Mathematical Finance
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QST MF 825: Advanced Topics in Investments
This course is designed for students seeking to work as quants in a quantitative finance investments group. It covers utility theory, portfolio optimization, asset pricing, and some aspects of factor models, incorporating the impact of parameter uncertainty. The course does not cover risk management or fixed income instruments, nor does it describe how the financial services industry works. Rather, it teaches how a quant should optimize a portfolio. The course makes extensive use of R (Excel or VBA are not substitutes), optimization theory, statistics, regression theory (OLS, GLS, testing theory), and matrix algebra. Students should be very comfortable with these concepts before taking the course; further, students should already have taken a finance course covering expected returns models (CAPM), options and futures. The course emphasizes the ability to prove theoretical results and their validity, an essential trait for investments quants. Students who completed QST FE825 may not take this course for credit. (Mathematical Finance courses are reserved for students enrolled in the Mathematical Finance program.) -
QST MF 840: Data Analysis and Financial Econometrics
Graduate Prerequisites: QST MF 793.
This is the second course of the econometrics sequence in the Mathematical Finance program. The course quickly reviews OLS, GLS, the Maximum Likelihood principle (MLE). Then, the core of the course concentrates on Bayesian Inference, now an unavoidable mainstay of Financial Econometrics. After learning the principles of Bayesian Inference, we study their implementation for key models in finance, especially related to portfolio design and volatility forecasting. We also briefly discuss the Lasso and Ridge methods, and contrast them with the Bayesian approach Over the last twenty years, radical developments in simulation methods, such as Markov Chain Monte Carlo (MCMC) have extended the capabilities of Bayesian methods. Therefore, after studying direct Monte Carlo simulation methods, the course covers non-trivial methods of simulation such as Markov Chain Monte Carlo (MCMC), applying them to implement models such as stochastic volatility. (Mathematical Finance courses are reserved for students enrolled in the Mathematical Finance program.) -
QST MF 850: Deep Learning, Statistical Learning
Graduate Prerequisites: QST MF 796.
This course explores algorithmic and numerical schemes used in practice for the pricing and hedging of financial derivative products. The focus of this course lies on data analysis. It covers such topics as: stochastic models with jumps, advanced simulation methods, optimization routines, and tree-based approaches. It also introduces machine learning concepts and methodologies, including cross validation, dimensionality reduction, random forests, neural networks, clustering, and support vector machines. (Mathematical Finance courses are reserved for students enrolled in the Mathematical Finance program.) -
QST MF 921: Topics in Dynamic Asset Pricing
This course provides a comprehensive and in-depth treatment of modern asset pricing theories. Extensive use is made of continuous time stochastic processes, stochastic calculus and optimal control. Particular emphasis will be placed on (i) stochastic calculus with jumps; (ii) asset pricing models with jumps; (iii) the Hamilton-Jacobi-Bellman equation and stochastic control; (iv) numerical methods for stochastic control problems in finance. (Mathematical Finance courses are reserved for students enrolled in the Mathematical Finance program.) -
QST MF 930: Advanced Corporate Finance
This doctoral level class on corporate finance covers both theoretical and empirical work. Rather than explaining the underpinnings of basic corporate research (e.g., model/applications dealing with asymmetric information, agency problems, and capital market frictions), we go deeper in understanding "how to operationalize" research on concrete topics that are central to contemporary corporate finance, such as bankruptcy, capital structure, mergers and acquisitions, the firm boundaries, investment, and much more. The class also looks at the interface between corporate finance and other research areas, such as asset pricing and banking. The course is a blend of new approaches to modeling in corporate research (e.g., dynamic, structural models of financial policy that generate typically quantitative predictions) and new approaches to testing design (e.g., regression discontinuities and natural experiments). The goal is to expose the students to the "state-of-the-art" of research in corporate finance and prepare them to do research in corporate finance using new methods and tools. (Mathematical Finance courses are reserved for students enrolled in the Mathematical Finance program.) -
QST MF 990: Current Topics Seminar
For PhD students in the Mathematical Finance program. Registered by permission only. -
QST MF 998: Directed Study: Mathematical Finance
Graduate Prerequisites: Consent of instructor and the program director
PhD-level directed study in Mathematical Finance. 1, 2, or 3 cr. Application available on the Graduate Center website. -
QST MF 999: Directed Study: Mathematical Finance
Graduate Prerequisites: Consent of instructor and the program director
PhD-level directed study in Mathematical Finance. 1, 2, or 3 cr. Application available on the Graduate Center website.
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