkably, we found no existing research on the prediction of an asset's market implied volatility within this context. This forward-looking measure gauges the sentiment on the future volatility of an asset, and is deemed one of the most important parameters in the world of derivatives. The ability to predict this statistic may therefore provide a competitive edge to practitioners of market making and asset management alike. Consequently, in this paper we investigate Google News statistics and Wikipedia site traffic as alternative data sources to quantitative market data and consider Logistic Regression, Support Vector Machines and AdaBoost as machine learning models. We show that movements in market implied volatility can indeed be predicted through the help of machine learning techniques. Although the employed alternative data appears to not enhance predictive accuracy, we reveal preliminary evidence of non-linear relationships between features obtained from Wikipedia page traffic and movements in market implied volatility.

American options are the reference instruments for the model calibration of a large and important class of single stocks. For this task, a fast and accurate pricing algorithm is indispensable. The literature mainly discusses pricing methods for American options that are based on Monte Carlo, tree and partial differential equation methods. We present an alternative approach that has become popular under the name de-Americanization in the financial industry. The method is easy to implement and enjoys fast run-times. Since it is based on ad hoc simplifications, however, theoretical results guaranteeing reliability are not available. To quantify the resulting methodological risk, we empirically test the performance of the de-Americanization method for calibration. We classify the scenarios in which de-Americanization performs very well. However, we also identify the cases where de-Americanization oversimplifies and can result in large errors., Comment: Key words: American options, calibration, binomial tree model, CEV model, Heston model, L\'evy models, model reduction, variational inequalities