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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.


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