Web Site of the Program

Head of Program : Talat Ulussever

Professors : Vedat Akgiray, Necati Aras, Ali Rana Atılgan, Gülay Barbarosoğlu, Alp Eden,  Metin R. Ercan, Refik Güllü, Nesrin Okay, İlhan Or, Mine Uğurlu, Fatih Ecevit

Associate Professors : 

Assistant Professors : Mehmet Yasin Ulukuş*

The School of Engineering of Bogazici University, in collaboration with the School of Economics and Administrative Sciences and the School of Arts and Sciences, in the year 2002 established a Master of Science degree program in Financial Engineering (MSFE). This is an interdisciplinary program offered jointly by the Department of Industrial Engineering, Department of Mathematics and the Department of Management. It is the first academic program in Financial Engineering in Turkey. This program is being offered by the Institute for Graduate Studies in Science and Engineering.

The main objective of the program is to provide graduate level technical education to students who want to work in the new and growing finance industry. This includes investment banks and corporations, financial management and consulting companies, insurance companies and firms that invest in financial markets. Recent developments during the last decade has shown the need for an educational program whose graduates are equipped with the necessary tools and techniques to evaluate financial markets, determine investment strategies, as well as design, engineer and market new financial products. The topic has become more appealing with the emergence of new securities and financial instruments, like options, swaps, interest rate derivatives, credit derivatives and private retirement plans. A graduate of the program is expected to work not only in companies that market financial products, but also in the finance department of general service or manufacturing firms. 

Students will be exposed to a technically rigorous curriculum that provides a strong base in optimization techniques and stochastic modeling. The main emphasis is on the application of these techniques and models in financial markets through computational methods and simulation. Due to the apparent diversity of the educational program, it has an interdisciplinary structure that involves the three main schools of the university.

The targeted student body mainly consists of working professionals who are graduates of engineering, business and science schools with a minimum 2-year work experience. Although work experience is recommended, it is not required and new graduates with successful academic records can also apply. The enrollment plan for the FE program is to admit 35 new students every year. In order to apply, the students should have an undergraduate degree in a technical field like engineering, mathematics, physics, operations research and statistics or in a related field like economics or management.

Students who have successfully completed the requirements of the FE program will receive an MS degree. The graduation requirement is to complete 31 credits of course work consisting of 9 required, 2 elective courses and a graduation project. This can be accomplished in 3 semesters under normal circumstances. The graduation project requires teamwork by groups of 2-4 students on an applied topic under the supervision of a faculty member for 2 semesters. Those applicants who do not have the necessary background to follow the academic program may be required to take additional remedial courses. This background mainly consists of undergraduate level probability and statistics, linear algebra, calculus, differential equations, computer programming, basic economics and corporate finance.

** This program is subject to additional tuition and fees.

GRADUATE PROGRAM IN FINANCIAL ENGINEERING
 

Total: 33 Credits/90 ECTS.

The courses of the program are listed below:

Required Courses 
FE 500 Introduction to Financial Engineering
FE 501 Optimization Models in Economics and Finance
FE 502 Fundamentals of Economics
FE 507 Mathematics of Uncertainty 
FE 515 Financial Econometrics
FE 520 Financial Calculus 
FE 521 Derivative Securities and Markets
FE 522 Computational Finance
FE 523 Investment Analysis and Portfolio Theory

Elective Courses
FE 514 Corporate 
FE 519 Money and Capital Markets
FE 524 Dynamics of Financial Systems
FE 526 Decision Analysis
FE 532 Risk Analysis and Insurance Pricing
FE 534 Life Insurance and Pension Plans
FE 536 Risk Management in Financial Institutions
FE 538 Valuation with Real Options
FE 580-599 Special Topics in FE

Project or Thesis 
FE 571/572 Financial Engineering Project

COURSES DESCRIPTIONS

FE 500 Introduction to Financial Engineering (0+2+0) 1 ECTS 4
(Finans Mühendisliğine Giriş)
Introduction and orientation to financial engineering (FE); illustrations of basic research, models and applications presented in a lecture series by FE faculty and expert speakers from the finance sector. 

FE 501 Optimization Models in Economics and Finance (3+0+0) 3 ECTS 9
(Ekonomi ve Finansta Eniyileme Modelleri)
Overview of optimization concepts: modeling-analysis-decision loop in financial and economic practice; linear, non-linear, integer and dynamic programming applications in finance and economics. Discrete optimization models in finance: modeling possibilities through binary and integer variables; relaxation methods; branch-and-bound methods; simulated annealing and genetic algorithms. Quadratic and convex programming, applications in portfolio management by using of linear and nonlinear programming software.

FE 502 Fundamentals of Economics (3+0+0) 3 ECTS 8
(Ekonominin Temelleri)
Basics of macroeconomics: money, inflation, income, and unemployment; banking and financial markets; exchange rate determination; emerging markets. Basics of microeconomics: demand, supply, and market equilibrium; perfect competition; imperfect competition; cooperative and non-cooperative solutions in game theory with financial applications. 

FE 507 Mathematics of Uncertainty
(Belirsizliğin Matematiği) (3+0+0) 3 ECTS 9
Random variables, expectations and variance, Binomial, Poisson and Normal Distributions, Law of Large Numbers. Methods of data analysis, univariate and multi-variate models, estimation, confidence intervals, hypothesis testing problems, analysis of variance, regression and correlation analysis, goodness of fit tests, maximum likelihood estimation. Central Limit Theorems, generating and characteristic functions, moments, conditional probabilities; Markov Chains, random walks as martingales, discrete to continuous stochastic processes, binomial model of stock prices, Arbitrage Pricing Theory, pricing of a European Call Option, Black-Scholes equation.

FE 514 Corporate Finance
(Şirket Finansı) (3+0+0) 3 ECTS 6
Fundamental concepts; time value, risk and return; valuing stocks and bonds; financial statement analysis; break-even and risk analysis; investment criteria; optimal capital structure; types of financing; discussion on Initial Public Offerings (IPOs), mergers and acquisitions.

FE 515 Financial Econometrics (3+0+0) 3 ECTS 6
(Finansal Ekonometri)
Introduction to forecasting techniques; univariate and multi-variate time series; volatility dynamics; Box-Jenkins approach and ARIMA models; seasonal ARIMA models; martingales, random walks and non-linearity; stochastic variance models and ARCH processes; practical modelling and forecasting of financial time series; applications of neural networks and genetic algorithms. 

FE 519 Money and Capital Markets (3+0+0) 3 ECTS 6
(Para ve Sermaye Piyasaları)
Introduction to the Turkish economy; facts and figures; information on financial institutions; Central Bank; financial assets, their size, types and issues; legal structure; creation of the Central Bank money and bank money; government budget and its financing problems; flows and stocks of foreign exchange, balance of payments, international reserves and external debt.

FE 520 Financial Calculus (3+0+0) 3 ECTS 8
(Finans Matematiği)
From random walk to Brownian motion, quadratic variation and volatility, stochastic integrals, martingale property, Ito formula, geometric Brownian motion, solution of Black-Scholes equation, stochastic differential equations, Feynman-Kac theorem, Cox-Ingersoll-Ross and Vasicek term structure models, Girsanov's theorem and risk neutral measures, Heath-Jarrow-Morton term structure model, exchange-rate instruments.

FE 521 Derivative Securities and Markets (3+0+0) 3 ECTS 6
(Türev Ürünler ve Pazarları) 
Introduction to options and futures; determinants of option values; portfolio strategies using options; put - call parity, spot - futures parity, early exercise; binomial model; Black - Scholes model; option deltas and elasticities; delta hedging, pitfalls of dynamic hedging; forward rate agreements (FRA), futures implied forward rates; motivations for swaps, interest rate swaps, cross currency swaps, equity swaps; combining derivatives to engineer new products: stripping, reconstitution.

FE 522 Computational Finance
(İşlemsel Finans) (3+0+0) 3 ECTS 9
Simulation methodology; software packages; uniform and non-uniform random variate generation; Monte-Carlo methods; variance reduction techniques; splines; matrix factorisations; finite difference methods; value-at-risk and option pricing computations.

FE 523 Investment Analysis and Portfolio Theory (3+0+0) 3 ECTS 7
(Yatırım Analizi ve Portföy Kuramı)
Money markets and instruments; debt capital markets; term structure models; bond valuation, duration and convexity; bond ratings; tools of bond portfolio management; equity markets and instruments; common stock valuation; mathematics of portfolio selection; mean-variance and index models; models of market equilibrium; market efficiency; performance measurement and attribution; active and passive portfolio management; uses of derivative assets in portfolio management; global investments.

FE 524 Dynamics of Financial Systems (3+0+0) 3 ECTS 6
(Finansal Sistemlerin Dinamiği)
Financial problems as dynamical systems; simulation as a solution procedure for complex dynamic models; complex nonlinear dynamic phenomena; stochastic dynamic models; system dynamics methodology; stock-flow modeling; policy design and improvement by simulation experiments; financial strategy applications and cases.

FE 526 Decision Analysis (3+0+0) 3 ECTS 6
(Karar Analizi)
Utility theory; use of judgmental probability; Bayesian decision models; decision trees; probabilistic networks; influence diagrams; value of information; study of strategies; economics of sampling; risk sharing and decisions; implementation of decision models.

FE 532 Risk Analysis and Insurance Pricing (3+0+0) 3 ECTS 6
(Risk Analizi ve Sigorta Fiyatlandırma)
Principles of risk theory; ruin models; credibility premiums and experience rating; operations research techniques in insurance and reinsurance decision making.

FE 534 Life Insurance and Pension Plans (3+0+0) 3 ECTS 6
(Hayat Sigortası ve Emeklilik Planları)
Design and financing of life insurance products and retirement plans in both the private and public sectors; stochastic investment models for life insurance and pension funds; Wilkie's model.

FE 536 Risk Management in Financial Institutions (3+0+0) 3 ECTS 6
(Finansal Kurumlarda Risk Yönetimi)
Financial innovation; new types of risk and evolution of risk management products; sources of risk and risk profile; measuring market risk, credit risk, operational and legal risks; analytical models and estimation problems; using and designing derivative instruments to manage risk; securitization, hedging and arbitrage fundamentals; examples and applications of risk management in financial and non-financial institutions.

FE 538 Valuation with Real Options (3+0+0) 3 ECTS 6
(Opsiyonlar ile Değerlendirme)
Traditional capital budgeting; conceptual options framework for capital budgeting; quantifying flexibility in capital budgeting; discrete and continuous time models; interactions among multiple real options; hybrid real options valuation of risky projects; strategic planning and control; compound real options; case studies.

FE 540 Nonlinear Programming (3+0+0) 3 ECTS 6
(Doğrusal Olmayan Programlama)
Convex analysis; necessary and sufficient conditions for optimality; methods of unconstrained optimization; necessary and sufficient conditions for constrained optimization; methods for equality constraints; nonlinear programming procedures using primal and penalty function methods.

FE 544 Dynamic Programming (3+0+0) 3 ECTS 6
(Dinamik Programlama)
Multi-stage problem solving; several state variables; recursive equations; principle of optimality; computational procedures; decomposition in dynamic programming and uncertainty; non-serial systems; dynamic programming and decision processes.

FE 571, 572 Financial Engineering Project (0+4+0) 0 ECTS 2,6
(Finans Mühendisliği Projesi)
Project undertaken by students under the supervision of a faculty member with a special focus to design a solution procedure for a real-life problem. 
(A written midterm progress report and a final report required.)

FE 580-599 Special Topics in Financial Engineering (3+0+0) 3 ECTS 6
(Finans Mühendisliği Özel Konuları)
Special topics in financial engineering selected to suit the interests of the individual students.

FE 594 Guided Research I (1+0+0) 1 ECTS 2
(Rehberli Araştırmalar I)
Research methods in Financial Engineering, theoretical and computational approaches in Financial Engineering, supervised by faculty.

FE 595 Guided Research II (1+0+0) 1 ECTS 2
(Rehberli Araştırmalar II)
Research methods in Financial Engineering, theoretical and computational approaches in Financial Engineering, supervised by faculty.

FE 599 Directed Studies (0+4+0) 0 Pass/Fail ECTS 4
(Yönlendirilmiş Çalışmalar)
Research in financial market structures, financial instruments, and other financial engineering topics under supervised by faculty.

FE 59A Directed Studies (0+4+0) 0 Pass/Fail ECTS 4
(Yönlendirilmiş Çalışmalar )
Continued research in the field of Financial Engineering, supervised by faculty.

FE 59B Directed Studies (0+4+0) 0 Pass/Fail ECTS 4
(Yönlendirilmiş Çalışmalar) 
Continued research in the field of Financial Engineering, supervised by faculty.