# 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.

## 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 |