### Financial Engineering Courses at Northwestern

#### Graduate Courses

Students in the PhD program in IEMS can major in financial engineering.

*Courses at McCormick*

**IEMS 461:**Advanced Stochastic Models- Martingales, Markov processes, Gaussian processes. Brownian motion, its construction and properties. Stochastic integration, Ito's formula. Stochastic differential equations. Connections with partial differential equations. Processes with jumps. Levy processes. Financial modeling applications.

**IEMS 473-1:**Financial Engineering I- Introduction to derivative securities markets. Forward and futures contracts. Options basics. The binomial model. The Black-Scholes-Merton model. Dynamic replication and hedging. Risk-neutral valuation. The Greeks. Exotic and path-dependent options. Computational tools: simulation, lattice methods, numerical solution of PDEs. The multi-asset Black-Scholes-Merton model and multi-asset derivatives. Volatility.

**IEMS 473-2:**Financial Engineering II- Continuous-time asset pricing theory. Fundamental theorems of asset pricing. Advanced derivative securities. Fixed income markets and derivatives. Credit risk modeling. Mathematical models and computational tools of financial engineering.

**IEMS 475:**Simulation in Financial Engineering- Simulation of models of equity and fixed-income markets applied to derivative security pricing and risk management. Topics include discretization of stochastic differential equations and efficiency of simulation algorithms.

**ESAM 401:**Options Pricing: Theory and Applications- Pricing and trading of equity and index options. Elementary and advanced trading strategies illustrated through mock trades. Modeling of stock price movement. Basic concepts of stochastic differential equations and Ito calculus. Derivation of Black-Scholes equation. Solution techniques for European and American options.

**ESAM 442-1,2,3:**Stochastic Differential Equations- Brownian motion and Langevin's equation. Ito and Stratonovich Stochastic integrals. Stochastic calculus and Ito's formula. SDEs and PDEs of Kolmogorov, Fokker-Planck, and Dynkin. Boundary conditions, exit times, exit distributions, stability. Asymptotic analysis of SDE, the Smoluchowski-Kramers approximation, diffusion approximation to Markov chains. Applications.

*Related courses in other schools at Northwestern*

**MATH 455-1,2,3:**Stochastic Analysis

**FINC 483-1:**Advanced Derivatives

**FINC 485:**Introduction to Financial Theory

**FINC 487:**Dynamic Asset Pricing Theory

**FINC 488:**Econometrics of Financial Markets

#### Undergraduate Courses

*Courses at McCormick*

**IEMS 326:**Economics and Finance for Engineers- Principles of corporate finance; financial decisions of firms; value; risk and return; investment and capital budgeting decisions under certainty and uncertainty; performance evaluation.

**IEMS 373:**Introduction to Financial Engineering- Financial markets, derivative securities, risk management, mathematical models in finance. Foreign exchange, debt, equity, commodity markets. Investing, trading, hedging, arbitrage. Forwards, futures, options, swaps, exotic derivatives. Models of price dynamics, binomial model, introduction to Black-Scholes theory and Monte Carlo simulation.

**EECS 328:**Numerical Methods for Engineers.- Introduction to numerical methods; numerical differentiation, numerical integration, solution of ordinary and partial differential equations. A case study concerns the numerical solution of American options pricing based on the discretization of the Black-Scholes equations.

*Related courses in other schools at Northwestern *

**MATH 366-1:**Mathematical Models in Finance

**STAT 365:**Introduction to the Analysis of Financial Data

- KELLG_FE 310: Principles of Finance
- KELLG_FE 312-0: Investments
- KELLG_FE 314: Derivatives
- KELLG_FE 316: Topics in Financial Economics

The Kellogg School of Management offers a certificate in Financial Economics. The certificate program consists of four courses related to financial engineering:

These courses are open only to Northwestern undergraduate students who have been accepted into the certificate program. More information can be found on the program's web site.