Prerequisites: MATH UN1202, MATH UN3027, STAT GR5203, or their equivalents.
The mathematics of finance, principally the problem of pricing of derivative securities, developed using only calculus and basic probability. Topics include mathematical models for financial instruments, Brownian motion, normal and lognormal distributions, the Black├╗Scholes formula, and binomial models.
It is commonly believed that one cannot be blamed for actions that one is compelled to perform. Addiction is often taken to be an archetypical; case of a condition that can compel actions. But what is addiction? Is there a principled division between paradigmatic addictive behaviors such as heroin use and, e.g., excessive cell phone use? The answers to questions like these turn out to be highly controversial. Drawing on psychiatric as well as philosophical literatures, we will seek an analysis of the concept of addiction that can illuminate its moral significance. We will conclude by discussing arguments for skepticism about responsibility judgments more broadly. According to such arguments, none of us are responsible for anything, not because responsible action is incompatible with determinism, but because there is no principled explanation for why addicts would fail to be responsible which not overgeneralize to non-addicts.
Prerequisites: STAT GR5205
Least squares smoothing and prediction, linear systems, Fourier analysis, and spectral estimation. Impulse response and transfer function. Fourier series, the fast Fourier transform, autocorrelation function, and spectral density. Univariate Box-Jenkins modeling and forecasting. Emphasis on applications. Examples from the physical sciences, social sciences, and business. Computing is an integral part of the course.
This course covers features of the C++ programming language which are essential in quantitative/computational finance and its applications. We start by covering basic C++ programming features and then move to some more advance features. We utilize these features for financial engineering and quantitative finance applications primarily for pricing of financial derivatives and computational finance. Those applications include transform techniques, Monte Carlo simulation, calibration and parameter estimation techniques.
Prerequisites: STAT GR5204 or the equivalent. STAT GR5205 is recommended.
A fast-paced introduction to statistical methods used in quantitative finance. Financial applications and statistical methodologies are intertwined in all lectures. Topics include regression analysis and applications to the Capital Asset Pricing Model and multifactor pricing models, principal components and multivariate analysis, smoothing techniques and estimation of yield curves statistical methods for financial time series, value at risk, term structure models and fixed income research, and estimation and modeling of volatilities. Hands-on experience with financial data.
Prerequisites: STAT GR5205 or the equivalent.
Available to SSP, SMP Modeling and inference for random processes, from natural sciences to finance and economics. ARMA, ARCH, GARCH and nonlinear models, parameter estimation, prediction and filtering.
Prerequisites: STAT GR5203 or the equivalent.
Basics of continuous-time stochastic processes. Wiener processes. Stochastic integrals. Ito's formula, stochastic calculus. Stochastic exponentials and Girsanov's theorem. Gaussian processes. Stochastic differential equations. Additional topics as time permits.
Prerequisites: STAT GR5264
Available to SSP, SMP. Mathematical theory and probabilistic tools for modeling and analyzing security markets are developed. Pricing options in complete and incomplete markets, equivalent martingale measures, utility maximization, term structure of interest rates.
Risk/return tradeoff, diversification and their role in the modern portfolio theory, their consequences for asset allocation, portfilio optimization. Capitol Asset Pricing Model, Modern Portfolio Theory, Factor Models, Equities Valuation, definition and treatment of futures, options and fixed income securities will be covered.
The hedge fund industry has continued to grow after the financial crisis, and hedge funds are increasingly important as an investable asset class for institutional investors as well as wealthy individuals. This course will cover hedge funds from the point of view of portfolio managers and investors. We will analyze a number of hedge fund trading strategies, including fixed income arbitrage, global macro, and various equities strategies, with a strong focus on quantitative strategies. We distinguish hedge fund managers from other asset managers, and discuss issues such as fees and incentives, liquidity, performance evaluation, and risk management. We also discuss career development in the hedge fund context.
Prerequisites: Student expected to be mathematically mature and familiar with probability and statistics, arbitrage pricing theory, and stochastic processes.
The course will introduce the notions of financial risk management, review the structure of the markets and the contracts traded, introduce risk measures such as VaR, PFE and EE, overview regulation of financial markets, and study a number of risk management failures. After successfully completing the course, the student will understand the basics of computing parametric VaR, historical VaR, Monte Carlo VaR, cedit exposures and CVA and the issues and computations associated with managing market risk and credit risk. The student will be familiar with the different categories of financial risk, current regulatory practices, and the events of financial crises, especially the most recent one.
Prerequisites: Comfortable with algebra, calculus, probability, statistics, and stochastic calculus.
The course covers the fundamentals of fixed income portfolio management. Its goal is to help the students develop concepts and tools for valuation and hedging of fixed income securities within a fixed set of parameters. There will be an emphasis on understanding how an investment professional manages a portfolio given a budget and a set of limits.
This course provides an opportunity for MAFN students to engage in off-campus internships for academic credit that counts towards the degree. Graded by letter grade. Students need to secure an internship and get it approved by the instructor.
This course provides an opportunity for MAFN students to engage in unpaid internships for academic credit on a pass / fail basis. Students need to secure an internship and get it approved by the instructor. For unpaid internships only.
Prerequisites: Calculus
This course covers the following topics: Fundamentals of probability theory and statistical inference used in data science; Probabilistic models, random variables, useful distributions, expectations, law of large numbers, central limit theorem; Statistical inference; point and confidence interval estimation, hypothesis tests, linear regression.
Prerequisites: working knowledge of calculus and linear algebra (vectors and matrices), and STAT GR5203 or the equivalent.
In this course, we will systematically cover fundamentals of statistical inference and testing, and give an introduction to statistical modeling. The first half of the course will be focused on inference and teesting, covering topics such as maximum likelihood estimates, hypothesis testing, likelihood ratio test, Bayesian inference, etc. The second half of the course will provide introduction to statistical modeling via introductory lectures on linear regression models, generalized linear regression models, nonparametric regression. and statistical computing. Throughpout the course, real-data examples will be used in lecture discussion and homework problems. This course lays the foundation, preparing the MA in Data Science studnets, for other courses in machine learning, data mining and visualization.