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MS in Financial Engineering Curriculum
All students enrolled in the MS in Financial Engineering Program must successfully complete 36 graduate credit hours in a common set of analytical, financial, and computational courses. The program includes a capstone practicum project with a financial services firm. The students will have first-hand experience solving real-world problems and make final presentations to a group of potential recruiters.
The program design allows students to complete the course requirements on campus or online in two calendar years. The program can be completed in less than two years with approval from a Program Director after a transcript review to determine if the previous coursework taken prior to Lehigh University aligns with a shorter degree completion timeline for the program. Lehigh University undergraduates accepted to the 4+1 Masters in Financial Engineering program have a pathway to complete the graduate degree in one year.
Online vs On Campus
All courses for both online and in-person students are synchronous and mostly held during the day with occasional evening classes.
All Core, Capstone, and Professional Development courses listed below are available to online and in-person students.
Online students are not eligible to pursue tracks listed under "Electives"; however, the elective requirements will be fulfilled by choosing a mix of courses from within the various track options. Online students will work with their academic advisor to find 9 credits that are available online.
International applicants are not eligible to complete this degree online.
Core required courses (21 credits)
MATH 467 STOCHASTIC CALCULUS (3 CREDITS): Brownian Motion, Martingales. Introduction to the theory of Stochastic Calculus, Itô Formula, and Stochastic Differential Equations, Black-Scholes model. Development of the Martingale Representation Theorem and Girsanov's theorem for change of measure. Multidimensional Stochastic Calculus. Applications to different problems from finance, physics, biology, etc.
Choose 1 of the following 2 courses:
- MATH 312 STATISTICAL COMPUTING AND APPLICATIONS (3 CREDITS): Use of statistical computing packages; exploratory data analysis; Monte Carlo methods; randomization and resampling, application and interpretation of a variety of statistical methods in real world problems.
- STAT 410 RANDOM PROCESSES AND APPLICATIONS (3 CREDITS): See MATH 310. Using programing language learn the probabilistic and statistical functions relevant to real world analysis. Theory and applications of stochastic processes. Limit theorems, introduction to random walks, Markov chains, Poisson processes, birth and death processes, and Brownian motion. Applications to financial mathematics, biology, business and engineering.
- GBUS 421 ADVANCED INVESTMENTS (3 CREDITS): Course provides comprehensive and exhaustive lecture implementation. Advanced topics relating to specific areas within investment finance such as valuation/security analysis; portfolio/risk management; fixed investment securities; mutual funds; hedge funds; microstructure; and trading. Consent of designated finance faculty representative required. Make extensive use of Bloomberg Terminals to complete assignments based on real world calculations (pricing bonds, duration/convexity, analyzing CMOs). Bloomberg Terminal and Excel Used
- GBUS 422 DERIVATIVES AND RISK MANAGEMENT (3 CREDITS): Project based course focused on tracking the price value of options and futures to see how price changes affect a margin account. The theory and application of a variety of derivative instruments (options, futures contracts, etc.) used in corporation finance and the financial services industry. The focus is on the risk management application vs. a rigorous development of option pricing theory and similar topics. Consent of designated finance faculty representative required.
ISE 426 OPTIMIZATION MODELS AND APPLICATIONS (3 CREDITS): Modeling and analysis of operations research problems using techniques form mathematical programming. Linear programming, integer programming, multicriteria optimization, stochastic programming and nonlinear programming using an algebraic modeling language. This course is a version of IE 316 for graduate students, with research projects and advanced assignments. Closed to students who have taken IE 316. Programing Language Used: AMPL
ISE 447 FINANCIAL OPTIMIZATION (3 CREDITS): Making optimal financial decisions under uncertainty. Financial topics include asset/liability management, option pricing and hedging, risk management, and portfolio optimization. Optimization techniques covered include linear and nonlinear programming, integer programming, dynamic programming, and stochastic programming. Emphasis on use of modeling languages and solvers in financial applications. Requires basic knowledge of linear programming and probability. This course is a version of IE 347 for graduate students and requires advanced assignments. Credit will not be given for both IE 347 and IE 447.
Choose 1 of the following 3 courses:
- CSE 326/426 FUNDAMENTALS OF MACHINE LEARNING (3 CREDITS): Bayesian decision theory and the design of parametric and nonparametric classification and regression: linear, quadratic, nearest-neighbors, neural nets. Boosting, bagging. Credit will not be given for both CSE 326 and CSE 426.
Prerequisites: (CSE 002 or CSE 012) and (MATH 205 or MATH 043) and (MATH 231 or ISE 121 or ECO 045) - ISE 364 INTRODUCTION TO MACHINE LEARNING (3 CREDITS): Techniques of applied machine learning rather than deep theory behind the algorithms and methods. Programming solutions for machine learning problems using a high-level programming language and associated machine learning libraries. Regression, clustering, principal component analysis, Bayesian methods, decision trees, random forests, support vector machines, and neural networks.
Prerequisites: CSE 002 - STAT 465 STATISTICAL MACHINE LEARNING (3 CREDITS): This course provides a broad introduction to concepts, methods, and practices of statistical machine learning: parametric and nonparametric regression, logistic regression, classification, and basic neural networks; kernel and nearest neighbor estimation, clustering, Bayesian and mixture models. In addition, we will explore selected topics like model selection, cross-validation; PCA, dimension reduction, regularized regression; trees, and ensemble learning. Knowledge of scientific programming in a language such as R required.
Prerequisites: (MATH 205 or MATH 241 or MATH 242) and (MATH 264 or MATH 312) and (MATH 263 or MATH 309)
Electives (9 credits)
Online students are not eligible to pursue the tracks listed below; however, the elective requirements will be fulfilled by choosing a mix of courses from within the various track options.
On-Campus students will choose three courses from within their desired choice of track.
- MATH 468 FINANCIAL STOCHASTIC ANALYSIS (3 CREDITS): Expect to be challenged via rigorous use of theoretical framework to derivation (mathematical proofs). Problems are created in a way that make students think about the material. Some homework requires coding in order to price options. Using programming of choice (python, excel, etc.) learn how to price derivative securities using binomial options pricing and Black-Scholes models. Application of Stochastic Calculus to the pricing of a variety of financial instruments: multiple stock models, American and exotic options, and foreign currency interest rate. Hedging and pricing by arbitrage in the setting of binary trees and Black-Scholes model. Heath-Jarrow-Morton model for the term structure of interest rates and short rate models.
Programing Language Used: Python - STAT 439 TIME SERIES AND FORECASTING (3 CREDITS): This course introduces the student to the statistical analysis of time series data and useful models: autocorrelation, stationarity, trend removal, and seasonal adjustment, basic time series models like AR, MA, ARMA; estimation, forecasting, and GARCH models; multivariate models, and factor models. The course emphasizes the main ideas and the most popular and widely used methods, and the use of a computer to practice the methods. Knowledge of scientific programming in a language such as R required.
Prerequisites: (MATH 264 or MATH 312) and (MATH 263 or MATH 309) - GBUS 424 ADVANCED TOPICS IN FINANCIAL MANAGEMENT (3 CREDITS): Advanced and stimulating case study based topics relating to specific areas of corporate finance such as: theoretical and empirical examination of recent developments in financial management, asset valuation and capital budgeting including the role of uncertainty, imprecise forecasts, risk preferences, inflation, market conditions, and the global marketplace, working capital management, leasing, mergers, and financing. The course content may vary between instructors or each time the course is offered. Consent of designated finance representative.
Programing Language Used: Python, SAS / Matlab
- ISE 465 APPLIED DATA MINING (3 CREDITS): Introduction to the data mining process including business problem understanding, data understanding and preparation, modeling and evaluation, and model deployment. Emphasis on hands-on data preparation and modeling using techniques from statistics, artificial intelligence, such as regression, decision trees, neural networks, and clustering. A number of application areas are explored. This course is a graduate version of IE 365 possessing some advanced assignments. Credit will not be given for both IE 365 and IE 465.
Prerequisites: ISE 121 or IE 121 or ISE 328 or IE 328 - ISE 467 MINING OF LARGE DATASETS (3 CREDITS): Explores how large datasets are extracted and analyzed. Discusses suitable algorithms for high dimensional data, graphs, and machine learning. Introduces the use of modern distributed programming models for large-scale data processing. A graduate version of ISE 367 that will require graduate students to do more rigorous assignments. Credit will not be given for both ISE 367 and ISE 467. Students are expected to have basic knowledge of programming and probability.
- ISE 444 OPTIMIZATION METHODS IN MACHINE LEARNING (3 CREDITS): Machine learning models and advanced optimization tools that are used to apply these models in practice. Machine learning paradigm, machine learning models, convex optimization models, basic and advanced methods for modern convex optimization.
Prerequisites: ISE 406 or IE 406 - STAT 438 LINEAR MODELS IN STATISTICS WITH APPLICATIONS (3 CREDITS): Least square principles in multiple regression and their interpretations; estimation, hypotheses testing, confidence and prediction intervals, modeling, regression diagnostic, multicollinearity, model selection, analysis of variance and covariance; logistic regression. Introduction to topics in time series analysis such as ARMA, ARCH, and GARCH models. Applications to natural sciences, finance and economics. Use of computer packages.
Prerequisites: (MATH 012 or MATH 231 or MATH 264) and (MATH 043 or MATH 205 or MATH 241 or MATH 242 or STAT 342) - CSB 442 BLOCKCHAIN: MATHEMATICAL FOUNDATIONS AND FINANCIAL APPLICATIONS (3 CREDITS): Technical and mathematical foundations of blockchain (algorithms, data structures, cryptography) with application to finance. Blockchain properties (immutability, irrefutability), security, consensus (proof-of-work, proof-of-stake, Byzantine consensus). Blockchain governance and trust models. Blockchain and finance: policy, regulation, compliance, systemic risk, relative power of nation-states, the role of central banks, economic justice. Broader impacts in such areas as foreign policy, surveillance and individual freedoms, non-financial applications. Smart contract coding and issues in blockchain software development. Lab experience interacting with a blockchain.
- GBUS 426 FINANCIAL MARKETS AND INSTITUTIONS (3 CREDITS): Functions and portfolios of financial intermediaries. Sectional demand and supply of funds, nature and role of interest rates, term structure and forecasting, impact of inflation and regulations on financial intermediaries and markets, and current developments in the financial system. Management of assets and liabilities within the U.S. financial institution's legal and economic constraints. Consent of designated finance faculty representative.
Prerequisites: GBUS 420 - GBUS 421 ADVANCED INVESTMENTS (3 CREDITS): Course provides comprehensive and exhaustive lecture implementation. Advanced topics relating to specific areas within investment finance such as valuation/security analysis; portfolio/risk management; fixed investment securities; mutual funds; hedge funds; microstructure; and trading. Consent of designated finance faculty representative required. Make extensive use of Bloomberg Terminals to complete assignments based on real world calculations (pricing bonds, duration/convexity, analyzing CMOs)
Bloomberg Terminal and Excel Used - GBUS 424 ADVANCED TOPICS IN FINANCIAL MANAGEMENT (3 CREDITS): Advanced and stimulating case study based topics relating to specific areas of corporate finance such as: theoretical and empirical examination of recent developments in financial management, asset valuation and capital budgeting including the role of uncertainty, imprecise forecasts, risk preferences, inflation, market conditions, and the global marketplace, working capital management, leasing, mergers, and financing. The course content may vary between instructors or each time the course is offered. Consent of designated finance representative.
Programing Language Used: Python, SAS / Matlab - ISE 413 ASSET VALUATION (3 CREDITS): Valuation of projects and companies by discounted cash flow models. Mechanics of present value calculations. Understanding financial statements. The determinants of equity risk, expected return, earnings, reinvestment needs and growth. Role of debt and taxation. Valuing start-up companies, distressed companies, cyclical companies, firms with exclusive rights.
Capstone Practicum (4 credits)
GBUS 485 PRACTICUM CAPSTONE I (2 CREDITS): MFE students work in teams with a faculty mentor on the scoping, reach, coding, and technical feasibility of portfolio theory-based tools, risk management models, trading algorithms, or blockchain-based trading strategies initiated by the course’s corporate sponsors. Projects can be initiated by enterprising students. These sponsors are asset managers, algorithmic traders, blockchain professionals, bankers, published authors, investor advisors to ensure that the projects have real-world applicability. Written reports and oral presentations to sponsors are required.
GBUS 487 PRACTICUM CAPSTONE II (2 CREDITS): MFE students continue to work on team projects designed in GBUS 485 via conference participation, reaching to experts in the field, further developing their coding, risk assessment skills. Written reports and oral presentations to sponsors are required. Open to MFE students only. Class meets every week while periodic team meetings with and without sponsors are also held.
Prerequisites: GBUS 485
Professional Development (2 credits)
GBUS 482 MFE PROFESSIONAL DEVELOPMENT (1 CREDIT): MFE alumni speakers provide weekly insights on coding languages and industry trends. Preparations for placement in internships and full-time positions are undertaken for finance and data science positions. Students must show progress toward crafting their professional profile and are required to submit bi-weekly summaries of completed course activities that tie into the learning objectives of the course and build upon prior course activities to advance job preparations and career foundations.
GBUS 483 MFE PROFESSIONAL DEVELOPMENT (1 CREDIT): MFE speakers provide insights into job search strategies and current job opportunities. Mock interviews and further preparation targeted to tracks (Trading, Data Analytics, Advisory, Risk), prepare students for targeted interviews. Students must show progress toward crafting their professional profile and are required to submit bi-weekly summaries of completed course activities that tie into the learning objectives of the course and build upon prior course activities to advance job preparations and career foundations. Prerequisites: GBUS 482
Certificate Programs
Online students are not eligible to pursue certificate programs.
Certificate Programs are available in Data Science & Financial Analytics, Quantitative Risk Management or Financial Operations Research by completing an additional 6-9 credit hours beyond the 36 credit hours required for the degree.
Candidates for the MS in Financial Engineering degree do not need to apply initially for certificate programs - students would meet with the Program Directors to select their certificate choice (if any) once they are enrolled in the program.
Students with equivalent courses from an undergraduate degree program will be given credit for fulfilling the field requirement and will be permitted to replace the credits from the list of approved electives. The program director must approve the student’s choice of electives.
