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Math 174E: General Course Outline

Catalog Description

174E. Mathematics of Finance for Mathematics/Economics Students. (Formerly numbered 174.) Lecture, three hours; discussion, one hour. Enforced requisites: courses 33A, 170A (or Statistics 100A), Economics 11. Not open for credit to students with credit for course 174A, Economics 141, or Statistics C183/C283. Modeling, mathematics, and computation for financial securities. Price of risk. Random walk models for stocks and interest rates. No-arbitrage theory for pricing derivative securities; Black/Scholes theory. European and American options. Monte Carlo, trees, finite difference methods. P/NP or letter grading.

General Information. In the past several decades mathematics has become an integral part of the financial industry.

Math 174 has been developed by Russel Caflisch, in consultation with the Department of Economics. The initial offering was given by Caflisch in the Fall Quarter of 1997 with an enrollment of 29. The course is related to course Economics 103D, which was developed and taught Winter Quarter 1997 by William Zame. It is expected that further offerings on the mathematics of finance will be developed jointly by Mathematics and Economics, in which these two courses will play a role.

Textbook

Hull, John C., Options, Futures and Other Derivatives, 10th Edition. Pearson 2018.

It is recommended to run course with one midterm in Week 6 and quizzes in discussion section in Weeks 2, 4, 8, and 10 whose total value is one midterm.

Schedule of Lectures

Lecture Section Topics

Week 1

Ch. 1-3

Forwards, Futures, Options; Types of Traders; Examples of positions.

Week 2

Ch. 3-4

Hedging Using Futures, Interest Rates (zero, forward, term structure) Bonds (duration, convexity)

Week 3

Ch. 7 & 10

Swaps, Mechanics of Option Markets, Basic Properties of Stock Options (Put-Call Parity, Upper and Lower Bounds for Prices, Effect of Dividends)

Week 4

Ch. 12

Trading Strategies

Week 5

Ch. 13

Binomial Tree Model of Option Pricing (include Proof in Appendix of Black Scholes model)

Week 6

Ch. 14

Wiener Process (Brownian Motion) and Ito?s Lemma (include proof as per Appendix)

Week 7

Ch. 15

Black-Scholes model (include risk neutral derivation in appendix)

Week 8

Ch. 19

The Greeks

Week 9

Ch. 17 or Ch. 20

Instructor Choice: Do topics from Chapter 17 (Options on Stock Indices and Currencies) and Chapter 20 Volatility Smiles (Concerns deviation of real-world pricing from Black-Scholes model).

Week 10

Ch. 21

Basic Numerical Procedures