Financial Engineering and Risk Management Part I

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.

Course Overview
-An introduction to the course.

Introduction to Basic Fixed Income Securities
-Review of interest and basic fixed income securities; introduction to arbitrage pricing.

Introduction to Derivative Securities
-The mechanics of forwards, futures, swaps and options. Option pricing in the 1-period binomial model.

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.

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.

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.

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.

Background Material