# Department of Mathematics Financial Mathematics

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## Course Information

### Course Listing

Autumn Quarter 1

Winter Quarter

Spring Quarter

Summer Quarter

Autumn Quarter 2

** FINM 32200 Computing for Finance I**As the first course in a three-part series, no previous programming knowledge is assumed. In Computing for Finance I, we will introduce the syntax and semantics of C++ and basics of OO programming. As part of the course work, students will develop an OO option pricer using the Monte Carlo technique. Classes are taught using a combination of lectures and in class hands-on lab sessions.

Instructor: Chanaka Liyanaarachchi Units: 100

*This course is a program requirement if the student does not pass the computer programming placement exam.*

*FINM 33000 Mathematical Foundations of Option Pricing*

Introduction to the theory of arbitrage-free pricing and hedging of financial derivatives. Topics include: Arbitrage; Fundamental theorems of asset pricing; Binomial and other discrete models; Black-Scholes and other continuous-time Gaussian models in one-dimensional and multidimensional settings; PDE and martingale methods; Change of numeraire.

Instructor: Roger Lee Units: 100 Program requirement

** FINM 33400 Statistical Risk Management**The course starts at a rather introductory level, but the progress is swift. It covers a brief survey of basic probability theory, and provides an introduction to some useful statistical distributions, both univariate and multivariate. A discussion of copulas and various correlation measures. Risk measures and ideas behind a reasonable risk measure. A few elements from Monte Carlo simulation. Statistical estimation, the maximum likelihood method and nonparametric methods. Asymptotic properties of estimators. Goodness of fit tests and model selection. Extreme value theory.

Instructor: Jostein Paulsen Units: 100 Program requirement

* FINM 35000 Topics in Economics*This course explores the economics of asset pricing. Going beyond no-arbitrage valuation, students learn how asset prices can be linked to economic fundamentals. As the recent recession and financial crisis show, there are important links between financial markets and the real economy. This course gives students a systematic way for understanding these links. Several important areas and puzzles of financial economics are presented. Topics in equity pricing include return-predictability, excess volatility, and factor-models. In fixed income, the course covers the empirical evidence of the term structure and how it compares to the Expectations Hypothesis, as well as how these facts fit with classes of common term-structures models. In international finance, the course covers the carry trade, the home-equity bias, and the currency trilemma.

Instructor: Mark Hendricks Units: 100 Elective

*FINM 37700 Introduction to Finance and Markets*

This course is an introduction to the basics of finance and financial markets. It assumes minimal finance/markets background with the option for experienced students to test out during a placement exam in the first week. Topics include: financial systems, financial returns, capital markets, and financial management.

Instructor: Peter Hirschboeck Units: 50 *This course is a program requirement if the student does not pass the Intro to Finance placement exam. *

* FINM 38000 Financial Mathematics Practicum*Curricular Practical Training (CPT) can be used

Units: 25 Program elective

**FINM 32300 Computing for Finance II**We will discuss new programming techniques, including more OO features and Templates in C++. We will also examine the use of the Standard Library in C++. Students will extend the option pricer to use Tree methods. Classes are taught using a combination of lectures and in class hands-on lab sessions.

Instructor: Chanaka Liyanaarachchi Units: 100

*This course is a program requirement if the student does not pass the computer programming placement exam.*

** FINM 36700 Portfolio Theory and Risk Management I**The course introduces investment analysis, allocation, risk control. The course begins with classic topics such as mean-variance analysis, priced and un-priced risk, hedging, and the efficient frontier of investment opportunities. Factor models are used to understand the relation between risk and expected return. Examples covered in the course include the CAPM, Black-Litterman, and principal component factors. Finally, the course discusses modern risk control, including risks from interest-rates, liquidity, and credit. Value-at-risk, and expected shortfall are discussed. This is a 5-week course offered in the first half of the quarter.

Instructor: Mark Hendricks Units: 50 Program requirement

* FINM 36702 Portfolio Theory and Risk Management II*This course combines a technical topic with an analysis of situations that produce outsized losses. Students gain familiarity with the credit portfolio loss models that are used to limit trading, allocate costs, and determine required bank capital. They also review the interplay between the technical and human factors that has led to prominent risk control failures. Unique in the Financial Math program, students make in-class presentations that detail the optimal responses of various market participants to unexpected circumstances. This is a 5-week course offered in the second half of the quarter.

Instructor: Jon Frye Units: 50 Program requirement

*Prerequisite: FINM 36700 Portfolio Theory and Risk Management I*

*FINM 32000 Numerical Methods *mplementing the theory introduced in Mathematical Foundations of Option Pricing (FINM 33000), this course takes a numerical/computational approach to the pricing and hedging of financial derivatives. Topics include: Trees as diffusion approximations; Finite difference methods for PDE solution; Monte Carlo methods for simulation; Fourier transform methods for pricing.

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Instructor: Roger Lee Units: 100 Program requirement

* FINM 34500 Stochastic Calculus*The course starts with a quick introduction to martingales in discrete time, and then Brownian motion and the Ito integral are defined carefully. The main tools of stochastic calculus (Ito's formula, Feynman-Kac formula, Girsanov theorem, etc.) are developed. The treatment includes discussions of simulation and the relationship with partial differential equations. Some applications are given to option pricing, but much more on this is done in other courses. The course ends with an introduction to jump process (Levy processes) and the corresponding integration theory.

Instructor: Greg Lawler Units: 100 Program requirement

* FINM 36000 Project Lab*Instructor: Roger Lee Units: 50 Program elective

*Prerequisite: Consent of instructor*

* FINM 38000 Financial Mathematics Practicum*Curricular Practical Training (CPT) can be used

Units: 25 Program elective

** FINM 33150 Regression Analysis and Quantitative Trading Strategies**Quantitative trading strategies, employing investment decisions based on model output, are a major component of business operations in the finance industry worldwide. We will present the major components of these strategies as found in several asset classes (equities, futures, credit, FX, interest rates and energy).

A large proportion of the models involved in quantitative strategies are expressible in terms of regressions. We will cover most of the ways they are used, including practical tricks and considerations, and concentrating particularly on achieving trustworthy performance. Mathematically, we will cover the computation of linear regressions with and without weights, in univariate and multivariate cases, having least squares or other objective functions.

Of the major computation technologies actively used by the finance industry (C/C++, Matlab, Java, R, VB/Excel, C\#, Python) we have chosen R and Python for numerical computation, with (very) light usage of Excel and with data coming from Quandl and some proprietary sources.

Instructor: Brian Boonstra Units: 100 Program requirement

** FINM 33601 Fixed Income Derivatives **The topics in this course include an introduction to fixed income markets, a detailed review of fixed income derivative instruments, and a general approach to bootstrapping the LIBOR term curve from available market quotes. We also discuss the application of the Black-Scholes-Merton model to pricing European swaptions and caps/floors. Students will study a statistical approach to building a foundation for the Heath-Jarrow-Morton framework of interest rate models. Students should be prepared for the extensive use of Stochastic Calculus.

Instructors: Yuri Balasanov, Lida Doloc, and Jeffrey Greco

Units: 100 Program requirement

* FINM 32400 Computing for Finance III*We will discuss topics relevant to implementing a basic electronic trading system using programming techniques taught in Computing for Finance I and II. Topics will include the implementation of a trading algorithm, handling the connectivity to an exchange/brokerage house and issues related to performance. Different design choices and tradeoffs between those different choices; concurrent and parallel programming will be discussed within the context of this project. Classes are taught using a combination of lectures and in class hands-on lab sessions.

Instructor: Chanaka Liyanaarachchi Units: 100

*This course is a program requirement if the student does not pass the computer programming placement exam. This course can be used to fulfill elective credit.*

* FINM 37300 Foreign Exchange and Fixed Income Derivatives*This course will examine international currency markets, financial products, applications of quantitative models and FX risk management with an emphasis on the derivative products and quantitative methods in common use today. Topics will include a) the behavior of FX rates: exchange rate regimes, international monetary systems, FX modeling and forecasting, b) FX markets and products: spot, forward, futures, deposits, cross-currency swaps, non-deliverable contracts, FX options, exotic options, hybrid products and structured notes, and c) Risk management: from the trading book, trading institution, global asset manager and multinational corporation perspectives. This is a 5-week course offered in the first half of the quarter.

Instructor: Anthony Capozzoli Units: 50 Program requirement

* FINM 36000 Project Lab 1*Instructor: Roger Lee Units: 50 Program elective

*Prerequisite: Consent of instructor*

*FINM 36001 Project Lab 2*Instructor: Roger Lee Units: 0 Program elective

*Prerequisite: FINM 36000 and consent of instructor*

* FINM 38000 Financial Mathematics Practicum*Curricular Practical Training (CPT) can be used

Units: 25 Program elective

* FINM 36000 Project Lab*Instructor: Roger Lee Units: 50 Program elective

*Prerequisite: Consent of instructor*

*FINM 36001 Project Lab 2*Instructor: Roger Lee Units: 0 Program elective

*Prerequisite: FINM 36000 and consent of instructor*

* FINM 38000 Financial Mathematics Practicum*Curricular Practical Training (CPT) can be used

Units: 25 Program elective

* FINM 39000 Regulatory and Compliance Requirements for Financial Institutions *The course introduces students to the key regulatory and compliance requirements for bank and non-bank financial institutions under the Dodd-Frank Act. Students first learn the basics of the regulatory framework governing the U.S. capital markets and financial institutions, and are given an overview of the financial crisis of 2008-09 that led to the Dodd-Frank legislation. Next, we examine the primary areas under the Act that a risk-management system must address. Topics include: a) regulation of systemic risk, including stress testing of large depository and systemically important non-depository institutions, b) Basel III's capital adequacy requirements issued by the Federal Reserve Board for such institutions and the SEC's net capital rules for broker-dealers, and c) the regulation of the derivatives market and counterparty risk. The course covers the Act's basic modeling requirements relating to these regulations. Students learn the primary components of a financial institution compliance program pertaining to corporate governance, supervision, internal controls, management of conflicts of interest, and gain an understanding of a risk management system optimally designed to achieve compliance with the Dodd-Frank Act. Case studies illustrate both compliance breakdowns and best practices.

This is a 5-week course offered in the first half of the quarter.

Instructor: Alexander Dill Units: 50 Program elective

* FINM 33180 Data Analysis for Finance and Statistics *This course is about using matrix computations to infer useful information from observed data. One may view it as an "applied" version of Stat 30900 although it is not necessary to have taken Stat 30900; the only prerequisite for this course is basic linear algebra. The data analytic tools that we will study will go beyond linear and multiple regression and often fall under the heading of "Multivariate Analysis" in Statistics. These include factor analysis, correspondence analysis, principal components analysis, multidimensional scaling, linear discriminant analysis, canonical correlation analysis, cluster analysis, etc. Understanding these techniques require some facility with matrices in addition to some basic statistics, both of which the student will acquire during the course.

Instructor: Lek-Heng Lim Units: 100 Program elective

* FINM 37601 Mathematical Market Microstructure: An Optimization Approach for Dynamic Inventory Management and Market Maker Quoting*This course is an introduction to mathematical theory of market microstructure, with key applications in solving optimal execution problems with inventory management. We will start from discussions of market design, global market structure, algorithmic trading and market making practices. We will then present traditional market microstructure theory in the context of dealer inventory management and information-based quoting and pricing. Latest literature about realized volatility calculations and intraday implied volatility surface modeling using high-frequency data will be reviewed. The subject of order book dynamics research with applications to market impact modeling will be discussed as well. Finally, a review on continuous-time stochastic control theory will be provided and a discussion will be given on execution algorithm development and market making strategy design using stochastic programming techniques. The main goal of this course is to provide a clear discussion on key mathematical treatments and their practical applications of market microstructure problems, in particular relating to price discovery and utility optimization for certain transaction processes with non-trivial transaction cost present.

This is a 5-week course offered in the first half of the quarter.

Instructor: Hongsong Chou Units: 50 Program elective

* FINM 37602 Mathematical Market Microstructure without Rationality Assumptions *Just like the view on micro world made us rethink our theories about the laws of physics previously based on macro world experience, algorithmic trading at extremely low latency exposes us to new phenomena and demands new mathematical models for their analysis.

Objectives of this course are: introducing students to some models that have become important for analysis of market microstructure in recent years and show how they can be applied to low latency trading and risk management. We start with a review of the main features of the market behavior at ultra-low latency, explain why we prefer to look at the market events with “frog’s eye” and concentrate on mathematical models consistent with Principle of Ma. During the course we study stochastic processes that describe market behavior at the microstructure level. Among them are Poisson, Cox, Ammeter, Hawkes and other processes. Students will learn how simulate each of the processes, fit it to market data and interpret the results. We will relate these processes to common approaches to modeling market price formation and limit order book behavior.

Demonstrations and applications will be implemented in R. Students will work with some real market data examples. Classes consist of lecture part and in-class workshop. Students are required to come with their laptop computers with installed R. Some background in probability theory, statistical methods and statistical data analysis with R is recommended.

This is a 5-week course offered in the first half of the quarter.

Instructor: Yuri Balasanov Units: 50 Program elective

* FINM 35910 Applied Algorithmic Trading *Applied Algorithmic Trading will introduce the required background knowledge and processes necessary for the design and implementation of algorithmic trading models within the context of industry requirements. The objective of the course is to bring together the numerous disciplines covered in other Financial Mathematics courses, focused on quantitative trading, and combine them into a workable industry level presentation. This course will walk students through the process of generating trading ideas, quantifying the trading process, risk-based modeling concepts, back-testing and optimization techniques, and key industry metrics used to evaluate algorithmic trading model performance. Lastly, the course will stress the leadership and presentation skills necessary to make a successful pitch in an industry setting.

Prerequisites: FINM 32400 Computing for Finance III, FINM 33150 Regression Analysis and Quantitative Trading Strategies or consent of instructors.

This is a 5-week course offered in the first half of the quarter.

Instructors: Chris Gersch and Bernardo Jorge Units: 50 Program elective

* FINM 37701 Case Studies of Implementations in Computational Finance*This course will introduce participants to the field of Computational Finance through real-world “end-to-end” case studies. The course will focus on the importance of data analytics and algorithmic processing and it will be centered around a series of examples that are representative of problems that practitioners in finance have to solve.

The course is structured to cover 2 major themes:

· Intro to Data analysis and Numerical algorithms in Computational Finance

· Case studies of "end-to-end" system implementations.

Prerequisites and recommended background: As a prerequisite, students will be required to have successfully completed the Computing course sequence, or to have passed the placement exam of the Computing course sequence. The participants should also have basic familiarity with the use of MS Excel spreadsheets & VBA, as well as with the use of a high level programming language such as Python or R.

Instructor: Cristian Doloc Units: 100 Program elective

* FINM 36000 Project Lab*Instructor: Roger Lee Units: 50 Program elective

*Prerequisite: Consent of instructor*

*FINM 36001 Project Lab 2*Instructor: Roger Lee Units: 0 Program elective

*Prerequisite: FINM 36000 and consent of instructor*

* FINM 38000 Financial Mathematics Practicum*Curricular Practical Training (CPT) can be used

Units: 25 Program elective

**Updated September 16, 2015**