ACADEMICS

FALL SEMESTER

• Computing In Finance
  

  MATH-GA.2041-001

  Computing In Finance

  Lee Maclin and Eran Fishler

  Prerequisites: Procedural programming, some knowledge of Java recommended.

  Description: The purpose of this course is threefold: 1) It will teach students the popular Python programming language. 2) Students will learn the five most important concepts of modern, object-oriented software development, which are testing, data structures, design, working with data, and distributed computing. 3) All of the examples used in class will have a financial context. Projects we will work on include developing a toy exchange, building a framework for managing live price data, and tools for preparing high frequency data for simulations and backtests. Additional topics include Google’s Firebase real-time database and using Python to work with SQL. Extensive use of the Anki study system will be made to allow students to gauge their own progress and prepare for tests.

• Data Science And Data-Driven Modeling
  

  MATH-GA.2070-001

  Data Science And Data-Driven Modeling

  Miquel Noguer I Alonso

  Prerequisites: N/A

  Description: This is a half-semester course covering practical aspects of econometrics/statistics and data science/machine learning in an integrated and unified way as they are applied in the financial industry. We examine statistical inference for linear models, supervised learning (Lasso, ridge and elastic-net), and unsupervised learning (PCA- and SVD-based) machine learning techniques, applying these to solve common problems in finance. In addition, we cover model selection via cross-validation; manipulating, merging and cleaning large datasets in Python; and web-scraping of publicly available data.

• Financial Securities And Markets
  

  MATH-GA.2791-001

  Financial Securities And Markets

  Alireza Javaheri

  Prerequisites: Multivariate calculus, linear algebra, and calculus-based probability.

  Description: This course provides a quantitative introduction to financial securities for students who are aspiring to careers in the financial industry. We study how securities traded, priced and hedged in the financial markets. Topics include: arbitrage; risk-neutral valuation; the log-normal hypothesis; binomial trees; the Black-Scholes formula and applications; the Black-Scholes partial differential equation; American options; one-factor interest rate models; swaps, caps, floors, swaptions, and other interest-based derivatives; credit risk and credit derivatives; clearing; valuation adjustment and capital requirements. It is important that students taking this course have good working knowledge of multivariate calculus, linear algebra and calculus-based probability.

• Risk & Portfolio Management
  

  MATH-GA.2751-001

  Risk & Portfolio Management

  Kenneth Winston

  Prerequisites: Multivariate calculus, linear algebra, and calculus-based probability.

  Description: Risk management is arguably one of the most important tools for managing investment portfolios and trading books and quantifying the effects of leverage and diversification (or lack thereof). This course is an introduction to portfolio and risk management techniques for portfolios of (i) equities, delta-1 securities, and futures and (ii) basic fixed income securities. A systematic approach to the subject is adopted, based on selection of risk factors, econometric analysis, extreme-value theory for tail estimation, correlation analysis, and copulas to estimate joint factor distributions. We will cover the construction of risk measures (e.g. VaR and Expected Shortfall) and portfolios (e.g. portfolio optimization and risk). As part of the course, we review current risk models and practices used by large financial institutions. It is important that students taking this course have good working knowledge of multivariate calculus, linear algebra and calculus-based probability.

• Stochastic Calculus
  

  MATH-GA.2903-001

  Stochastic Calculus

  Jonathan Goodman

  Prerequisites: Multivariate calculus, linear algebra, and calculus-based probability.

  Description: The goal of this half-semester course is for students to develop an understanding of the techniques of stochastic processes and stochastic calculus as it is applied in financial applications. We begin by constructing the Brownian motion (BM) and the Ito integral, studying their properties. Then we turn to Ito’s lemma and Girsanov’s theorem, covering several practical applications. Towards the end of the course, we study the linkage between SDEs and PDEs through the Feynman-Kac equation. It is important that students taking this course have good working knowledge of calculus-based probability.

SPRING SEMESTER

• Financial Securities And Markets
  

  MATH-GA.2791-001

  Financial Securities And Markets

  Alireza Javaheri

  Prerequisites: Multivariate calculus, linear algebra, and calculus-based probability.

  Description: This course provides a quantitative introduction to financial securities for students who are aspiring to careers in the financial industry. We study how securities traded, priced and hedged in the financial markets. Topics include: arbitrage; risk-neutral valuation; the log-normal hypothesis; binomial trees; the Black-Scholes formula and applications; the Black-Scholes partial differential equation; American options; one-factor interest rate models; swaps, caps, floors, swaptions, and other interest-based derivatives; credit risk and credit derivatives; clearing; valuation adjustment and capital requirements. It is important that students taking this course have good working knowledge of multivariate calculus, linear algebra and calculus-based probability.

• Risk & Portfolio Management
  

  MATH-GA.2751-001

  Risk & Portfolio Management

  Kenneth Winston

  Prerequisites: Multivariate calculus, linear algebra, and calculus-based probability.

  Description: Risk management is arguably one of the most important tools for managing investment portfolios and trading books and quantifying the effects of leverage and diversification (or lack thereof). This course is an introduction to portfolio and risk management techniques for portfolios of (i) equities, delta-1 securities, and futures and (ii) basic fixed income securities. A systematic approach to the subject is adopted, based on selection of risk factors, econometric analysis, extreme-value theory for tail estimation, correlation analysis, and copulas to estimate joint factor distributions. We will cover the construction of risk measures (e.g. VaR and Expected Shortfall) and portfolios (e.g. portfolio optimization and risk). As part of the course, we review current risk models and practices used by large financial institutions. It is important that students taking this course have good working knowledge of multivariate calculus, linear algebra and calculus-based probability.

• Stochastic Calculus
  

  MATH-GA.2903-001

  Stochastic Calculus

  Jonathan Goodman

  Prerequisites: Multivariate calculus, linear algebra, and calculus-based probability.

  Description: The goal of this half-semester course is for students to develop an understanding of the techniques of stochastic processes and stochastic calculus as it is applied in financial applications. We begin by constructing the Brownian motion (BM) and the Ito integral, studying their properties. Then we turn to Ito’s lemma and Girsanov’s theorem, covering several practical applications. Towards the end of the course, we study the linkage between SDEs and PDEs through the Feynman-Kac equation. It is important that students taking this course have good working knowledge of calculus-based probability.

SUMMER SEMESTER

• Stochastic Calculus
  

  MATH-GA.2903-001

  Stochastic Calculus

  Jonathan Goodman

  Prerequisites: Multivariate calculus, linear algebra, and calculus-based probability.

  Description: The goal of this half-semester course is for students to develop an understanding of the techniques of stochastic processes and stochastic calculus as it is applied in financial applications. We begin by constructing the Brownian motion (BM) and the Ito integral, studying their properties. Then we turn to Ito’s lemma and Girsanov’s theorem, covering several practical applications. Towards the end of the course, we study the linkage between SDEs and PDEs through the Feynman-Kac equation. It is important that students taking this course have good working knowledge of calculus-based probability.

FALL SEMESTER

• Dynamic Asset Pricing
  

  MATH-GA.2793-001

  Dynamic Asset Pricing

  Samim Ghamami

  Prerequisites: Calculus-based probability, Stochastic Calculus, and a one semester course on derivative pricing (such as what is covered in Financial Securities and Markets).

  Description: This is an advanced course on asset pricing and trading of derivative securities. Using tools and techniques from stochastic calculus, we cover (1) Black-Scholes-Merton option pricing; (2) the martingale approach to arbitrage pricing; (3) incomplete markets; and (4) the general option pricing formula using the change of numeraire technique. As an important example of incomplete markets, we discuss bond markets, interest rates and basic term-structure models such as Vasicek and Hull-White. It is important that students taking this course have good working knowledge of calculus-based probability and stochastic calculus. Students should also have taken the course “Financial Securities and Markets” previously. In addition, we recommend an intermediate course on mathematical statistics or engineering statistics as an optional prerequisite for this class.

• Project & Presentation
  

  MATH-GA.2755-001

  Project & Presentation

  Petter Kolm

  Prerequisites: N/A

  Description: Students in the Mathematics in Finance program conduct research projects individually or in small groups under the supervision of finance professionals. The course culminates in oral and written presentations of the research results.

• Scientific Computing
  

  MATH-GA.2043-001

  Scientific Computing

  Jonathan Goodman

  Prerequisites: Undergraduate multivariate calculus and linear algebra. Programming experience strongly recommended but not required.

  Description: This course is intended to provide a practical introduction to computational problem solving. Topics covered include: the notion of well-conditioned and poorly conditioned problems, with examples drawn from linear algebra; the concepts of forward and backward stability of an algorithm, with examples drawn from floating point arithmetic and linear-algebra; basic techniques for the numerical solution of linear and nonlinear equations, and for numerical optimization, with examples taken from linear algebra and linear programming; principles of numerical interpolation, differentiation and integration, with examples such as splines and quadrature schemes; an introduction to numerical methods for solving ordinary differential equations, with examples such as multistep, Runge Kutta and collocation methods, along with a basic introduction of concepts such as convergence and linear stability; An introduction to basic matrix factorizations, such as the SVD; techniques for computing matrix factorizations, with examples such as the QR method for finding eigenvectors; Basic principles of the discrete/fast Fourier transform, with applications to signal processing, data compression and the solution of differential equations. This is not a programming course but programming in homework projects with MATLAB/Octave and/or C is an important part of the course work. As many of the class handouts are in the form of MATLAB/Octave scripts, students are strongly encouraged to obtain access to and familiarize themselves with these programming environments. Recommended Texts: Bau III, D., & Trefethen, L.N. (1997). Numerical Linear Algebra. Philadelphia, PA: Society for Industrial & Applied Mathematics Quarteroni, A.M., & Saleri, F. (2006). Texts in Computational Science & Engineering [Series, Bk. 2]. Scientific Computing with MATLAB and Octave (2nd ed.). New York, NY: Springer-Verlag Otto, S.R., & Denier, J.P. (2005). An Introduction to Programming and Numerical Methods in MATLAB. London: Springer-Verlag London

SPRING SEMESTER

• Dynamic Asset Pricing
  

  MATH-GA.2793-001

  Dynamic Asset Pricing

  Samim Ghamami

  Prerequisites: Calculus-based probability, Stochastic Calculus, and a one semester course on derivative pricing (such as what is covered in Financial Securities and Markets).

  Description: This is an advanced course on asset pricing and trading of derivative securities. Using tools and techniques from stochastic calculus, we cover (1) Black-Scholes-Merton option pricing; (2) the martingale approach to arbitrage pricing; (3) incomplete markets; and (4) the general option pricing formula using the change of numeraire technique. As an important example of incomplete markets, we discuss bond markets, interest rates and basic term-structure models such as Vasicek and Hull-White. It is important that students taking this course have good working knowledge of calculus-based probability and stochastic calculus. Students should also have taken the course “Financial Securities and Markets” previously. In addition, we recommend an intermediate course on mathematical statistics or engineering statistics as an optional prerequisite for this class.

• Project & Presentation
  

  MATH-GA.2755-001

  Project & Presentation

  Petter Kolm

  Prerequisites: N/A

  Description: Students in the Mathematics in Finance program conduct research projects individually or in small groups under the supervision of finance professionals. The course culminates in oral and written presentations of the research results.

• Scientific Computing In Finance
  

  MATH-GA.2048-001

  Scientific Computing In Finance

  Richard Lindsey and Mehdi Sonthonnax

  Prerequisites: Risk and Portfolio Management, Financial Securities and Markets, and Computing in Finance.

  Description: This is a version of the course Scientific Computing (MATH-GA 2043.001) designed for applications in quantitative finance. It covers software and algorithmic tools necessary to practical numerical calculation for modern quantitative finance. Specific material includes IEEE arithmetic, sources of error in scientific computing, numerical linear algebra (emphasizing PCA/SVD and conditioning), interpolation and curve building with application to bootstrapping, optimization methods, Monte Carlo methods, and the solution of differential equations. Please Note: Students may not receive credit for both MATH-GA 2043.001 and MATH-GA 2048.001

• Machine Learning & Computational Statistics
  

  MATH-GA.2071-001

  Machine Learning & Computational Statistics

  Ivailo Dimov

  Prerequisites: Multivariate calculus, linear algebra, and calculus-based probability. Students should also have working knowledge of basic statistics and machine learning (such as what is covered in Data Science & Data-Driven Modeling).

  Description: Description TBA

FALL SEMESTER

• Advanced Statistical Inference And Machine Learning
  

  MATH-GA.2046-001

  Advanced Statistical Inference And Machine Learning

  Gordon Ritter

  Prerequisites: The following four courses, or equivalent: (1) Data Science and Data-Driven Modeling, (2) Financial Securities and Markets, (3) Machine Learning & Computational Statistics, and (4) Risk and Portfolio Management. It is important you have experience with the Python stack.

  Description: A rigorous background in Bayesian statistics geared towards applications in finance. The early part of the course will cover the Bayesian approach to modeling, inference, point estimation, and forecasting, sufficient statistics, exponential families and conjugate priors, and the posterior predictive density. We will then undertake a detailed treatment of multivariate regression including Bayesian regression, variable selection techniques, multilevel/hierarchical regression models, and generalized linear models (GLMs). We will continue to discuss Bayesian networks and belief propagation with applications to machine learning and prediction tasks. Solution techniques include Markov Chain Monte Carlo methods, Gibbs Sampling, the EM algorithm, and variational mean field theory. We shall then introduce reinforcement learning with applications to transaction cost minimization and realistic optimal hedging of derivatives. Real world examples will be given throughout the course, including portfolio optimization with transaction costs, and a selection of the most important prediction tasks arising in buy-side quant trading.

• Alternative Data In Quantitative Finance
  

  MATH-GA.2049-001

  Alternative Data In Quantitative Finance

  Gene Ekster

  Prerequisites: Risk and Portfolio Management; and Computing in Finance. In addition, students should have a working knowledge of statistics, finance, and basic machine learning. Students should have working experience with the Python stack (numpy/pandas/scikit-learn).

  Description: This half-semester elective course examines techniques dealing with the challenges of the alternative data ecosystem in quantitative and fundamental investment processes. We will address the quantitative tools and technique for alternative data including identifier mapping, stable panel creation, dataset evaluation and sensitive information extraction. We will go through the quantitative process of transferring raw data into investment data and tradable signals using text mining, time series analysis and machine learning. It is important that students taking this course have working experience with Python Stack. We will analyze real-world datasets and model them in Python using techniques from statistics, quantitative finance and machine learning.

• Trends In Financial Data Science
  

  MATH-GA.2047-001

  Trends In Financial Data Science

  Petter Kolm and Ivailo Dimov

  Prerequisites: The following four courses, or equivalent: (1) Data Science and Data-Driven Modeling, (2) Financial Securities and Markets, (3) Machine Learning & Computational Statistics, and (4) Risk and Portfolio Management. It is important you have experience with the Python stack.

  Description: This is a full semester course covering recent and relevant topics in alternative data, machine learning and data science relevant to financial modeling and quantitative finance. This is an advanced course that is suitable for students who have taken the more basic graduate machine learning and finance courses Data Science and Data-Driven Modeling, and Machine Learning & Computational Statistics, Financial Securities and Markets, and Risk and Portfolio Management.

• Fixed Income Derivatives: Models & Strategies In Practice
  

  MATH-GA.2803-001

  Fixed Income Derivatives: Models & Strategies In Practice

  Leon Tatevossian

  Prerequisites: Familiarity with the foundational mathematical tools of finance; basic understanding of the motivation for and the machinery of pricing models in the interest-rate domain; programming skills; basic proficiency in Excel. Some product knowledge of interest-rate products is helpful but not required.

  Description: Armed with a foundation in bond math and the theory and implementation of interest-rate models, many fixed-income quants are challenged to understand how these concepts and tools are deployed in the sales/trading environment. Often the economic content of a simple trade idea gets obscured by market jargon, especially in a competitive transactional environment. The class will focus on the practical workings of the fixed-income and rates-derivatives markets. The content is motivated by a representative set of real-world trading, investment, and hedging objectives. Each situation will be examined from the ground level; risk and reward attributes will be identified. This strategy will reinforce the link from underlying market views to the applicable product set and to the tools for managing the position. Common threads among products – structural or model-based – will be emphasized. We plan on covering bonds, swaps, flow options, semi-exotics, and some structured products. This problem-oriented holistic view is a productive way to understand the line from product creation to modeling, marketing, trading, and hedging. We hope to convey intuition about both the power and limitations of models. How do sell-side practitioners manage the various constraints and imperfections in the context of changing market backdrops and customer demands?

• Time Series Analysis & Statistical Arbitrage
  

  MATH-GA.2707-001

  Time Series Analysis & Statistical Arbitrage

  Farshid Asl and Robert Reider

  Prerequisites: Financial Securities and Markets; Scientific Computing in Finance (or Scientific Computing); and familiarity with basic probability.

  Description: The term "statistical arbitrage" covers any trading strategy that uses statistical tools and time series analysis to identify approximate arbitrage opportunities while evaluating the risks inherent in the trades (considering the transaction costs and other practical aspects). This course starts with a review of Time Series models and addresses econometric aspects of financial markets such as volatility and correlation models. We will review several stochastic volatility models and their estimation and calibration techniques as well as their applications in volatility based trading strategies. We will then focus on statistical arbitrage trading strategies based on cointegration, and review pairs trading strategies. We will present several key concepts of market microstructure, including models of market impact, which will be discussed in the context of developing strategies for optimal execution. We will also present practical constraints in trading strategies and further practical issues in simulation techniques. Finally, we will review several algorithmic trading strategies frequently used by practitioners.

• Trends In Sell-Side Modeling: Xva, Capital And Credit Derivatives
  

  MATH-GA.2805-001

  Trends In Sell-Side Modeling: Xva, Capital And Credit Derivatives

  Leif Andersen and Irena Khrebtova

  Prerequisites: Advanced Risk Management; Financial Securities and Markets, or equivalent familiarity with market and credit risk models; and Computing in Finance, or equivalent programming experience.

  Description: This class explores technical and regulatory aspects of counterparty credit risk, with an emphasis on model building and computational methods. The first part of the class will provide technical foundation, including the mathematical tools needed to define and compute valuation adjustments such as CVA and DVA. The second part of the class will move from pricing to regulation, with an emphasis on the computational aspects of regulatory credit risk capital under Basel 3. A variety of highly topical subjects will be discussed during the course, including: funding costs, XVA metrics, initial margin, credit risk mitigation, central clearing, and balance sheet management. Students will get to build a realistic computer system for counterparty risk management of collateralized fixed income portfolios, and will be exposed to modern frameworks for interest rate simulation and capital management.

• Cryptocurrency And Blockchains: Mathematics And Technologies
  

  MATH-GA.1234-001

  Cryptocurrency And Blockchains: Mathematics And Technologies

  Amir Sadr and Petter Kolm

  Prerequisites: Multivariate calculus and calculus-based probability. Students should have completed Computing in Finance (MATH-GA-2401) or equivalent, have strong coding skills in Python, and working experience with the Python stack (numpy/pandas/scikit-learn).

  Description: This course is only offered in the Fall Semester. This half-semester course examines the building technologies and concepts in distributed ledger technologies and the workings of crypto financial markets. We begin by an overview of the traditional central banking system and the mechanics of central bank money and commercial bank lending as the two dominant mechanisms of money creation. We explore the current network of banking in traditional finance (TradFi) and its hierarchy of commercial banks, central banks, correspondent banks, settlement and clearing mechanism, and the instruments used to create and transmit money. We cover the principles of private and public key cryptography and its usage in encryption, digital signature, and message authentication. Hash functions serve as one-way functions that play a prominent role in creating message digests and solving the cryptographic puzzle in proof-of-work-based blockchains. We cover the main challenges of secure communication and typical attacks such as replay, man-in-the-middle, Sybil attacks and the cryptographic techniques used to tackle them. Next, we take a deep-dive in the original Bitcoin whitepaper and show how the integration of cryptographic digital signatures, recursive blockchains, hash-based proof-of-work consensus mechanism to solve the 51% attack, and double-spend problem gave rise to the pioneering Bitcoin blockchain. The Ethereum blockchain and its smart contracts have given rise to a variety of distributed apps (dApps), prominent among them decentralized exchanges (DEX) using constant function demand curves for creating automatic market-making. We cover the mechanics of these markets and concepts of swapping, liquidity pairs, yield farming and the general landscape of decentralized finance (DeFi). Blockchain data is public by design and there is a wealth of real-time and historical data. We discuss some of the data analysis and machine learning methods utilized to analyze this type of data. Given that blockchain is a software protocol, it is important that students taking this course have strong coding skills in Python and working experience with the Python stack (numpy/pandas/scikit-learn).

SPRING SEMESTER

• Active Portfolio Management
  

  MATH-GA.2752-001

  Active Portfolio Management

  Jerome Benveniste

  Prerequisites: Risk & Portfolio Management and Computing in Finance.

  Description: The first part of the course will cover the theoretical aspects of portfolio construction and optimization. The focus will be on advanced techniques in portfolio construction, addressing the extensions to traditional mean-variance optimization including robust optimization, dynamical programming and Bayesian choice. The second part of the course will focus on the econometric issues associated with portfolio optimization. Issues such as estimation of returns, covariance structure, predictability, and the necessary econometric techniques to succeed in portfolio management will be covered. Readings will be drawn from the literature and extensive class notes.

• Advanced Risk Management
  

  MATH-GA.2753-001

  Advanced Risk Management

  Ken Abbott and Irena Khrebtova

  Prerequisites: Financial Securities and Markets, and Computing in Finance or equivalent programming experience.

  Description: The importance of financial risk management has been increasingly recognized over the last several years. This course gives a broad overview of the field, from the perspective of both a risk management department and of a trading desk manager, with an emphasis on the role of financial mathematics and modeling in quantifying risk. The course will discuss how key players such as regulators, risk managers, and senior managers interact with trading. Specific techniques for measuring and managing the risk of trading and investment positions will be discussed for positions in equities, credit, interest rates, foreign exchange, commodities, vanilla options, and exotic options. Students will be trained in developing risk sensitivity reports and using them to explain income, design static and dynamic hedges, and measure value-at-risk and stress tests. Students will create Monte Carlo simulations to determine hedge effectiveness. Extensive use will be made of examples drawn from real trading experience, with a particular emphasis on lessons to be learned from trading disasters. Text: Allen, S.L. (2003). Wiley Finance [Series, Bk. 119]. Financial Risk Management: A Practitioner’s Guide to Managing Market and Credit Risk. Hoboken, NJ: John Wiley & Sons.

• Advanced Topics In Equity Derivatives
  

  MATH-GA.2801-001

  Advanced Topics In Equity Derivatives

  Alireza Javeheri

  Prerequisites: Financial Securities and Markets, Stochastic Calculus, and Computing in Finance or equivalent programming experience.

  Description: This half-semester course will give a practitioner’s perspective on a variety of advanced topics with a particular focus on equity derivatives instruments, including volatility and correlation modeling and trading, and exotic options and structured products. Some meta-mathematical topics such as the practical and regulatory aspects of setting up a hedge fund will also be covered.

• Algorithmic Trading & Quantitative Strategies
  

  MATH-GA.2708-001

  Algorithmic Trading & Quantitative Strategies

  Petter Kolm and Lee Maclin

  Prerequisites: Computing in Finance, and Risk and Portfolio Management, or equivalent.

  Description: In this course we develop a quantitative investment and trading framework. In the first part of the course, we study the mechanics of trading in the financial markets, some typical trading strategies, and how to work with and model high frequency data. Then we turn to transaction costs and market impact models, portfolio construction and robust optimization, and optimal betting and execution strategies. In the last part of the course, we focus on simulation techniques, back-testing strategies, and performance measurement. We use advanced econometric tools and model risk mitigation techniques throughout the course. Handouts and/or references will be provided on each topic.

• Interest Rate & Fx Models
  

  MATH-GA.2798-001

  Interest Rate & Fx Models

  Fabio Mercurio and Alexey Kuptsov

  Prerequisites: Financial Securities and Markets, Stochastic Calculus, and Computing in Finance (or equivalent familiarity with financial models, stochastic methods, and computing skills).

  Description: The course is divided into two parts. The first addresses the fixed-income models most frequently used in the finance industry, and their applications to the pricing and hedging of interest-based derivatives. The second part covers the foreign exchange derivatives markets, with a focus on vanilla options and first-generation (flow) exotics. Throughout both parts, the emphasis is on practical aspects of modeling, and the significance of the models for the valuation and risk management of widely-used derivative instruments.

• Market Microstructure
  

  MATH-GA.2802-001

  Market Microstructure

  Merrell Hora

  Prerequisites: Financial Securities and Markets, Risk and Portfolio Management, and Computing in Finance or equivalent programming experience.

  Description: This is a half-semester course covering topics of interest to both buy-side traders and sell-side execution quants. The course will provide a detailed look at how the trading process actually occurs and how to optimally interact with a continuous limit-order book market. We begin with a review of early models, which assume competitive suppliers of liquidity whose revenues, corresponding to the spread, reflect the costs they incur. We discuss the structure of modern electronic limit order book markets and exchanges, including queue priority mechanisms, order types and hidden liquidity. We examine technological solutions that facilitate trading such as matching engines, ECNs, dark pools, multiple venue problems and smart order routers. The second part of the course is dedicated pre-trade market impact estimation, post-trade slippage analysis, optimal execution strategies and dynamic no-arbitrage models. We cover Almgren-Chriss model for optimal execution, Gatheral’s no-dynamic-arbitrage principle and the fundamental relationship between the average response of the market price to traded quantity, and properties of the decay of market impact. Homework assignments will supplement the topics discussed in lecture. Some coding in Java will be required and students will learn to write their own simple limit-order-book simulator and analyze real NYSE TAQ data.

• Modeling And Risk Management Of Bonds And Securitized Products
  

  MATH-GA.2799-001

  Modeling And Risk Management Of Bonds And Securitized Products

  Rodney Sunada-Wong

  Prerequisites: Stochastic Calculus, and Financial Securities and Markets or equivalent knowledge of basic bond mathematics and bond risk measures (duration and convexity).

  Description: This half-semester course is designed for students interested in Fixed Income roles in front-office trading, market risk management, model development (“Quants”, “Strats”), or model validation. We begin by modeling the cash flows of a generic bond, emphasizing how the bond reacts to changes in markets, how traders may position themselves given their views on the markets, and how risk managers think about the risks of a bond. We then focus on Mortgages, covering the fundamentals of Residential Mortgages, and Mortgage-Backed Securities. Students will build pricing models for mortgages, pass-throughs, sequentials and CMO’s that generate cash flows and that take into account interest rates, prepayments and credit spreads (OAS). The goals are for students to develop: (1) an understanding of how to build these models and how assumptions create “model risk”, and (2) a trader’s and risk manager’s intuition for how these instruments behave as markets change, and (3) a knowledge how to hedge these products. We will graph cash flows and changes in market values to enhance our intuition (e.g. in Excel, Python or by using another graphing tool). In the course we also review the structures of CLO’s, Commercial Mortgage Backed Securities (CMBS), Auto Asset Backed Securities (ABS), Credit Card ABS, subprime mortgages and CDO’s and credit derivatives such as CDX, CMBX and ABX. We discuss the modeling risks of these products and the drivers of the Financial Crisis of 2008. As time permits, we touch briefly on Peer-to-peer / MarketPlace Lending.

• Trading Energy Derivatives
  

  MATH-GA.2800-001

  Trading Energy Derivatives

  Ilia Bouchouev

  Prerequisites: Financial Securities and Markets, and Stochastic Calculus.

  Description: The course provides a comprehensive overview of most commonly traded quantitative strategies in energy markets. The class bridges quantitative finance and energy economics covering theories of storage, net hedging pressure, optimal risk transfer, and derivatives pricing models. Throughout the course, the emphasis is placed on understanding the behavior of various market participants and trading strategies designed to monetize inefficiencies resulting from their activities and hedging needs. We discuss in detail recent structural changes related to financialization of energy commodities, crossmarket spillovers, and linkages to other financial asset classes. Trading strategies include traditional risk premia, volatility, correlation, and higher-order options Greeks. Examples and case studies are based on actual market episodes using real market data.