Fred Fontaine

    This course approaches quantitative finance from a signal processing perspective. Stochastic processes: random walks, Brownian motion, Ito calculus, continuous models including Black-Scholes, discrete models including negative binomial, martingales, stopping times. Representation and analysis of financial concepts such as price, risk, volatility, futures, options, arbitrage, derivatives, portfolios and trading strategies. Analysis of single and multiple nonstationary time series, GARCH models. Optimization methods, big data and machine learning in finance.

    3 credits. Prerequisites: MA224 Probability, ECE211 Signal Processing or permission of instructor.

Graduate level.

Last offered: Fall 2018.

In addition to quizzes and simulation projects, each student is required to read a technical article from a peer-reviewed journal and give a presentation. The presentations for Fall 2018 were based on the following:

• Taylor Series Approach to Pricing and Implied Volatility for Local-Stochastic Volatility Models (Lorig, Pagliarani, Pascucci)
• Multifractal Random Walks with Fractional Brownian Motion via Malliavin Calculus (Fauth, Tudor)
• Forecasting High-Frequency Futures Returns Using Online Langevin Dynamics (Christensen, Murphy, Godsill)
• Performance Analysis and Optimal Selection of Large Minimum Variance Portfolios Under Estimation Risk (Rubio, Mestre, Palomar)
• Evaluation of the Stochastic Modelling on Options (Mao, Liang, Lian, Zhang)
• Gaussian Process Regression Stochastic Volatility Model for Financial Time Series
• Improved Estimation of the Covariance Matrix of Stock Returns with an Application to Portfolio Selection (Ledoit & Wolf)
• Risk-Averse Multi-Armed Bandit Problems Under Mean-Variance Measure (Vakili, Zhao)
• Portfolio Optimization Using Novel Co-Variance Guided Artificial Bee Colony Algorithm (Kumar, Mishra)
• Option Pricing with an Illiquid Underlying Asset Market (Liu, Yong)
• Sparse Portfolios for High-Dimensional Financial Index Tracking (Benidis, Feng, Palomar)
• Mixed Effects in Stochastic Differential Equation Models (Ditlevsen, DeGaetano)
• Forecasting of Power Corporations’ Default Probability with Nonlinear Kalman Filtering (Rigatos, Siano)
• Estimation of Ornstein-Uhlenbeck Process Using Ultra-High-Frequency Data with Application to Intraday Pairs Trading Strategy (Holy, Tomanova)
• The Measurement and Asymmetry Tests of Business Cycle: Evidence from China (Liu, Liao)
• Out-of-Sample Forcasting of Housing Bubble Tipping Points (Ardila, Sanadgol, Sornett)