About this course: Financial Engineering is a multidisciplinary field drawing from finance and economics, mathematics, statistics, engineering and computational methods. The emphasis of FE & RM Part I will be on the use of simple stochastic models to price derivative securities in various asset classes including equities, fixed income, credit and mortgage-backed securities. We will also consider the role that some of these asset classes played during the financial crisis. A notable feature of this course will be an interview module with Emanuel Derman, the renowned ``quant'' and best-selling author of "My Life as a Quant". We hope that students who complete the course will begin to understand the "rocket science" behind financial engineering but perhaps more importantly, we hope they will also understand the limitations of this theory in practice and why financial models should always be treated with a healthy degree of skepticism. The follow-on course FE & RM Part II will continue to develop derivatives pricing models but it will also focus on asset allocation and portfolio optimization as well as other applications of financial engineering such as real options, commodity and energy derivatives and algorithmic trading.
Created by: Columbia University
Taught by: Martin Haugh, Co-Director, Center for Financial Engineering
Industrial Engineering & Operations Research
Taught by: Garud Iyengar, Professor
Industrial Engineering and Operations Research Department
| Commitment | 12 hours videos and quizzes |
| Language | English |
| How To Pass | Pass all graded assignments to complete the course. |
| User Ratings |
Syllabus
WEEK 1
Course Overview
An introduction to the course.
1 video, 2 readings
- Leyendo: Course Overview
- Leyendo: About Us
WEEK 2
Introduction to Basic Fixed Income Securities
Review of interest and basic fixed income securities; introduction to arbitrage pricing.
4 videos, 2 readings
- Leyendo: Lesson Supplements
- Video: Interest Rates and Fixed Income Instruments
- Leyendo: Lesson Supplements
- Video: Floating Rate Bonds and Term Structure of Interest Rates
- Video: Forward Contracts
Graded: Introduction to Basic Fixed Income Securities
WEEK 3
Introduction to Derivative Securities
The mechanics of forwards, futures, swaps and options. Option pricing in the 1-period binomial model.
7 videos, 2 readings
- Leyendo: Lesson Supplements
- Video: Futures
- Video: Futures Excel
- Leyendo: Lesson Supplements
- Video: Options
- Video: Options Pricing
- Video: The 1-Period Binomial Model
- Video: Option Pricing in the 1-Period Binomial Model
Graded: Introduction to Derivative Securities
WEEK 4
Option Pricing in the Multi-Period Binomial Model
Derivatives pricing in the binomial model including European and American options; handling dividends; pricing forwards and futures; convergence of the binomial model to Black-Scholes.
8 videos, 2 readings
- Leyendo: Lesson Supplements
- Video: What’s Going On?
- Video: Pricing American Options
- Video: Replicating Strategies
- Video: Including Dividends
- Video: Pricing Forwards and Futures in the Binomial Model
- Video: The Black-Scholes Model
- Video: An Example: Pricing a European Put on a Futures Contract
- Leyendo: Quiz Instructions
Graded: Option Pricing in the Multi-Period Binomial Model
WEEK 5
Term Structure Models I
Binomial lattice models of the short-rate; pricing fixed income derivative securities including caps, floors swaps and swaptions; the forward equations and elementary securities.
8 videos, 2 readings
- Leyendo: Lesson Supplements
- Video: The Cash Account and Pricing Zero-Coupon Bonds
- Video: Fixed Income Derivatives: Options on Bonds
- Video: Fixed Income Derivatives: Bond Forwards
- Video: Fixed Income Derivatives: Bond Futures
- Video: Fixed Income Derivatives: Caplets and Floorlets
- Video: Fixed Income Derivatives: Swaps and Swaptions
- Video: The Forward Equations
- Leyendo: Quiz Instructions
Graded: Term Structure Models I
WEEK 6
Term Structure Models II and Introduction to Credit Derivatives
Calibration of term-structure models; the Black-Derman-Toy and Ho-Lee models. Limitations of term-structure models and derivatives pricing models in general. Introduction to credit-default swaps (CDS) and the pricing of CDS and defaultable bonds.
8 videos, 3 readings
- Leyendo: Lesson Supplements
- Video: An Application: Pricing a Payer Swaption in a BDT Model
- Video: Fixed Income Derivatives Pricing in Practice
- Leyendo: Lesson Supplements
- Video: Modeling Defaultable Bonds
- Video: Pricing Defaultable Bonds
- Video: Credit Default Swaps
- Video: Pricing Credit Default Swaps
- Video: Interview with Emmanuel Derman
- Leyendo: Quiz Instructions
Graded: Term Structure Models II and Introduction to Credit Derivatives
WEEK 7
Introduction to Mortgage Mathematics and Mortgage-Backed Securities
Basic mortgage mathematics; mechanics of mortgage-backed securities (MBS) including pass-throughs, principal-only and interest-only securities, and CMOs; pricing of MBS; MBS and the financial crisis.
7 videos, 2 readings
- Leyendo: Lesson Supplements
- Video: Prepayment Risk and Mortgage Pass-Throughs
- Video: Mortgage Pass-Throughs in Excel
- Video: Principal-Only and Interest-Only MBS
- Video: Risks of Principal-Only and Interest-Only MBS
- Video: Collateralized Mortgage Obligations (CMOs)
- Video: Pricing Mortgage-Backed Securities
- Leyendo: Quiz Instructions
Graded: Introduction to Mortgage Mathematics and Mortgage-Backed Securities
WEEK 8
Background Material
10 videos, 1 reading
- Leyendo: Lesson Supplements
- Video: Review of Conditional Expectations and Variances
- Video: Review of Multivariate Distributions
- Video: The Multivariate Normal Distribution
- Video: Introduction to Martingales
- Video: Introduction to Brownian Motion
- Video: Geometric Brownian Motion
- Video: Review of Vectors
- Video: Review of Matrices
- Video: Review of Linear Optimization
FAQs
How It Works
Trabajo del curso
Cada curso es como un libro de texto interactivo, con videos pregrabados, cuestionarios y proyectos.
Ayuda de tus compañeros
Conéctate con miles de estudiantes y debate ideas y materiales del curso, y obtén ayuda para dominar los conceptos.
Certificados
Obtén reconocimiento oficial por tu trabajo y comparte tu éxito con amigos, compañeros y empleadores.
Creators
Columbia University
For more than 250 years, Columbia has been a leader in higher education in the nation and around the world. At the core of our wide range of academic inquiry is the commitment to attract and engage the best minds in pursuit of greater human understanding, pioneering new discoveries and service to society.
Ratings and Reviews
This course is definitely for people who really like to use their math skills in finance. I admit that quizzes a little bit challenging and check the learners' understanding. After some practice I'll definitely take FE&RM II. My only feedback is that is would be better to add some more practical examples to slides instead of emphasizing only theory. Thanks a lot:))
Interesting and well laid-out, the only improvements I would suggest are more effective ways to troubleshoot questions around the quizzes, as well as better integration of the optional sections at the end, which jump into heavy maths without practical examples, limiting the motivation for students to stick with them.
Good course to brush up basics when attempting to learn more complex financial theory
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Excellent course, which give you pretty good understanding of valuation of equity and interest rates derivatives. I want to recomend this course for all students who want to focus on financial field.