MSc in Financial Engineering

In this pilot course for the MScFE program, students are introduced to the world of professional finance: markets, products, participants, and regulation. The activities within financial markets will be discussed, including trading, financing, brokering, pricing, hedging, optimizing, and managing risk. Throughout the course, students identify a list of significant factors that affect the financial industry. Students will be able to interact with web apps that illustrate these concepts. Understanding the asset classes, activities, and influential aspects of the financial landscape will provide a solid foundation on which students will build mathematical and computational tools to develop models for financial engineering. No background in finance is required.

This course introduces students to financial data: the source of energy for financial models. Students will learn how to apply Python to properly select, import, filter, structure, visualize, summarize, and analyze financial data for interest rates, equities, cryptocurrencies, ETFs, securitized products, and other asset classes. Students will also learn how to prepare data to be used in models for financial markets, from which decisions can be made, and how to accomplish fundamental analysis with accounting data, technical analysis with trading data, statistical analysis with transformed data, and sentiment analysis with textual data. Software engineering, visualization techniques, probability and statistics, linear algebra, and presentation skills will be developed throughout the course. The ultimate goal of this course is to build foundational skills that enable students to understand the type of data needed depending on their goals, how to source it, structure it, shape it, build with it, and discover what it tells. At their best, financial engineers turn data into empirically based, well-calibrated financial models whose output provides investors and risk managers with sound decisions in the uncertain world of finance.

This course provides a comprehensive introduction to financial econometrics. Students will learn how to model probability distributions of returns, including graphical, Bayesian, and non-parametrical methods. They will also learn how to model univariate time series, focusing on their moving average, autocorrelations, and volatilities, including GARCH models. Students will build additional tools to see how two financial series can relate to each other, using correlation, vector autoregressions, and cointegration. Further, they will build the statistical foundation and Python coding skills to run econometric models to apply in financial decision making. Finally, they will see how the ideas of bias, variance, and overfitting apply to machine learning.

Derivative Pricing is a hands-on course focused on pricing options. Students will build a conceptual background that deepens their understanding of why classical calculus is not sufficient for detecting rates of change in stochastic processes. Course content focuses on the concept of no-arbitrage and perfect replication using the world of stochastic calculus, including the Black-Scholes Model. Students will be able to construct pricing models such as binomial trees and finite difference methods to price an array of vanilla and exotic options. They will also measure sensitivities of the price to variables, such as the underlying price, volatility, time, interest rates, and carry costs. Finally, some extensions to classical models, such as the Heston Model and jump models will be addressed. Much of the course will include Python illustrations to build practical skills.

In this course, students increase their knowledge of modeling stochastic processes. Students will investigate advanced volatility models that upgrade Black Scholes parameters to variables, increasing their stochastic modeling skills to address heteroskedasticity and variable costs as well as jump diffusions. Students will dive into Markov processes, including hidden Markov process and Markov decision process to financial applications, and will build a mathematical foundation for deep learnings, a tool they will use for machine learnings. Overall, students will be able to evaluate the assumptions, benefits, and difficulties associated with stochastic models.

This course addresses the fundamentals of machine learning. It continues the topics from the Financial Econometrics course whereby students will be able to apply algorithms to learn from data. Students will cover the mathematical and computational foundations of both the supervised and unsupervised machine learning problems, and they will use Python modules and a Tensorflow framework to predict, explain, or compare outcomes across different financial series. Students will apply machine learning techniques to determine if financial models are overfit, and use methods of regularization, cross-validation, and resampling techniques to mitigate it. In addition, students will develop a theoretical and practical background in deep learning models to improve the power of their financial model predictions.

Directly building on their skills from Machine Learning, students will further explore neural networks in Deep Learning for Finance. Students will build mastery in Python with TensorFlow to build and train neural networks and apply them to real life financial examples. They will expand their toolkits to perform regularization. During this course, students will use various algorithms to tune hyperparameters, including classical, Bayesian, and stochastic methods. Different neural network architectures will be addressed, particularly CNNs (Convolutional Neural Networks), RNNs (Recurrent Neural Networks), LSTMs (Long Short-Term Memory), and GRUs (Gated Recurring Units). These neural networks will be built from scratch, then illustrated in financial examples such as predicting stock prices, discovering investment factors, and back-testing trading strategies. Students will apply state-of-the-art techniques such as transfer learning and data augmentation. These methods will be used to improve the learning capability and performance of the networks, resulting in better predictions. In addition, students will learn the theory behind these tools, as well as richly exploring how to combine architectures with optimization techniques applied to real world data for comprehensive intraday trading strategy development.

This course provides students with methodologies and skills to perform portfolio optimization. From the previous coursework, students will have a solid foundation on which to engage in the portfolio management process. In the first two modules, students will review classical methods of portfolio theory, including Markowitz portfolio optimization. Subsequent modules address more modern versions of the portfolio optimization process, including Black-Litterman, probabilistic scenario optimization, prospect theory, Kelly criterion, and risk parity. In addition, advanced econometrics and machine learning methods will be applied to the classical techniques, including the use of neural networks, genetic algorithms, information theory, and reinforcement learning. The course requires students to engage with the mathematical foundations, code implementation, and practical applications of portfolio management across many asset classes.

This course provides students with both classical and modern methods of modeling and managing risk. The course begins by reviewing metrics and models for market, credit, and systemic risk, and applying these ideas to multiple asset classes, including derivatives. Machine learning methods will be integrated with both classical methods like VaR and GARCH and with robust methods like Extreme Value Theory. Then a comprehensive review of Bayesian methods will be given that builds towards a Bayesian network of modeling systemic risk. By taking the course, students will be able to synthesize a complex network and scenario analysis for both portfolio risk and systemic risk.

The Capstone Course is designed to put the students’ knowledge of financial engineering to the test. Students practically apply their understanding of the program content by accomplishing project milestones from developing a problem statement, identifying the required technology to find a solution to the problem, submitting multiple drafts for peer review and instructor feedback, and finalizing and presenting their fully developed project. The goal of the Capstone Course is to ensure that students have met the program outcomes and are able to apply their knowledge and skills to real-world scenarios.