Approved by: Graduate Council
Implementation Date: Summer 2014
Note: Deletions are strikethroughs. Insertions are underlined.
Catalog Copy
Master of Science in Mathematical Finance
The Master of Science in Mathematical Finance program is designed to prepare students to pursue careers in quantitative finance. Increasingly firms of all types, but especially financial institutions, investment banks, and commodities firms, rely upon highly sophisticated mathematical models to identify, measure, and manage risk. The advent of these models has triggered the emergence of a new discipline, Mathematical Finance. This new discipline, sometimes also referred to as “financial engineering,” “computational finance,” or “quantitative finance,” requires professionals with extensive skills in both finance and mathematics.
The Mathematical Finance program at UNC Charlotte is a joint program of the Departments of Finance and Economics in the Belk College of Business and the Department of Mathematics and Statistics in the College of Liberal Arts & Sciences. Students take courses from all three departments in an integrated curriculum. Students may use electives to tailor the program to their specific interests.
Additional Admission Requirements
In addition to the general requirements for admission to the Graduate School, the following are required for admission to the Master of Science in Mathematical Finance program.
- A baccalaureate degree in a related field with a GPA of at least 2.75 out of 4.0 with an average of 3.0 in the junior and senior years.
- Acceptable scores on each portion of the GRE or GMAT.
- For applicants from non-English speaking countries, a language requirement score of 557 on the TOEFL or 220 on the new computer-based TOEFL or 78% on the MELAB. Non-native speakers of English, may, at the discretion of either the Graduate School or the Program Committee for the MS in Mathematical Finance, be required to enroll in English as a Second Language (ESL) courses at the English Language Training Institute.
- Specific coursework equivalent to the following: introductory course in the Theory of Finance; a standard three semester sequence in Calculus; Linear algebra; working knowledge of a suitable programming language; at least one upper-level course in Probability and Statistics. Students lacking this coursework may be admitted subject to the condition that they satisfactorily complete such coursework during the first two semesters that they are enrolled in the program and prior to their taking any program courses where prerequisites are missing.
Prerequisite Requirements
Students may enter this program from a variety of undergraduate backgrounds, including finance, mathematics, economics, computer science, actuarial science, statistics, information systems and engineering. As a result, many students admitted will not have the required background to immediately begin taking advanced courses from each of three areas of study. In such cases, the student may be required to take prerequisite courses prior to enrolling in advanced courses in specific fields. These prerequisites would be in addition to the advanced 30 semester hours required for the degree. In general students must have the following background in each field before taking advanced courses in that field:
- Finance: Have earned an acceptable grade in an introductory course in finance from an AACSB-accredited business school at either the undergraduate or MBA level.
- Economics: Have earned an acceptable grade in microeconomics and macroeconomics courses at either the undergraduate or MBA level.
- Mathematics: Have earned acceptable grades in the equivalent of a three course sequence in calculus (differential and integral calculus), a course in linear algebra, and an upper-level course in probability and statistics.
- Programming: Students should be familiar with at least one programming language, most preferably C or C++.
Again, students may be admitted to the program without meeting all of these requirements. The Program Director, in conjunction with the Departmental Graduate Coordinators, will evaluate each incoming student's academic background to determine in which prerequisite courses the student will be required to enroll. A student whothat meets the prerequisites in a field may begin taking advanced courses in that field while still taking prerequisite courses in another field. A student must, however, be making satisfactory progress toward fulfilling theirhis or her prerequisites in all fields to remain enrolled in the program.
Degree Requirements
Total hours required:
A minimum of thirty hours of coursework beyond the bachelor's degree is required to earn the degree. The student must complete the required six program core courses and four concentration courses corresponding with the selected concentrationA minimum of thirty hours of coursework beyond the bachelor's degree is required to earn the degree. The student must complete the required 24 hours from the program core and 6 hours of approved electives.
The Program Core:
- ECON/FINN 6203 Financial Economic Theory (3)
- STAT 6113/ECON 6113 Cross-Section and Time Series Econometrics (3)
MATH 6201 Statistical Techniques in Finance (3) -OR- ECON 6113 Cross-Section and Time Series Econometrics (3) - FINN/ECON 6219 Financial Econometrics (3)
- FINN 6210
Derivatives I:Financial Elements of Derivatives (3) - FINN 6211
Risk Management andFixed IncomeDerivativesSecurities and Credit Risk (3) MATH 6202 Derivatives II: Partial Differential Equations for Finance (3)- MATH 6203 Stochastic Calculus for Finance (3)
MATH 6204 Numerical Methods for Financial Derivatives (3)
Approved Mathematical Finance Electives:
ECON 6090 Topics in Economics (3)ECON 6100 Mathematical Economics (3)ECON 6201 Advanced Macroeconomic Theory (3)ECON 6202 Advanced Microeconomic Theory (3)ECON 6235 Monetary Theory and Financial Theory (3)ECON 6800 Directed Study Economics (3)FINN 6058 Special Topics in Financial Services (3)MATH 5128 Applied Probability I (3)MATH 5129 Applied Probability II (3)MATH 5143 Analysis I (3)MATH 5171 Numerical Solution of Ordinary Differential Equations (3)MATH 6205 Financial Computing (3)
Concentrations
The program offers three concentrations leading to a Master of Science in Mathematical Finance Degree. Students who plan to pursue careers in quantitative modeling and pricing analysis are encouraged to elect the Computational Finance Concentration. Students planning to pursue a career in risk management and insurance are encouraged to pursue the program with the Risk Management Concentration. Students interested in a career in financial data analysis and applications are encouraged to elect the Financial Data Analytics concentration.
Computational Finance Concentration
In addition to the six courses specified in “The Program Core” section, the following four courses are required for a Master of Science in Mathematical Finance Degree with a Computational Finance Concentration.
MATH 6204 Numerical Methods for Financial Derivatives (3)
MATH 6205 Financial Computing (3)
MATH 6206 Stochastic Calculus for Finance II (3)
FINN 6212 Advanced Financial Derivatives (3)
Risk Management Concentration
In addition to the six courses specified in “The Program Core” section, the following four courses are required for a Master of Science in Mathematical Finance Degree with a Risk Management Concentration.
FINN 6213 Risk Management and Financial Institutions (3)
FINN 6214 Asset and Portfolio Management (3)
FINN 6215 Risk Management in Insurance Companies (3)
FINN 6216 Quantitative Risk Management (3)”
Financial Data Analytics Concentration
In addition to the six courses specified in “The Program Core” section, the following four courses are required for a Master of Science in Mathematical Finance Degree with a Financial Data Analytics Concentration.
ECON 6217 Advanced Microeconometrics (3)
ITCS 6114 Algorithm and Data Structures (3)
ITCS 6160 Database Systems (3) OR ITIS 5160 Applied Databases
MBAD 6201 Business Intelligence and Analytics (3)
Admission to Candidacy Requirements
An Admission to Candidacy form listing graduate-level courses that apply to the degree must be submitted to the Mathematical Finance Program Director four weeks prior to the semester in which the student plans to complete the coursework for the degree.
Assistantships
A number of assistantships are available each year. In order to be competitive, applications should be submitted by March 15. Additional information is available from the Program Director.
Advising
Advising is done by the Program Director, in conjunction with the Area Coordinators of each of the participating Departments.
Transfer Credit
No more than 6 credit hours and only courses with a grade of A or B at an accredited institution. Requires the recommendation of the Program Director and approval of the Graduate School.
Comprehensive Examination
Student will be required to pass a comprehensive examination. An examining committee will be appointed by the program director and will be constituted from the program’s faculty. The exam may be, at the committee’s discretion, either written or oral.
Application for Degree
Each student should make application for his/her degree by completing the online Application for Degree through Banner Self Service no later than the filing date specified in the University Academic Calendar.
Courses In Mathematical Finance
Economics Courses (ECON)
See descriptions of ECON courses under Economics in the Belk College of Business section of this Catalog.
Mathematics Courses (MATH)
See descriptions of MATH courses under Mathematics in the College of Liberal Arts & Sciences section of this Catalog.
FINN 5158. Student Managed Investment Fund I. (3) Cross-listed as MBAD 5158. Prerequisites: FINN 3120 or MBAD 6152, FINN 3222 or FINN/MBAD 6153, and permission of instructor. Management of an actual portfolio consisting of a portion of the University’s Endowment Fund. Students are required to take FINN 5159 following this course. (Fall)
FINN 5159. Student Managed Investment Fund II. (3) Cross-listed as MBAD 5159. Prerequisites: FINN 5158, FINN 3120 or MBAD 6152, FINN 3222 or FINN/MBAD 6153, and permission of instructor. Management of an actual portfolio consisting of a portion of the University’s Endowment Fund. (Spring)
FINN 6058. Special Topics in Financial Services. (3) Cross-listed as MBAD 6160. Prerequisite: MBAD 6152. Each year, the subject matter of this course deals with a different specialized and contemporary topic of interest to students who are preparing for management careers in the financial services industry. The topics are chosen and covered in a way that builds on and supplements the topics covered in other courses in the Financial Institutions/Commercial Banking concentration. Emphasis is placed on the managerial implications of the subject matter as well as the impact on the financial system. Topics covered may vary from semester to semester, and the course may be repeated a maximum of one time for academic credit. (On demand)
FINN 6151. Financial Institutions and Markets. (3) Cross-listed as MBAD 6151. Major financial institutions, particularly commercial banks, and their role in the intermediation process and as suppliers of funds to the money and capital markets. Comparative financial policies of these institutions are examined in the context of their legal and market environment. (Yearly)
FINN 6152. Financial Management. (3) Cross-listed as MBAD 6152 and MSRE 6152. Theory and practice of corporate finance including asset management, cost of capital and capital budgeting, optimization problems and socio-economic aspects of financial management. Computer technology may be employed when applicable. (Fall, Spring)
FINN 6153. Investment Management. (3) Cross-listed as MBAD 6153. Prerequisite: MBAD 6152. Theory and practice of investment decisions of individuals and fund managers. Topics include: the status of capital market theory, the efficient market hypothesis literature, and a portfolio performance measurement. Standard institutional and investment analysis topics, futures and options markets, and international investment topics are covered. (Yearly)
FINN 6154. Applied Business Finance. (3) Cross-listed as MBAD 6154. Prerequisite: MBAD 6152. Examination of business finance topics which typically confront the firm’s primary finance functional areas (CFO, Treasurer, Controller). The purpose is to develop advanced analytical skills in those topic areas. Topics include: lease vs. buy (borrow); leveraged buy-outs: merger analysis (emphasis on valuation); international operations of American firms (capital budgeting and cost of capital); capital structure; risk management. Such additional topics as working capital management; risk management; and relevant current topics are included as time permits. (On demand)
FINN 6155. Multinational Financial Management. (3) Cross-listed as MBAD 6155. Prerequisite: MBAD 6152. Financial management of the multinational firm including management of foreign exchange risk and political risk, and the control and evaluation of financial policies of multinational firms. (Yearly)
FINN 6156. Commercial Bank Management. (3) Cross-listed as MBAD 6156. Prerequisite: MBAD 6152. Techniques for the management of commercial banks. Topics include: industry structure, administrative organization, management of assets, liabilities, and capital, and financial analysis of the banking firm. (Yearly)
FINN 6157. Advanced Corporate Finance. (3) Cross-listed as MBAD 6157. Prerequisite: MBAD 6152. Theories of modern corporate finance, including theory of efficient capital markets; uncertainty and the theory of choice; market equilibrium asset pricing models (capital asset pricing model, arbitrage pricing theory, Black-Scholes); theories of capital structure and the cost of capital; dividend policy; and leasing. (Yearly)
FINN 6203. Financial Economic Theory. (3) Cross-listed as ECON 6203. Prerequisite: Admission to Graduate Program and Permission of Program Director. This course offers the fundamental principles of risk pricing and risk allocation in a unified framework. Discrete-time model is employed to underscore the relationship between the techniques used in finance and the economic analysis of risk. The objective is to understand the economics of asset pricing and how derivatives and options are used in practice and their limitations. (On demand)
FINN 6203. Financial Economic Theory. (3) Cross-listed as ECON 6203. Prerequisites: Admission to Graduate Program and Permission of program director. Review of financial economic theory using discrete-time models. Topics include: risk measurement; choices under uncertainty; portfolio selection; capital asset pricing model (CAPM); Arrow-Debreu pricing; options and market completeness; the Martingale measure; arbitrage theory; consumption-based CAPM; and valuation of the firm. (On demand)
FINN 6210. Financial Elements of Derivatives. (3) Prerequisite: FINN 6152 or equivalent, or permission of Department. This course examines the nature and functions of futures and options markets. Topics include hedging for risk reduction and the role of derivative instruments in the capital markets. The course focuses on basic pricing techniques which are derived from no arbitrage relations. (On demand)
FINN 6210. Derivatives I: Financial Elements of Derivatives. (3) Prerequisite: FINN 6152 or equivalent, or permission of Department. Theory and practice of financial derivatives markets including forwards, futures, and options markets. Topics include: the economics of derivatives markets, pricing models for instruments in these markets, strategies for hedging and speculation, as well as regulatory and governance issues. (On demand)
FINN 6211. Fixed Income Securities and Credit Risk. (3) Prerequisite: FINN 6210 or permission of Department. This course studies fixed income securities and portfolios as well as the theory and practice of fixed income markets. Topics include fixed income instruments and sectors, duration and convexity, term structure of interest rates, securitization, portfolio management, hedging, and credit risk. (On demand)
FINN 6211. Risk Management and Fixed Income Derivatives. (3) Prerequisite: FINN 6210 or permission of Department. Risk management of fixed income portfolios as well as the theory and practice of fixed income markets. Topics include: fixed income instruments, term structure models, pricing methods, portfolio management, duration and convexity, securitization, and hedging. (On demand)
FINN 6212 Advanced Financial Derivatives (3)
FINN 6212. Advanced Financial Derivatives. (3) Prerequisite: FINN 6210 or permission of Department. The course covers multi-factor derivative pricing models. Topics include the discrete-time and discrete-state models, Ito processes, relevant topics on stochastic calculus, Risk Neutral Valuation, and review of the Black-Scholes model. Additional topics include commodity pricing models, stochastic volatility models, multi-period discrete-time (GARCH) models, and the interest rate models such as the Vasicek and CIR models. (On demand)
FINN 6213 Risk Management and Financial Institution (3)
FINN 6213. Risk Management and Financial Institutions. (3) Prerequisite: FINN 6203 or permission of Department. This course describes the following: how market risk, credit risk and operational risk are quantified; Basel II regulatory framework; estimation of aggregate economical capital; calculation and use of RAROC; and recent bank risk management tools: back test, CCAR and Dodd-Frank proposals. It will also address recent big losses that have occurred in financial markets and how they can be avoided. (On demand)
FINN 6214 Asset and Portfolio Management (3)
FINN 6214 Asset and Portfolio Management. (3) Prerequisite: FINN 6203 or permission of Department. This course provides students with a foundation in investments and portfolio management from the perspective of an institutional investor. Particular attention will be given to the issues associated with managing assets of an insurance company. Topics include: measuring and modeling return and risk, expected return models, information ratio, valuation theory and practice, forecasting, portfolio construction, transaction costs, turnover and trading, performance analysis, asset allocation, securities analysis, and the legal and regulatory landscape of institutional investing. (On demand)
FINN 6215 Risk Management in Insurance Companies (3)
FINN 6215 Risk Management in Insurance Companies. (3) Prerequisite: FINN 6203 or permission of Department. This course examines the operations and risks of an insurance firm and how to evaluate and manage those operations and risks in a dynamic business environment. The following topics are covered: 1. The role of insurance firms within the financial services industry, 2. The functions of insurance firms with emphasis on operations unique to insurers, 3. Insurer financial and risk management in the complex regulatory environment and 4. Financial and strategic analysis of insurance firms. (On demand)
FINN 6216 Quantitative Risk Management (3)
FINN 6216. Quantitative Risk Management. (3) Prerequisite: FINN 6203 or permission of Department. This course offers the quantitative techniques and tools for the risk management. It starts with the basic concepts and methodologies. Topics include risk measures such as VaR and Expected Shortfall, univariate and multivariate models, copulas and tail dependence in risk management framework, and back testing. This course also discusses how to estimate VaR and Expected Shortfall parametrically, semi parametrically and non-parametrically. (On demand)
FINN 6219. Financial Econometrics. (3) Cross-listed as ECON 6219. Prerequisites: ECON 6218 or MATH 6201. Advanced time series with financial applications. Topics covered include time series regressions (univariate and multivariate, stationary and non-stationary) and time series models (including ARMA, ARCH, GARCH, stochastic volatility and factor models). The emphasis will be on model properties, estimators, test statistics, and applications in finance. (On demand)
MATH 6203. Stochastic Calculus for Finance I. (3) Prerequisite: Admission to Graduate Program and Permission of Program Director. This course starts with the probability theory in discrete probability space, discrete-time stochastic processes, and derivatives pricing in the Binomial model. The second part covers probability theory in general probability space and continuous-time martingale and Markov processes. Topics include the It’o integral, Black-Scholes model, It’o-Doeblin formula, Girsanovs theorem, and Martingale Representation theorem. Applications to pricing of exotic derivatives and American options are discussed.
MATH 6203. Stochastic Calculus for Finance. (3) An introduction to those aspects of partial differential equations and diffusion processes most relevant to finance, Random walk and first-step analysis, Markov property, martingales and semi-martingales, Brownian motion. Stochastic differential equations: Ito’s lemma, backward and forward Kolmogorov equations, the Feynman-Kac formula, stopping times, Hull and White Models, Cox-Ingersoll-Ross Model. Applications to finance including portfolio optimization and option pricing.
MATH 6206 Stochastic Calculus for Finance II (3)
MATH 6206. Stochastic Calculus for Finance II. (3) Prerequisite: MATH 6203 or permission of Department. This course focuses on the applications of stochastic calculus techniques to advanced financial modeling. Topics include pricing of European, American and fixed-income derivatives in the Black-Scholes and stochastic volatility models. The Jump-diffusion model will also be introduced. (On demand)
STAT 6113. Cross-Section and Time-Series Econometrics. (3) Cross-listed as ECON 6113. Prerequisite: permission of department. This course introduces the advanced study of the theory and application of statistics to economic problems. Topics include: derivation of the least-squares estimator; methods with which to detect and correct for potential problems with the classical regression model; maximum likelihood estimation; instrumental variables regression; the problems with multicollinearity, heteroscedasticity, and autocorrelation; introduction to the time-series estimation, including ARIMA models and basic forecasting tools. (Spring)