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Class of 2014 Resume Book
Mathematics in Finance M.S. Program
Courant Institute of Mathematical Sciences
New York University
April 13, 2015
For the latest version, please go to
http://math.nyu.edu/financial_mathematics
Job placement contact: Michelle Shin, (212) 998-3009
Shin@cims.nyu.edu
New York University
A private university in the public service
U
Courant Institute of Mathematical Sciences
Mathematics in Finance MS Program
251 Mercer Street
New York, NY 10012-1185
Phone: (212) 998-3104; Fax: (212) 995-4195
Dear Colleague,
Attached are the resumes of third semester students in the Courant Institute's Mathematics in Finance Master's
Program. These are full-time students, who completed summer internships in the finance industry and graduated
from our Master’s program in December 2014.
We believe ours is the most elite, the most capable, and the best trained group of students of any program. This year, we
admitted less than 7% of those who applied. Their resumes describe their distinguished backgrounds. For the past five
years we have a placement record close to 100% both for summer internships and full-time positions. Our students enter
into front office roles such as trading or risk management, on the buy and the sell side. Their computing and hands on
practical experience make them useful and productive from day one.
Our curriculum is dynamic and challenging. For example, the first semester investments class does not end with CAPM
and APT, but is a serious data driven class that, for example, examines the statistical principles and practical pitfalls of
covariance matrix estimation. During the second semester electives include a class on modern algorithmic trading
strategies and one on energy and mortgage backed securities. Instructors are high level industry professionals and faculty
from the Courant Institute, the top ranked department worldwide in applied mathematics. You can find more information
about the curriculum and faculty at the end of this document, or at http://math.nyu.edu/financial_mathematics/.
Sincerely yours,
Peter Carr, Executive Director
Jonathan Goodman, Chair
Petter Kolm, Director
Ziwei (Sylvia) Deng
1 River Court, Apt 606 ▪ Jersey City, NJ 07310 ▪ 347-282-3560 ▪ ziwei.deng@nyu.edu
EDUCATION
NEW YORK UNIVERSITY
New York, NY
The Courant Institute of Mathematical Sciences
MS in Mathematics in Finance (expected – January 2015)
●
Finance: Portfolio Theory, CAPM, option pricing, Black-Scholes model, MBS
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Mathematics: Stochastic calculus, Brownian motion, Ito’s lemma, Monte Carlo simulation
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Future Courses: Time series analysis and statistical arbitrage, Bayesian statistics in finance
UNIVERSITY OF TORONTO
Toronto, Canada
BSc (Honors) in Mathematics and Statistics, Minor in Economics (September 2009 – June 2013)
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Cumulative GPA: 3.92/4.0, Math GPA: 4.0/4.0; Dean’s List
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Honors: Coxeter Scholarship; C.L. Burton Scholarships; Graduated with High Distinction
EXPERIENCE
ATHENA CAPITAL RESEARCH
New York, NY
Summer Intern, Quantitative Research (May 2014 – August 2014)
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Investigated rolling intraday correlations of price moves using high-frequency data in Python
Pandas and identified signals for trading strategy making
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Designed regression models to conduct PnL performance explanation using R and Python and
discovered stylized factors that were significant to PnL changes
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Created automated programs in Python to generate PnL report of strategy performance
CHINA CONSTRUCTION BANK
Guangzhou, China
Summer Intern, Investment Banking Department (July 2012 – August 2012)
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Established an innovative Gold/Foreign Exchange-linked structured product
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Collected and analyzed the gold price/exchange rate within recent 2 years
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Built up Yield Calculation Model and Risk Exposure Model of the structured product
ROYAL BANK OF CANADA (RBC)
Toronto, Canada
Investment Advisor Assistant, Wealth Management Division (November 2011 – March 2012)
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Conducted 80-cold calls per day, introduced portfolio construction and investment reports service
to high-net-worth clients
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Helped solve clients’ issues, promoted RBC wealth management products and services
PROJECTS
NEW YORK UNIVERSITY
New York, NY
Mortgage-Backed Securities Models (February 2014 – March 2014)
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Built MBS Pass-through model, solved for option adjusted spread (OAS) in Excel
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Created sequential structure with 4 tranches, and PAC structure with cash flows under different
PSA in Excel
Options Pricing and Order Book Trading Simulation Models (September 2013 – November 2013)
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Built Monte Carlo based simulation model for pricing European and Asian options in both Java
and VBA
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Implemented exchange side of order book that supported different types of orders in Java
UNIVERSITY OF TORONTO
Toronto, Canada
Stochastic Optimal Control in Pairs Trading (October 2012 – April 2013)
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Constructed stochastic optimal control model for pairs trading and solved the optimization
problems
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Simulated sample paths of trading speeds, inventories and running wealth and analyzed their
patterns with the changes in different parameters of the pairs trading model in Matlab
COMPUTER SKILLS/OTHER
Programming – Python (with Pandas, Numpy, Rpy2, Matplotlib, Datetime), Java, LINUX, MySQL,
Matlab, R, SAS, Mathematica
Languages – Cantonese (Native), Mandarin (Native), English (Fluent)
RUIKUN HONG
465 Washington Blvd, Apt #2607S, Jersey City, NJ, 07310 ▪ (917)593-4986 ▪ ruikun.hong@nyu.edu
EDUCATION
NEW YORK UNIVERSITY
..
New York, NY
The Courant Institute of Mathematical Sciences
MS in Mathematics in Finance (expected – January 2015)
 Derivative Securities: forward, futures and option pricing, Black-Scholes model
 Stochastic Calculus: Ito’s lemma, reflection principle, Girsanov’s theorem
 Computing in Finance: OOP, data structure, design pattern, order book simulation
 Risk & Portfolio Management: linear regression, CAPM, mean-variance optimization
 Interest Rates: change-of-numeraire technique, Vasicek model, Hull-White model
ECOLE CENTRALE PARIS
Paris, France
Diplôme d’ingénieur (expected – January 2015)
 Relevant coursework: measure theory, martingale, statistical hypothesis testing
UNIVERSITY OF PARIS-SUD (Paris XI )
BS in Fundamental and Applied Mathematics (June 2012)
Orsay, France
EXPERIENCE
Cohen & Steers, Summer Intern in Quantitative Strategies Team (June 2014 – August 2014)
 Applied principal component analysis with orthogonal and oblique rotation methods to
…..identify the risk factors and the risk exposure of portfolio
 Estimated the marginal risk contribution of each asset in the portfolio
 Applied VAR model to estimate the tracking error of portfolio on weekly and monthly basis
 Built the Excel interface using VBA to visualize the tracking error analysis
PROJECTS
Portfolio Optimization With Fixed Transaction Cost (November 2013)
 Applied Lagrange relaxation method to estimate the lower bound of objective function
 Implemented subgradient method in Python and optimized a non-convex problem
 Presented the project as a finalist of the Prize for Excellence at Morgan Stanley
Stock Option Pricing with Monte Carlo Simulation(October 2013 – December 2013)
 Priced European and Asian options using Monte Carlo simulation with antithetic stock paths
 Implemented the simulation with middleware and multithreading approach separately
Using GPU for Financial Analysis and Modeling (September 2012- June 2013)
 The GPU architecture and CUDA programming model
 Tested functions related to linear algebra in the CUBLAS, and LAPACKPP .library
 Implemented the K-means algorithm with CUDA and achieved the classification based on
......eigenvalues of the correlation matrices with S&P 100
COMPUTER SKILLS/OTHER
Programming languages: Java, Python, R
Languages: Chinese (native), French (fluent), English (fluent)
Interests: basketball, piano, poker
SHUO LI
40 Newport Parkway, Apt 2610 ▪ Jersey City, NJ 07310 ▪ (609) 423-5125 ▪ li.shuo@nyu.edu
EDUCATION
NEW YORK UNIVERSITY
New York, NY
The Courant Institute of Mathematical Sciences
MS in Mathematics in Finance (expected – December 2014)
 Programming: Java programming for finance application including trading, research, hedging,
and portfolio management
 Derivatives: Futures, forwards, options, interest rate swaps
PRINCETON UNIVERSITY
B.A. in Economics with Finance Certificate (2006-2010)
Princeton, NJ
EXPERIENCE
JPMorgan Chase & Co.
Summer Associate – Risk and Modeling Analytics (summer 2014)
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Developed non-linear models to capture quartile characteristics of individual fico scores to
enhance default models’ predictions
Used R to back-test fico score models from aggregating individual forecasts and confirmed its
performance under stress scenarios such as financial crisis, in comparison with common
industry practice of assuming no change on individual scores
Applied SQL package in R for faster vectorized computation in large data set
Extensively used ggplot2 package to enhance visual clearance of graphical presentations
Compared different variable selection procedures and validated their stabilities under big but
noisy data
BOM Enterprise
Sports Trader/Analyst (2010-2013)
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New York, NY
Freehold, NJ
Assisted in the management of a $5+ million fund and monitored the portfolio to minimize
risk exposure and maximize potential gain
Projected security movements and set price alerts in order to adjust holding positions during
the trading period
Created comprehensive investment strategies based on event simulations dependent on market
pricing, agency rating, league, team and individual player’s historical performances
Utilized multi-threading technique to increase data collection and post calculation speed
Updated models and optimized trading algorithms using Python and VBA to enhance trading
efficiency
Executed trades daily, based on internal model estimation and real time volatilities
COMPUTER SKILLS/OTHER
Programming languages: R, JAVA, Python, MATLAB , VBA
Other Software: Stata, Excel
Languages: Mandarin (Native), English (Fluent)
Lin Shi
444 Washington Blvd, Apt 4314 ▪ Jersey City, NJ 07310 ▪ (917) 708-0200 ▪ lin.shi@nyu.edu
EDUCATION
NEW YORK UNIVERSITY
New York, NY
The Courant Institute of Mathematical Sciences
MS in Mathematics in Finance (expected – January 2015)
•
Finance: Black-Scholes, Monte Carlo simulations, VaR, CAPM, portfolio optimization
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Math: Linear regression and inference, Brownian motion
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Computing in Java: object-oriented design, data structure
NANJING UNIVERSITY
BS in Physics and BEcon in International Finance (July 2011)
Nanjing, China
EXPERIENCE
SOCIÉTÉ GÉNÉRALE CIB
Hong Kong, HK
Summer Intern, Global Markets (May 2014 – present)
• FX Derivatives Trading: priced CNH options using Local Volatility model, implemented a
specific interpolation method in both VBA and C# to build the CNH volatility surface;
• Cross Asset Solutions: studied and understood various structured products, analyzed
investment solution for inflation; provided a framework for hedging tail risk;
• Equity Index Trading: back tested the profitability of the HSI and HSCEI trading strategy
• CVA Trading: assisted traders in daily risk management tasks by building tools to automate
routine tasks
BANK OF CHINA
Beijing, China
Analyst, Global Market Division (Aug 2011 – Jan 2013)
• Researched FX options pricing models and made localized modification for CNY options
pricing methods
• Monitored FX updates and conducted fundamental and technical analysis on FX markets
• Prepared marketing materials and presented to corporate clients to promote FX products;
assessed clients’ risk tolerance
CHINA INTERNANTIONAL FUND MANAGEMENT CO.,LTD
Beijing, China
Intern, Sales Department (Jan 2009 – Feb 2009)
• Implemented sales skills, identified potential clients, promoted stocks of China’s Growth
Enterprise Markets (GEM), resulting in 40 new account openings
PROJECTS
RISK & PORTFOLIO MANAGEMENT IN MATLAB
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Analyzed movements in the market variables using PCA; Conducted mean-variance
optimization to construct optimal long-short equity portfolio
MONTE CARLO SIMULATION
• Priced European options and Asian options in JAVA by simulating continuous time process in
a multi-threaded environment
COMPUTER SKILLS/OTHER
Programming Languages& Other Software: Python, JAVA, C#, MATLAB, VBA, SQL, MS Office
Languages: Mandarin (native), English (fluent)
HUACHEN SONG
465 Washington Blvd, Apt 2607S▪ Jersey City, NJ 07310 ▪ (917) 573-6472 ▪ huachen.song@nyu.edu
EDUCATION
NEW YORK UNIVERSITY
New York, NY
The Courant Institute of Mathematical Sciences
MS in Mathematics in Finance (expected – January 2015)
 Finance: Black-Scholes model, Greeks, interest-rate models, FX models, local volatility
model, stochastic volatility model, VaR, Copula model, digital options, variance swaps
 Mathematics: stochastic calculus, backward and forward Kolmogorov equations, optimal
control, jump diffusion processes, Dupire’s formula, linear regression
 Programming: object-oriented design, design patterns, finite difference method
TSINGHUA UNIVERSITY
Beijing, China
BS in Mathematical Sciences (August 2009 - July 2013)
 Honors: Zhenggeru scholarship for academic excellence
EXPERIENCE
LINCOLN FINANCIAL GROUP
Philadelphia, PA
Quantitative Strategist Intern, Equity Risk Management Department (June-August, 2014)
 Constructed IR curve in C++, calculated convexity adjustments for futures in Hull-White
model, implemented 4 different interpolations and n-dimensional Newton-Raphson method
under polymorphism and template design, to provide discount factor for the pricing engine
 Acquired historical market data from Bloomberg in VBA, processed and loaded data into
MySQL database, implemented similar automatic daily procedure in Perl for back testing
 Completed the Hedge Trading System design, implemented data transmission among MySQL
database, spreadsheet, memory and XML file in C#, to provide the traders with an Excel plugin using C++ runtime library as the pricing engine for options, futures and swaps
 Performed C# code refactoring, implemented delegate and interface to generalize it, utilized
data structure, range processing and LINQ to reduce runtime from 4 minutes to 2 minutes
ZHONGSHAN SECURITIES
Beijing, China
Intern, Sales Department (July-August, 2012)
 Collaborated in a three-person team to analyze financial statements of four companies per day,
presented report on company performance to entire sales department
PROJECTS
Option Pricing with Monte Carlo Simulation (October 2013)
New York, NY
 Implemented Monte Carlo in Java to price arithmetic Asian option
Interest Rate and Foreign Exchange Modeling (March-May 2014)
New York, NY
 Implemented yield curve construction using CD, futures and interest rate swaps, computed the
partial PV01s for interest rate swaps to provide hedging strategies
 Valuated the Libor in arrears swap and CMS considering convexity adjustment
 Calibrated the SABR model for FX options to construct the volatility curve, utilized eventweighting scheme to take weekend effects into consideration
COMPUTER SKILLS/OTHER
Programming languages: C++, Java, SQL, C#, Perl, XML, LINQ
Other Software: Microsoft Word, Excel, PowerPoint, R, MATLAB, VBA, Python, Linux
Languages: English (Fluent), Mandarin (Native)
ZIQING (MICHAEL) TANG
255 Warren St., Apt. 806 • Jersey City, NJ 07302 • (201) 682-1469 • zt351@nyu.edu
EDUCATION
NEW YORK UNIVERSITY
New York, NY
The Courant Institute of Mathematical Sciences
Master of Science in Mathematics in Finance
Dec 2014
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Math & Finance: Itō calculus, Black-Scholes applications, quantitative trading strategies, portfolio optimization
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Computing: test-driven software development, distributed computing, multithreading
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Future coursework: Advanced Econometric Modeling and Big Data, Time Series Analysis and Statistical Arbitrage
UNIVERSITY OF TORONTO
Toronto, Canada
B.A.Sc. in Engineering Science with Honors: Major in Engineering Mathematics, Statistics and Finance
May 2013
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Project: Optimal execution model (Almgren-Chriss), finite difference method for Black-Scholes PDE
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Relevant coursework: Financial Optimization Models, Financial Trading Strategies, System Software
EXPERIENCE
LINCOLN FINANCIAL GROUP
Philadelphia, PA
Summer Intern – Trading Strategy
Jun 2014 – Aug 2014
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Developed back-testing algorithms for hedging strategies and systematic trading signals to improve current hedging
performance for Lincoln’s variable annuity (VA) guarantees
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Researched and replicated a market risk indicator that incorporates volatility information from equity, currency and
credit markets, helping make better trading decisions on timing
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Performed ad-hoc tasks including automating the process of generating daily market dashboard from Bloomberg,
vetting fund performance reports and existing fund mapping analysis in R
SIGNAL TECHNOLOGIES, LLC
New York, NY
Spring Intern – Algorithmic Trading
Jan 2014 – May 2014
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Developed and optimized the back-testing framework of the firm’s proprietary algorithmic trading system in Python
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Back tested the trading strategy with two years of high frequency data to find the appropriate parameters for
generating trading signals
HYDRO ONE NETWORKS
Toronto, Canada
Student Intern – Asset Analytics
Sept 2011 – Aug 2012
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Developed tools and processes for rationalizing asset databases, supporting a corporate-wide asset analytics project
that aims to achieve cost-effective maintenance practices
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Identified gaps in business process for updating database and implemented remedial actions, ensuring accuracy and
completeness of corporate information
PROJECT
NEW YORK UNIVERSITY
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Option pricing in Java: Priced European and Asian options using Monte Carlo simulation with multithreading
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Algorithmic trading: Built market impact model with high frequency trades and quotes data
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Corporate bond trading strategy (in progress): Construct a dataset of relevant trading data for liquid U.S. corporate
bonds, analyze and back test traditional bond trading strategies using empirical statistics and optimization techniques
ADDITIONAL
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Programming/Software: C/C++, Java, MATLAB, Python, MS Excel (VBA), Bloomberg, Morningstar Direct, Capital IQ
Languages: English (Fluent), Mandarin (Native)
Certification: 2015 Level II Candidate in the CFA Program
Investing: Canadian equity portfolio (+18.08%, Aug 2012 – May 2013)
LAI WEI
280 Marin Blvd., Unit 12N ▪ Jersey City, NJ 07302 ▪ (929) 271-9389 ▪ lai.wei@nyu.edu
EDUCATION
NEW YORK UNIVERSITY
New York, NY
The Courant Institute of Mathematical Sciences
MS in Mathematics in Finance (expected - January 2015)
 Portfolio & Risk: statistical (PCA), explicit (Fama-French) & implicit (Barra) factor models, VaR, CVaR
 Derivatives: Black-Scholes model, energy derivatives, options pricing, Monte Carlo simulation, Greeks
UNIVERSITY OF MICHIGAN
Ann Arbor, MI
MS in Electrical Engineering (April 2013) , GPA: 3.97/4.00
 Fellowship: University of Michigan Departmental Fellowship (full tuition waiver and monthly stipend)
BS in Electrical Engineering (January 2011), GPA: 3.85/4.00
 Award: Summa Cum Laude (graduated with the highest honor)
EXPERIENCE
NOMURA HOLDINGS
Hong Kong
Quant Investment Strategies Summer Intern (June 2014 – August 2014)
 Designed a fund of 33 Taiwan funds for ING Group based on Sharpe ratio, Calmar ratio, correlation with
risk parity portfolio, volatility control and market volatility/momentum-based risk filters in Matlab
 Augmented funds with shorter history using their corresponding USD funds as proxies after FX hedging
 Constructed a multi-asset portfolio of 15 ETFs by performing constrained principal component analysis;
assigned weights based on factor exposure to the principal components and ranking of past dividend paid
 Built a data acquisition framework to get data from Oracle Database and Bloomberg by Python and SQL
 Replicated MSCI price and total return indices in Python with constituents data extracted from database
 Designed a VIX trading signal involving Economic Policy Uncertainty Index, TED spread, PMI, and etc.
FOUNDER SECURITIES
Beijing, China
Quantitative Strategy Summer Intern (July 2013 – August 2013)
 Implemented a strategy using idiosyncratic volatility derived from the Fama-French three-factor model
 Backtested 8 years of data from the China Stock Market; on average, the portfolio of stocks with the
lowest idiosyncratic volatility outperformed that with the highest by 13% annually
 Programmed in Matlab to evaluate monthly idiosyncratic volatility to guide the rebalancing of portfolios
 Monitored portfolio risk by calculating 1-month 99% VaR through historical simulation of 4-year data
CREDIT SUISSE FOUNDER SECURITIES (JOINT VENTURE)
Beijing, China
Corporate Finance Summer Analyst (May 2013 – June 2013)
 Analyzed price trends and production data for different kinds of cargo ships to guide the issuance of stock
for China Shipbuilding Industry Corporation
PROJECTS
Trading and Pricing Simulation Framework in Java and Matlab (2013 - 2014)
 Established Monte Carlo simulations to price European and Asian options with specified stopping criteria
 Implemented order book programs for stock exchange dealing with FOK, IOC and ordinary limit orders
 Priced a spread option between PJM peak power and Henry Hub natural gas contracts in Matlab
Portfolio Management in Matlab (Fall 2013)
 Constructed optimal long-short equity portfolios by mean-variance optimization and CAPM
COMPUTER SKILLS
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Matlab, Java, Python, SQL, Bloomberg, FactSet, Excel, VBA, Linux
The Mathematics in Finance Masters Program
Courant Institute, New York University
Academic Year 2013-2014
The curriculum has four main components:
1. Financial Theory and Econometrics. These courses form the theoretical core of the
program, covering topics ranging from equilibrium theory to Black-Scholes to Heath-JarrowMorton.
2. Practical Financial Applications. These classes are taught by industry specialists from
prominent New York financial firms. They emphasize the practical aspects of financial
mathematics, drawing on the instructor’s experience and expertise.
3. Mathematical Tools. This component provides appropriate mathematical background in
areas like stochastic calculus and partial differential equations.
4. Computational Skills. These classes provide students with a broad range of software skills,
and facility with computational methods such as optimization, Monte Carlo simulation, and the
numerical solution of partial differential equations.
First Semester
Practical Financial
Applications
Financial Theory
and Econometrics
Derivative Securities
___
Risk & Portfolio
Mgmt. with
Econometrics
Second Semester
Third Semester
Advanced Risk
Management
___
Interest Rate and FX
Models
___
Securitized Products
and Energy
Derivatives
Fin. Eng. Models
for Corp. Finance
___
Active Portfolio
Management
___
Project and
Presentation
___
Algorithmic Trading
& Quant. Strategies
___
Time Series
Analysis & Stat.
Arbitrage
Continuous Time
Finance
Mathematical Tools
Stochastic Calculus
Credit Markets and
Models
___
Regulation &
Regulatory Risk
Models
PDE for Finance
Computational Skills
Computing in
Finance
Scientific
Computing for
Finance
Computational
Methods for
Finance
___
Advanced
Econometric
Modeling and Big
Data
Practical Training. In addition to coursework, the program emphasizes practical experience. All
students do Masters Projects, mentored by finance professionals. Most full-time students do internships
during the summer between their second and third semesters.
See the program web page http://math.nyu.edu/financial_mathematics for additional information.
MATHEMATICS IN FINANCE MS COURSES, 2014-2015
PRACTICAL FINANCIAL APPLICATIONS:
MATH-GA 2752.001 ACTIVE PORTFOLIO MANAGEMENT
Spring term: R. Lindsey
Prerequisites: Risk & Portfolio Management with Econometrics, Computing in Finance.
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.
MATH-GA 2753.001 ADVANCED RISK MANAGEMENT
Spring term: K. Abbott
Prerequisites: Derivative Securities, Computing in Finance or equivalent programming.
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.
MATH-GA 2757.001 REGULATION AND REGULATORY RISK MODELS
Fall term: K. Abbott and L. Andersen
Prerequisites: Risk Management, Derivative Securities (or equivalent familiarity with market and credit
risk models).
The course is divided into two parts. The first addresses the institutional structure surrounding capital
markets regulation. It will cover Basel (1, MRA, 2, 2.5, 3), Dodd-Frank, CCAR and model review. The
second part covers the actual models used for the calculation of regulatory capital. These models include
the Gaussian copula used for market risk, specific risk models, the Incremental Risk Calculation (single
factor Vasicek), the Internal Models Method for credit, and the Comprehensive Risk Measure.
MATH-GA 2796.001 SECURITIZED PRODUCTS AND ENERGY DERIVATIVES
Spring term: G. Swindle and L. Tatevossian
Prerequisites: basic bond mathematics and bond risk measures (duration and convexity); Derivative
Securities, Stochastic Calculus.
The first part of the course will cover the fundamentals and building blocks of understanding how
mortgage-backed securities are priced and analyzed. The focus will be on prepayment and interest rate
risks, benefits and risks associated with mortgage-backed structured bonds and mortgage derivatives.
Credit risks of various types of mortgages will also be discussed. The second part of the course will
focus on energy commodities and derivatives, from their basic fundamentals and valuation, to practical
issues in managing structured energy portfolios. We develop a risk neutral valuation framework starting
from basic GBM and extend this to more sophisticated multifactor models. These approaches are then
used for the valuation of common, yet challenging, structures. Particular emphasis is placed on the
potential pitfalls of modeling methods and the practical aspects of implementation in production trading
platforms. We survey market mechanics and valuation of inventory options and delivery risk in the
emissions markets.
MATH-GA 2797.001 CREDIT MARKETS AND MODELS
Fall term: V. Finkelstein
Prerequisites: Computing for Finance, or equivalent programming skills; Derivative Securities, or
equivalent familiarity with financial models; familiarity with analytical methods applied to Interest Rate
derivatives.
This course addresses a number of practical issues concerned with modeling, pricing and risk
management of a range of fixed-income securities and structured products exposed to default risk.
Emphasis is on developing intuition and practical skills in analyzing pricing and hedging problems. In
particular, significant attention is devoted to credit derivatives.
We begin with discussing default mechanism and its mathematical representation. Then we proceed to
building risky discount curves from market prices and applying this analytics to pricing corporate
bonds, asset swaps, and credit default swaps. Risk management of credit books will be addressed as
well. We will next examine pricing and hedging of options on assets exposed to default risk. After that,
we will discuss structural (Merton-style) models that connect corporate debt and equity through the
firm’s total asset value. Applications of this approach include the estimation of default probability and
credit spread from equity prices and effective hedging of credit curve exposures. A final segment of the
course will focus on credit structured products. We start with cross-currency swaps with a credit
overlay. We will next analyze models for pricing portfolio transactions using Merton-style approach.
We also will discuss portfolio loss model based on a transition matrix approach. These models will then
be applied to the pricing of collateralized debt obligation tranches and pricing counterparty credit risk
taking wrong-way exposure into account.
MATH-GA 2798.001 INTEREST RATE AND FX MODELS
Spring term: L. Andersen and A. Gunstensen
Prerequisites: Derivative Securities, Stochastic Calculus, and Computing in Finance (or equivalent
familiarity
with
financial
models,
stochastic
methods,
and
computing
skills).
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.
FINANCIAL THEORY AND ECONOMETRICS:
MATH-GA 2707.001 TIME SERIES ANALYSIS AND STATISTICAL ARBITRAGE
Fall term: F. Asl and R. Reider
Prerequisites: Derivative Securities, Scientific Computing, and familiarity with basic probability.
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.
MATH-GA 2708.001 ALGORITHMIC TRADING AND QUANTITATIVE STRATEGIES
Spring term: P. Kolm and L. Maclin
Prerequisites: Computing in Finance, and Capital Markets and Portfolio Theory, or equivalent.
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.
MATH-GA 2751.001 RISK AND PORTFOLIO MANAGEMENT WITH ECONOMETRICS
Fall term: P. Kolm. Spring term: M. Avellaneda
Prerequisites: univariate statistics, multivariate calculus, linear algebra, and basic computing (e.g.
familiarity with Matlab or co-registration in Computing in Finance).
A comprehensive introduction to the theory and practice of portfolio management, the central
component of which is risk management. Econometric techniques are surveyed and applied to these
disciplines. Topics covered include: factor and principal-component models, CAPM, dynamic asset
pricing models, Black-Litterman, forecasting techniques and pitfalls, volatility modeling, regimeswitching models, and many facets of risk management, both theory and practice.
MATH-GA 2755.001 PROJECT AND PRESENTATION
Fall term and spring term: P. Kolm
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.
MATH-GA 2791.001 DERIVATIVE SECURITIES
Fall term: M. Avellanda. Spring term: B. Flesaker
An introduction to arbitrage-based pricing of derivative securities. 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.
MATH-GA 2792.001 CONTINUOUS TIME FINANCE
Fall term: P. Carr and A. Javaheri. Spring term: B. Dupire and F. Mercurio
Prerequisites: Derivative Securities and Stochastic Calculus, or equivalent.
A second course in arbitrage-based pricing of derivative securities. The Black-Scholes model and its
generalizations: equivalent martingale measures; the martingale representation theorem; the market
price of risk; applications including change of numeraire and the analysis of quantos. Interest rate
models: the Heath-Jarrow-Morton approach and its relation to shortrate models; applications including
mortgage-backed securities. The volatility smile/skew and approaches to accounting for it: underlyings
with jumps, local volatility models, and stochastic volatility models.
MATHEMATICAL TOOLS:
MATH-GA 2706.001 PDE FOR FINANCE
Spring term: R. Kohn
Prerequisite: Stochastic Calculus or equivalent.
An introduction to those aspects of partial differential equations and optimal control most relevant to
finance. Linear parabolic PDE and their relations with stochastic differential equations: the forward and
backward Kolmogorov equation, exit times, fundamental solutions, boundary value problems,
maximum principle. Deterministic and stochastic optimal control: dynamic programming, HamiltonJacobi-Bellman equation, verification arguments, optimal stopping. Applications to finance, including
portfolio optimization and option pricing -- are distributed throughout the course.
MATH-GA 2902.001 STOCHASTIC CALCULUS
Fall term: J. Goodman. Spring term: A. Kuptsov
Prerequisite: Basic Probability or equivalent.
Discrete dynamical models: Markov chains, one-dimensional and multidimensional trees, forward and
backward difference equations, transition probabilities and conditional expectations. Continuous
processes in continuous time: Brownian motion, Ito integral and Ito’s lemma, forward and backward
partial differential equations for transition probabilities and conditional expectations, meaning and
solution of Ito differential equations. Changes of measure on paths: Feynman-Kac formula, CameronMartin formula and Girsanov’s theorem. The relation between continuous and discrete models:
convergence theorems and discrete approximations.
COMPUTATIONAL SKILLS:
MATH-GA 2041.001 COMPUTING IN FINANCE
Fall term: E. Fishler and L. Maclin
This course will introduce students to the software development process, including applications in
financial asset trading, research, hedging, portfolio management, and risk management. Students will
use the Java programming language to develop object-oriented software, and will focus on the most
broadly important elements of programming - superior design, effective problem solving, and the proper
use of data structures and algorithms. Students will work with market and historical data to run
simulations and test strategies. The course is designed to give students a feel for the practical
considerations of software development and deployment. Several key technologies and recent
innovations in financial computing will be presented and discussed.
MATH-GA 2044.001 SCIENTIFIC COMPUTING FOR FINANCE
Spring term: H. Cheng and Y. Li
Prerequisites: Risk and Portfolio Management with Econometrics, Derivative Securities, Computing in
Finance.
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 solution of differential
equations.
MATH-GA 2045.001 COMPUTATIONAL METHODS FOR FINANCE
Fall term: A. Hirsa
Prerequisites: Scientific Computing or Numerical Methods II, Continuous Time Finance, or permission
of instructor.
Computational techniques for solving mathematical problems arising in finance. Dynamic programming
for decision problems involving Markov chains and stochastic games. Numerical solution of parabolic
partial differential equations for option valuation and their relation to tree methods. Stochastic
simulation, Monte Carlo, and path generation for stochastic differential equations, including variance
reduction techniques, low discrepancy sequences, and sensitivity analysis.
MATH-GA 2046.001 ADVANCED EONOMETRIC MODELING AND BIG DATA
Fall term: G. Ritter
Prerequisites: Derivative Securities, Risk & Portfolio Management with Econometrics, and Computing
in Finance (or equivalent programming experience).
A rigorous background in Bayesian statistics geared towards applications in finance, including decision
theory and the Bayesian approach to modeling, inference, point estimation, and forecasting, sufficient
statistics, exponential families and conjugate priors, and the posterior predictive density. A detailed
treatment of multivariate regression including Bayesian regression, variable selection techniques,
multilevel/hierarchical regression models, and generalized linear models (GLMs). Inference for classical
time-series models, state estimation and parameter learning in Hidden Markov Models (HMMs)
including the Kalman filter, the Baum-Welch algorithm and more generally, Bayesian networks and
belief propagation. Solution techniques including Markov Chain Monte Carlo methods, Gibbs
Sampling, the EM algorithm, and variational mean field. Real world examples drawn from finance to
include stochastic volatility models, portfolio optimization with transaction costs, risk models, and
multivariate forecasting
Computational Skills
Computing in
Finance
Scientific
Computing
Computational
Methods for
Finance
___
Advanced
Econometric
Modeling and Big
Data
Practical Training. In addition to coursework, the program emphasizes practical experience. All
students do Masters Projects, mentored by finance professionals. Most full-time students do internships
during the summer between their second and third semesters.
See the program web page http://math.nyu.edu/financial_mathematics for additional information.
MATHEMATICS IN FINANCE MS COURSES, 2014-2015
PRACTICAL FINANCIAL APPLICATIONS:
MATH-GA 2752.001 ACTIVE PORTFOLIO MANAGEMENT
Spring term: R. Lindsey
Prerequisites: Risk & Portfolio Management with Econometrics, Computing in Finance.
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.
MATH-GA 2753.001 ADVANCED RISK MANAGEMENT
Spring term: K. Abbott
Prerequisites: Derivative Securities, Computing in Finance or equivalent programming.
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.
MATH-GA 2757.001 REGULATION AND REGULATORY RISK MODELS
Fall term: K. Abbott and L. Andersen
Prerequisites: Risk Management, Derivative Securities (or equivalent familiarity with market and credit
risk models).
The course is divided into two parts. The first addresses the institutional structure surrounding capital
markets regulation. It will cover Basel (1, MRA, 2, 2.5, 3), Dodd-Frank, CCAR and model review. The
second part covers the actual models used for the calculation of regulatory capital. These models include
the Gaussian copula used for market risk, specific risk models, the Incremental Risk Calculation (single
factor Vasicek), the Internal Models Method for credit, and the Comprehensive Risk Measure.
MATH-GA 2796.001 MORTGAGE-BACKED SECURITIES AND ENERGY DERIVATIVES
Spring term: G. Swindle and L. Tatevossian
Prerequisites: basic bond mathematics and bond risk measures (duration and convexity); Derivative
Securities, Stochastic Calculus.
The first part of the course will cover the fundamentals and building blocks of understanding how
mortgage-backed securities are priced and analyzed. The focus will be on prepayment and interest rate
risks, benefits and risks associated with mortgage-backed structured bonds and mortgage derivatives.
Credit risks of various types of mortgages will also be discussed. The second part of the course will
focus on energy commodities and derivatives, from their basic fundamentals and valuation, to practical
issues in managing structured energy portfolios. We develop a risk neutral valuation framework starting
from basic GBM and extend this to more sophisticated multifactor models. These approaches are then
used for the valuation of common, yet challenging, structures. Particular emphasis is placed on the
potential pitfalls of modeling methods and the practical aspects of implementation in production trading
platforms. We survey market mechanics and valuation of inventory options and delivery risk in the
emissions markets.
MATH-GA 2797.001 CREDIT MARKETS AND MODELS
Fall term: V. Finkelstein
Prerequisites: Computing for Finance, or equivalent programming skills; Derivative Securities, or
equivalent familiarity with financial models; familiarity with analytical methods applied to Interest Rate
derivatives.
This course addresses a number of practical issues concerned with modeling, pricing and risk
management of a range of fixed-income securities and structured products exposed to default risk.
Emphasis is on developing intuition and practical skills in analyzing pricing and hedging problems. In
particular, significant attention is devoted to credit derivatives.
We begin with discussing default mechanism and its mathematical representation. Then we proceed to
building risky discount curves from market prices and applying this analytics to pricing corporate
bonds, asset swaps, and credit default swaps. Risk management of credit books will be addressed as
well. We will next examine pricing and hedging of options on assets exposed to default risk. After that,
we will discuss structural (Merton-style) models that connect corporate debt and equity through the
firm’s total asset value. Applications of this approach include the estimation of default probability and
credit spread from equity prices and effective hedging of credit curve exposures. A final segment of the
course will focus on credit structured products. We start with cross-currency swaps with a credit
overlay. We will next analyze models for pricing portfolio transactions using Merton-style approach.
We also will discuss portfolio loss model based on a transition matrix approach. These models will then
be applied to the pricing of collateralized debt obligation tranches and pricing counterparty credit risk
taking wrong-way exposure into account.
MATH-GA 2798.001 INTEREST RATE AND FX MODELS
Spring term: L. Andersen and A. Gunstensen
Prerequisites: Derivative Securities, Stochastic Calculus, and Computing in Finance (or equivalent
familiarity
with
financial
models,
stochastic
methods,
and
computing
skills).
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.
FINANCIAL THEORY AND ECONOMETRICS:
MATH-GA 2707.001 TIME SERIES ANALYSIS AND STATISTICAL ARBITRAGE
Fall term: F. Asl and R. Reider
Prerequisites: Derivative Securities, Scientific Computing, and familiarity with basic probability.
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.
MATH-GA 2708.001 ALGORITHMIC TRADING AND QUANTITATIVE STRATEGIES
Spring term: P. Kolm and L. Maclin
Prerequisites: Computing in Finance, and Capital Markets and Portfolio Theory, or equivalent.
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.
MATH-GA 2751.001 RISK AND PORTFOLIO MANAGEMENT WITH ECONOMETRICS
Fall term: P. Kolm. Spring term: M. Avellaneda
Prerequisites: univariate statistics, multivariate calculus, linear algebra, and basic computing (e.g.
familiarity with Matlab or co-registration in Computing in Finance).
A comprehensive introduction to the theory and practice of portfolio management, the central
component of which is risk management. Econometric techniques are surveyed and applied to these
disciplines. Topics covered include: factor and principal-component models, CAPM, dynamic asset
pricing models, Black-Litterman, forecasting techniques and pitfalls, volatility modeling, regimeswitching models, and many facets of risk management, both theory and practice.
MATH-GA 2755.001 PROJECT AND PRESENTATION
Fall term and spring term: P. Kolm
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.
MATH-GA 2791.001 DERIVATIVE SECURITIES
Fall term: M. Avellanda. Spring term: B. Flesaker
An introduction to arbitrage-based pricing of derivative securities. 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.
MATH-GA 2792.001 CONTINUOUS TIME FINANCE
Fall term: P. Carr and A. Javaheri. Spring term: B. Dupire and F. Mercurio
Prerequisites: Derivative Securities and Stochastic Calculus, or equivalent.
A second course in arbitrage-based pricing of derivative securities. The Black-Scholes model and its
generalizations: equivalent martingale measures; the martingale representation theorem; the market
price of risk; applications including change of numeraire and the analysis of quantos. Interest rate
models: the Heath-Jarrow-Morton approach and its relation to shortrate models; applications including
mortgage-backed securities. The volatility smile/skew and approaches to accounting for it: underlyings
with jumps, local volatility models, and stochastic volatility models.
MATHEMATICAL TOOLS:
MATH-GA 2706.001 PDE FOR FINANCE
Spring term: R. Kohn
Prerequisite: Stochastic Calculus or equivalent.
An introduction to those aspects of partial differential equations and optimal control most relevant to
finance. Linear parabolic PDE and their relations with stochastic differential equations: the forward and
backward Kolmogorov equation, exit times, fundamental solutions, boundary value problems,
maximum principle. Deterministic and stochastic optimal control: dynamic programming, HamiltonJacobi-Bellman equation, verification arguments, optimal stopping. Applications to finance, including
portfolio optimization and option pricing -- are distributed throughout the course.
MATH-GA 2902.001 STOCHASTIC CALCULUS
Fall term: J. Goodman. Spring term: A. Kuptsov
Prerequisite: Basic Probability or equivalent.
Discrete dynamical models: Markov chains, one-dimensional and multidimensional trees, forward and
backward difference equations, transition probabilities and conditional expectations. Continuous
processes in continuous time: Brownian motion, Ito integral and Ito’s lemma, forward and backward
partial differential equations for transition probabilities and conditional expectations, meaning and
solution of Ito differential equations. Changes of measure on paths: Feynman-Kac formula, CameronMartin formula and Girsanov’s theorem. The relation between continuous and discrete models:
convergence theorems and discrete approximations.
COMPUTATIONAL SKILLS:
MATH-GA 2041.001 COMPUTING IN FINANCE
Fall term: E. Fishler and L. Maclin
This course will introduce students to the software development process, including applications in
financial asset trading, research, hedging, portfolio management, and risk management. Students will
use the Java programming language to develop object-oriented software, and will focus on the most
broadly important elements of programming - superior design, effective problem solving, and the proper
use of data structures and algorithms. Students will work with market and historical data to run
simulations and test strategies. The course is designed to give students a feel for the practical
considerations of software development and deployment. Several key technologies and recent
innovations in financial computing will be presented and discussed.
MATH-GA 2043.001 SCIENTIFIC COMPUTING
Fall term: A. Rangan. Spring term: Y. Chen
Prerequisites: multivariable calculus, linear algebra; programming experience strongly recommended
but not required.
A practical introduction to scientific computing covering theory and basic algorithms together with use
of visualization tools and principles behind reliable, efficient, and accurate software. Students will
program in C/C++ and use Matlab for visualizing and quick prototyping. Specific topics include IEEE
arithmetic, conditioning and error analysis, classical numerical analysis (finite difference and integration
formulas, etc.), numerical linear algebra, optimization and nonlinear equations, ordinary differential
equations, and (very) basic Monte Carlo.
MATH-GA 2045.001 COMPUTATIONAL METHODS FOR FINANCE
Fall term: A. Hirsa
Prerequisites: Scientific Computing or Numerical Methods II, Continuous Time Finance, or permission
of instructor.
Computational techniques for solving mathematical problems arising in finance. Dynamic programming
for decision problems involving Markov chains and stochastic games. Numerical solution of parabolic
partial differential equations for option valuation and their relation to tree methods. Stochastic
simulation, Monte Carlo, and path generation for stochastic differential equations, including variance
reduction techniques, low discrepancy sequences, and sensitivity analysis.
MATH-GA 2046.001 ADVANCED EONOMETRIC MODELING AND BIG DATA
Fall term: G. Ritter
Prerequisites: Derivative Securities, Risk & Portfolio Management with Econometrics, and Computing
in Finance (or equivalent programming experience).
A rigorous background in Bayesian statistics geared towards applications in finance, including decision
theory and the Bayesian approach to modeling, inference, point estimation, and forecasting, sufficient
statistics, exponential families and conjugate priors, and the posterior predictive density. A detailed
treatment of multivariate regression including Bayesian regression, variable selection techniques,
multilevel/hierarchical regression models, and generalized linear models (GLMs). Inference for classical
time-series models, state estimation and parameter learning in Hidden Markov Models (HMMs)
including the Kalman filter, the Baum-Welch algorithm and more generally, Bayesian networks and
belief propagation. Solution techniques including Markov Chain Monte Carlo methods, Gibbs
Sampling, the EM algorithm, and variational mean field. Real world examples drawn from finance to
include stochastic volatility models, portfolio optimization with transaction costs, risk models, and
multivariate forecasting