Financial Engineering

FE 501 Financial Mathematics 1 (3+0+0)

Basic mathematical functions (linear, polynomial, exponential). Modeling and regression. Time value of money, interest computations, cash flows, present value, credit payments, anuities.  Limiting case: continuous compounding.  Differentiation, maximum and minimum problems.  Ordinary differential equations, applicaitons to interest computations.  Matrices and systems of linear equations, inequalities, applicaitons to cash flows.  Functions of many variables, partial derivatives.  Optimization problems, linear programming, quadratic programming and constraints, portfolio optimization.

FE 502 Financial Engineering 2 (3+0+0)

Basic statistics, data types and decision making.  Probability, random variables, probability distirbution functions, conditional probabilities.  Stochastic processes, stationarity, stationarity tests.  Stochastic differential equations, Black-Sholes equation and applicaitons.  Stochastic properties of time series, modeling and prediction.

FE 511 Stochastic Differential Equations (3+0+0)

Probability space and axioms of probability, random variables, stochastic processes.  Brownian motion, Ito integrals.  Ito’s derivative theorem, existence and uniqueness theorem, strong and weak solutions. Solution methods for linear and nonlinear equations. Filtering problem.  Applicaitons to mathematical finance.  Financial markets, portfolio management and arbitrage, pricing. Numerical solutions to stochastic differential equations.

FE 512 Optimization Methods in Finance (3+0+0)

Introduction to optimization problems and applications. Linear programming, simplex method, duality, sensitivity analysis. Linear programming models.  Short term financial allocations, portfolio menagement.  Derivaqtives and CAMP.  Arbitrage pricing with linear programming.  Nonlinear programming, unconstrained optimization  and related algorithms, constrained optimization.  GARCH models.  Quadratic programming.  Portfolio optimization. Alternative pricing models and risk management.

FE 513 Numerical Methods (3+0+0)

Number formats and computational sensitivity.  Root finding, the methods of bisection, Newton-Raphson, secants; applicaitons to financial problems.  Accumulation of errors in iterative methods, sensitivity and computational errors in financial computational algorithms.  Matrix computations and solutions of linear systems, iterative methods (Gauss-Seidel, Jacobi, etc.) QR decomposition and the method of least squares.  Introduction to solution methods for ordinary differential equations.

FE 525 Financial Modeling (3+0+0)

Introduction to financial planning and modelling, understanding key financial statements, measuring and forecasting company financials, forecasting future cash flows of a company, construction a financial model to value acompany, learning the basics of risks, the decision between equity and debt and valuing a company with discounted cash flow analysis. Learning other methods of valuing a company such as dividend discount models and relative valuation.

FE 581 Finance Laboratory 1 (0+4+0)

Basic Excel, function definitions, graphing, modeling and regression.  Time value of money, interest computations, cash flows, present value, credit payments, anuities.  Statistical functions.  Function definitions, graphing, modeling and regression in Matlab.  Programming with Matlab, anuities and credit payments.  Matrix computations with Matlab, cash flows.  The quadradic programming package in Matlab and application to portfolio optimization.

FE 582 Finance Laboratory 2 (0+4+0)

Financial date terminals, page formation. Indicatiors, technical analysis, “Algorithmic Trading”, applicaiton to IMKB data.

FE 583 Finance Laboratory 3 (0+4+0)

Advanced research and reporting techniques.  Web interface.  Project management.