AMATH 540/ECON 424 Introduction to Computational Finance and Financial Econometrics
This course is an introduction to data analysis and econometric modeling using applications in finance. Equivalently, this course is an introduction to computational finance and financial econometrics. As such, the course utilizes concepts from microeconomics, finance, mathematical optimization, data analysis, probability models, statistical analysis, and econometrics. Topics include:
- Probability and statistics (univariate and multivariate distributions, covariance, descriptive statistics, time series concepts, estimation, hypothesis testing, Monte Carlo simulation, bootstrap)
- Optimization methods involving equality and inequality constraints
- Matrix algebra
- Asset return calculations
- Statistical distributions and models for asset returns
- Value-at-risk, expected shortfall and portfolio risk budgeting
- Mean-Variance Portfolio Theory
- Statistical analysis of portfolios
- Capital Asset Pricing Model
- Investment performance measurement and analysis
Instructor: Eric Zivot (Economics is home department)
Textbooks: Zivot. E., Intro. to Computational Finance and Financial Econometrics, manuscript in preparation. Ruppert, D (2010). Statistics and Data Analysis for Financial Engineering, Springer.
Software: R and R Finance Packages
Prerequisites: A year of calculus (through partial differentiation and constrained optimization using Lagrange multipliers), some familiarity with matrix algebra, a course in probability and statistics using calculus, intermediate microeconomics and an interest in financial economics.
AMATH 541 Investment Science
This course is an introduction to the mathematical, statistical and financial foundations of investment science. Learning of the theoretical concepts will be re-enforced through use of R computing exercises. The material is similar in scope to an MBA level investments course, but at a significantly higher quantitative level. Topics include:
- Basic Theory of Interest Rates (compounding, present value, internal rate of return)
- Fixed Income Securities (bonds, value formulas, yield, duration, convexity, immunization)
- Term Structure of Interest Rates (term structure, discount factors, forward rates, short rates)
- Mean-Variance Portfolio Theory (efficient frontiers, quadratic utility, benchmark tracking)
- Factor Models (CAPM, linear regression and prediction, multi-factor models, intro. to APT)
- General Principles (expected utility maximization, coherent risk measures, tail risk measures)
- Futures and Forwards (futures and forward prices, margin, hedging with futures)
- Options Part 1: (option payoffs, trading strategies, binomial models, risk neutral pricing)
- Options Part 2: (Ito process and lemma, GBM, Black-Scholes, hedging, implied volatility)
Instructors: K. K. Tung, R. Douglas Martin
Textbook: D. G. Luenberger (1998). Investment Science, Oxford University Press
Software: R and R Finance Packages
Prerequisites: Probability and statistics at the level of STAT/AMATH 506 or STAT/AMATH 481. AMATH 540/ECON 424 Introduction to Computational Finance and Financial Econometrics, or equivalent, including experience with R.
AMATH 542 Financial Data Modeling and Analysis in R
This course is an in-depth hands-on introduction to the R statistical programming language (www.r-project.org) for computational finance. The course will focus on R code and code writing, R packages, and R software development for statistical analysis of financial data including topics on factor models, time series analysis, and portfolio analytics. Topics include:
- The R Language. Syntax, data types, resources, packages and history
- Graphics in R. Plotting and visualization
- Statistical analysis of returns. Fat-tailed skewed distributions, outliers, serial correlation
- Financial time series modeling. Covariance matrices, AR, VecAR
- Factor models. Linear regression, LS and robust fits, test statistics, model selection
- Multidimensional models. Principal components, clustering, classification
- Optimization methods. QP, LP, general nonlinear
- Portfolio optimization. Mean-variance optimization, out-of-sample back testing
- Bootstrap methods. Non-parametric, parametric, confidence intervals, tests
- Portfolio analytics. Performance and risk measures, style analysis
Instructor: Guy Yollin
Textbooks: D. Ruppert (2010). Statistics and Data Analysis for Financial Engineering, Springer and J. Adler (2009). R in a Nutshell: A Desktop Reference, O’Reilly Media
Software: R and R packages.
Prerequisites: AMATH 541 Investment Science or equivalent educational experience. Introductory probability and statistics at the level of STAT/AMATH 506 or STAT/ECON 481, or equivalent. Familiarity with matrix algebra, multivariable calculus and optimization with Lagrange multipliers. Basic computer programming experience.
AMATH 543/STAT 549 Portfolio Construction and Risk Management
This computationally oriented course uses R and R+NuOPT for portfolio construction and risk management. The course is unique in focusing on not only classical mean-variance optimization methods but also on post-modern optimization based on new downside risk measures for dealing with fat-tailed and skewed asset returns distributions. Topics include:
- Portfolio risk analysis: Volatility, VaR and ETL risk at asset group level and portfolio level
- Mean-variance review and mean-ETL optimization: Basic theory of mean-ETL optimization.
- Numerical mean-variance optimization: Using R+NuOPT with real-world constraints, penalties
- Numerical mean-ETL optimization: R+NuOPT as above and Cognity for fat-tailed distributions
- Estimation error: Classical sampling distribution methods and bootstrap methods
- Active management: Alpha, benchmarks, information ratios, IC’s and TC’s
- Long-short portfolios: Market neutral versus dollar neutral, 130-30
- Factor models: Three types, optimization and risk management applications, robust fitting
- Leverage: Types of leverage, return versus risk considerations
- Liquidity and market impact: Liquidity risk, Sadka liquidity risk beta, market impact models
- Risk budgeting: Volatility risk versus tail risk budgets, implied returns
- Bayes methods: Bayes shrinkage, Bayes-Stein, Black-Litterman
Instructor: R. Douglas Martin
Textbooks: Scherer and Martin (2011). Modern Portfolio Optimization, 2nd edition, Qian, Hua and Sorensen (2007), Quantitative Equity Portfolio Management, Chapman and Hall/CRC Financial Mathematics Series.
Software: R, R-NuOPT, selected R packages, FinAnalytica’s Cognity portfolio optimization and risk management system. Other commercial portfolio optimization and risk management products, arrangements with vendors permitting.
Prerequisites: AMATH 541 Investment Science plus AMATH 542 Financial Data Modeling and Analysis in R, or equivalents.
AMATH 544/STAT 547 Options and Derivatives
This course provides basic knowledge of the theory, statistical modeling and computational methods of pricing options and other derivative products. The course blends mathematical and statistical theory with hands-on computing. The first part of the course will emphasize options on stocks, stock indices, currencies and futures, and the latter part will focus on interest rate derivatives. Course work includes assignments in theory and computation, and either a final exam or a project.
- Brief review of forwards, futures, and options basics
- Black-Scholes theory and dynamic hedging with the Greeks
- Volatility estimation, implied volatility, the volatility smile
- Option prices using additive and multiplicative binomial, and use of trinomial trees
- Option pricing under fat-tailed non-normality
- Computational methods for exotic options and complex derivatives
- Brief review of interest rate basics: zero rates, forward rates and term structure
- Interest rate derivatives: standard market models, short rate and advanced models
- Analytic models and tree models for pricing interest rate derivatives
- Valuation of bonds with embedded options, option adjusted spreads
Instructor: R. Douglas Martin
Textbooks: Hull, J. C. (2009). Options, Futures and Other Derivatives, 7th edition (or most recent edition available at time of course offering), Prentice Hall. Tuckman, B. (2002). Fixed Income Securities, 2nd edition, Wiley
Software: R and selected R packages
Prerequisites: AMATH 540/ECON 424 Introduction to Computational Finance and Financial Econometrics and AMATH 541 Investment Science coverage of forwards, futures and options, or equivalent. AMATH 542 Financial Data Modeling and Analysis in R is desirable.
AMATH 545/FIN 562 Introduction to Risk Management
This course covers the methodologies used to manage financial risk. Emphasis is given to fixed income and foreign exchange derivatives. The topics covered include:
- An overview of fixed income products.
- Duration and convexity and risk management of fixed income portfolios.
- Black and Scholes model. Hedging and trading parameters.
- Pricing options and swaps.
- Introduction to term structure models.
- Introduction to credit derivatives.
- Introduction to mortgage-backed securities and asset-backed securities.
- Introduction to hedge fund strategies and risk management.
Instructors: Mark Everitt (Blackrock) and Gino Perrina (Russell Investments)
Textbooks: Assigned readings.
Software: Microsoft Excel
Prerequisites: MBA core finance or AMATH 541 Investment Science, or equivalents. FIN 561 Financial Futures and Options Markets or AMATH 544 Options and Derivatives is a plus. Students must be comfortable with calculus and statistics.
AMATH 546/ECON 589/ Quantitative Risk Management
This is a course in quantitative risk management and financial econometrics. The focus will be on the statistical modeling of financial time series (asset prices and returns) with an emphasis on modeling volatility and correlation for quantitative risk management. The learning goals/objectives of the course are to (1) survey the relevant theoretical and practical literature; (2) introduce state-of-the-art techniques for modeling financial time series and managing financial risk; (3) use the open source R statistical software to get hands-on experience with real world data. Topics to be covered include:
- Empirical properties and stylized facts of asset returns
- Probability distributions and statistical models for asset returns
- Risk concepts
- Volatility modeling
- Extreme value theory
- Multivariate dependence using copulas
- Introduction to credit risk models and management
Instructor: Eric Zivot (Economics is home department)
Textbooks: McNeil, Frey, and Embrechts, Quantitative Risk Management: Concepts, Techniques, and Tools, Princeton University Press, 2005. Jondeau, E., Poon, S.-H., and Rockinger, M. (2006). Financial Modeling Under Non-Gaussian Distributions, Springer-Verlag.
Software: R and R Finance Packages
Prerequisites: AMATH 542 Financial Data Modeling and Analysis in R and its pre-requisites, or equivalent.
AMATH 547 Credit Risk Management
This course is an introduction to the mathematical, statistical and financial foundations of models for analyzing, predicting, and mitigating credit risks. Students will learn the theoretical basis for widely-used modeling methods for credit risk assessment and implement those methods through programming assignments using R. The course will focus on both obligor-level and portfolio-level credit risks, as well as valuation and risk analysis of assets and derivatives with credit risk. Topics include:
- Credit risk drivers and portfolio diversification (idiosyncratic and systemic risks)
- Applied logistic regression (credit scoring models)
- Credit rating products for individuals and corporations (FICO, S&P, Moodys, Experian)
- Merton model for default risk
- Credit risk economic capital
- Basel II credit capital framework for banks
- Modeling loss frequency (PD) and severity (LGD)
- Credit risks in structured asset backed securities
- Credit default swaps, models for valuation and risk measurement
Instructor: Jay Henniger
Textbook: Servigny and Renault (2004). Measuring and Managing Credit Risk, McGraw-Hill Professional
Software: R and R Finance Packages
Prerequisites: AMATH 540/ECON 424 Introduction to Computational Finance and Financial Econometrics, AMATH 541 Investment Science and AMATH 545/FIN 562 Introduction to Risk Management, or equivalents. AMATH 546/ECON 589 Quant. Risk Management is desirable.
AMATH 548 Monte Carlo Methods in Finance
This course covers a broad range of standard and specialized Monte Carlo methods in finance with a focus on accurate derivative pricing. Students will learn the theoretical rationale for the methods and will gain applications knowledge through programming assignments using R or Matlab. The course will begin with an overview Monte Carlo methods and a review of basic derivative pricing method. Topics covered will include:
- Derivative pricing methods: replication, no-arbitrage, risk-neutral pricing, change of numeraire
- Random number generators: linear congruential generators, lattice structure, simulation error
- Sampling methods: inverse transform, acceptance-rejection methods
- Mulivariate random numbers: normal distributions, t-distributions, stable distributions
- Simulating sample paths: univariate and multivariate GBM, path-dependent options, short-rate models and bond prices
- Simulating advanced models: square-root diffusions and bond prices, forward rate models and pricing derivatives, jump processes
- Variance reduction methods: antithetic variables, control variates, stratified sampling, Latin hypercube sampling, matching methods, importance sampling
- Discretization methods: Euler method, second-order methods, applications to extremes and barrier crossings
- Estimating the Greeks sensitivity measures: finite-difference approximations, pathwise derivative estimates, likelihood ratio method,
- Pricing American options: random tree methods, stochastic mesh methods, regression methods
- Risk management applications: calculating VaR and CVaR, calculating VaR and CVaR portfolio risk decompositions, delta-gamma based variance reduction, methods for fat-tailed distributions
Instructor: Hong Qian
Textbook: Glasserman, P. (2004). Monte Carlo Methods in Financial Engineering, Springer
Software: R and R Finance Packages or Matlab
Prerequisites: AMATH 541 Investment Science and AMATH 544 or equivalents.
AMATH 551 Foundations of Trading Systems
This course is an introduction to financial markets, exchanges, and the electronic trading process. Students will use the R language for statistical computing (www.r-project.org) to develop, evaluate, backtest, and optimize quantitative trading strategies. Further, students will apply their trading strategies through a live paper-trading account with an online broker using real time market data. Topics Include:
- Direct access trading and market microstructure
- Asset classes, financial instruments, and trade orders
- Interactive Brokers, Traders Workstation, and the IB Student Trading Lab
- IBrokers package: R interface to IB TWS
- Quantstrat package: Quantitative strategy model framework
- Quantitative trading strategy development
- Trading strategy evaluation, optimization, and backtesting
- Trading strategy deployment
Instructor: Guy Yollin (r-programming.org)
Textbooks:Algorithmic Trading and DMA: An introduction to direct access trading strategies by Barry Johnson, 4Myeloma Press, 2010
Software: R language for statistical computing (www.r-project.org); Interactive Brokers Traders Workstation and Student Trading Lab
Prerequisites: AMATH 540/ECON 424 Introduction to Computational Finance and Financial Econometrics (may be taken concurrently). AMATH 541 Investment Science is desirable.
AMATH 552 Portfolio Performance Analysis and Benchmarking
This course covers fundamental principles of portfolio performance measurement and benchmarking. Topics include:
- The role of performance evaluation in portfolio management
- Rate of return calculations for individual assets and for portfolios
- Manipulating returns: linking, averaging, annualizing
- Adjustments for inflation, currency, taxes, fees
- Cash flow methods: time-weighted returns, money-weighted returns, standard approximations
- Excess returns, arithmetic and geometric
- Sector-based performance attribution
- Volatility and asset pricing-based risk measures
- Risk-adjusted return measures
- Factor-based performance attribution
- Uses of indexes: benchmarking, asset allocation, and the basis for investment vehicles
- Benchmark construction principles and practical issues
- Index calculations, weighting, rebalancing, and maintenance
- Equity style indexes
- GIPS: Global Investment Performance Standards
Instructor: David R. Cariño
Textbook: J. A. Christopherson, D. R. Cariño, and W. E. Ferson (2009). Portfolio Performance Measurement and Benchmarking, New York: McGraw-Hill
Software: Spreadsheet applications and R
Prerequisites: AMATH 540/ECON 424 Introduction to Computational Finance and Financial Econometrics or equivalent, and AMATH 541 Investment Science or equivalent.
AMATH 553 Financial Time Series Forecasting Methods
This course is an introduction to the role that forecasts can play in investment decisions, especially investing that involves views on short-term opportunities that are implemented through informed rebalancing or explicit asset class tilts away from benchmark. Learning of the theoretical concepts will be re-enforced through use of computing exercises. Topics include:
- Types of forecasts, dynamic forecasts, direct forecasts
- Forecasts by simulation for nonlinear models
- The role of macroeconomic forecasts in investing
- An approach to macroeconomic forecasting
- Asset class returns forecasts
- Ways to combine forecasts using dynamically updated weights
- Ways to account for nonlinearity
- Foreign exchange (FX) forecasts: carry trade motive, momentum strategies, incorporating long-run valuation correction
Instructors: Michael Dueker
Textbook: TBD
Software: TBD
Prerequisites: Probability and statistics at the level of STAT/AMATH 506 or STAT/AMATH 481. AMATH 540/ECON 424 Introduction to Computational Finance and Financial Econometrics, or equivalent.
AMATH 554 Endowment Investment Management
The course will focus on the endowment management process and specific challenges facing institutional fund managers. These include evaluating the role of an endowment, portfolio construction, risk management, manager selection, and alternative asset class investing. As such, the course utilizes concepts from finance and investments, macroeconomics, and mathematical optimization. Specific topics include: Endowment policy background and philosophy, spending, risk and asset allocation, emerging market investing, fixed incomes role in endowment, liquidity and investing in private equity. Reading assignments will form the basis for class discussion and students areare expected to be prepared for case discussions.
Instructors: Garth Reistad, Keith Ferguson, and Yindeng Jiang
Textbooks: There is significant amount of reading for this course, including articles and investment research from multiple sources that will be assigned by the instructors.
Software: R will be useful in the event of some case applications.
Prerequisites: AMATH 541 Investment Science or equivalent. A general understanding of economics and a good background in core finance and portfolio optimization, e.g., AMATH 543 Portfolio Optimization and Risk Management is preferred.
AMATH 555 Optimization in Finance
This course provides an introduction to numerical optimization methods in finance. The course will discuss the theory and efficient solution methods for major classes of optimization problems. Theoretical concepts will be paired with example applications and computing exercises. Homework problems will include use of an industrial strength optimizer to solve finance applications. Topics include:
- Linear Programming Theory, Algorithms and Applications: feasible sets, duality, optimality conditions, simplex method, interior point methods, sensitivity analysis, asset/liability cash flow matching
- Quadratic Programming Theory, Algorithms and Applications: constrained and unconstrained programming, optimality conditions, solution methodologies, mean-variance optimization, relationships to statistical regression, Black-Litterman, returns-based style analysis, risk-neutral density estimation
- General Non-Linear Programming Theory, Algorithms and Applications: univariate and multivariate models, convexity, non-smooth optimization, GARCH model fitting, volatility surface estimation
- Integer Programming Theory, Algorithms and Applications: cutting plane methods, index replication
- Combinatorial and Network Programming Theory, Algorithms and Applications: shortest path, min-cost flow, foreign exchange, arbitrage checking
- Cone Programming Theory, Algorithms and Applications: second-order cone programming, tracking error and volatility constraints, estimating covariance matrices
- Dynamic Programming Theory, Algorithms and Applications: Bellman equations, forward and backward recursion, knapsack problem, option pricing, structured products
- Stochastic Programming Theory, Algorithms and Applications: data uncertainty, multi-stage models, recourse, value at risk, conditional value at risk, asset/liability management, CVaR, transaction costs
- Robust Optimization Theory, Algorithms and Applications: parameter uncertainty, robust constraints, robust objectives, single-period and multi-period portfolio selection
- Additional Topics: Decomposition and Column Generation, Genetic Algorithms, Non-gradient methods
Instructor: Steven Murray
Textbook: Cornuejols and Tutuncu (2007). Optimization Methods in Finance, Cambridge University Press.
Software: R and R-NuOPT. Other commercial portfolio optimization products such as CPLEX and Axioma, arrangements with vendors permitting.
Prerequisites: AMATH 541 Investment Science and AMATH 542 Financial Data Modeling and Analysis in R. AMATH 543 Portfolio Construction and Risk Analysis is desirable.
AMATH 582 Computational Methods for Data Analysis
See: www.amath.washington.edu/courses/582-winter-2011/.