# Department of Mathematics Financial Mathematics

### IN THIS SECTION

## 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 Program requirement

*Students can substitute FINM 33602 or BUSF 41202 for this requirement.*

*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 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 for Option Pricing*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.

I

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 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. The course is an elective if the student passes the exam and chooses to take the course.*

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

*Prerequisite: Consent of instructor*

* FINM 37700 Financial Mathematics Practicum*Curricular Practical Training (CPT)

Units: 50 Program elective

**Internship**

**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 Program requirement

*Students can substitute FINM 33602 or BUSF 41202 for this requirement.*

** FINM 33602 Advanced Fixed Income Derivatives**The course will focus on additional chapters of fixed income derivatives that were not included in Fixed Income Derivatives.

The topics include term curve bootstrapping and smoothing; in-depth derivation of the HJM framework; Black's model and forward measure; the statistical model and HJM; market models calibration; volatility skew adjustments for interest rate models; CVA counterparty risk; risk management with the statistical model; numerical methods for Hull-White model: trinomial trees, Monte Carlo and finite difference methods.

As a prerequisite, students will be required to have a solid understanding of the material covered in Fixed Income Derivatives.

Instructor: Yuri Balasanov, Lida Doloc, and Jeffrey Greco

Units: 100 Program requirement *Students can substitute FINM 35000 or BUSF 41202 for this requirement.*

* FINM 37600 Mathematical Market Microstructure *This course is an introduction to mathematical theory of market microstructure and its applications to low latency trading and risk management. We will study special classes of stochastic processes that can capture market behavior at micro level, review major approaches to modeling microstructure described in the literature. We will also present practical aspects of the subject in algorithmic and low-latency trading. Topics covered in the course include introduction to exchanges and trading practices in the world, application of Cox stochastic processes to modeling of low latency market behavior, review of mathematical models of limit order book dynamics, structural models of price formation process at microstructure level, information-based vs. inventory-based market microstructure models, stochastic control and optimization in trading algorithm development, real time risk management. This is a 5-week course offered in the first half of the quarter.

Instructors: Yuri Balasanov and Hongsong Chou

Units: 100 Program elective

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

*Prerequisite: Consent of instructor*

**Updated March 18, 2015**