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.

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.

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.
Prerequisite: Undergraduate level economics course.

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.

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.

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.

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.

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.
Prerequisite: FE 507.

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.

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.
Prerequisite: FE 520.

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.
Prerequisite: FE 501 and FE 507.

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.

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.

Principles of risk theory; ruin models; credibility premiums and experience rating; operations research techniques in insurance and reinsurance decision making.

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.

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.

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.

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.

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.

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.)

Research methods in Financial Engineering, theoretical and computational approaches in Financial Engineering, supervised by faculty.

Special topics in financial engineering selected to suit the interests of the individual students.

Research in financial market structures, financial instruments, and other financial engineering topics under supervised by faculty.