Course: MATH 174E, Mathematics of Finance, Lecture 3, Spring 2017
Prerequisite: Math 33A, Math 170A (or Statistics 100A), Economics 11. Not open for credit to students with credit for course 174A, Economics 141, or Statistics C183/C283.
Course Content: 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 simulations. Basics of Brownian motion and Stochastic Calculus.
Last update: 14 June 2017

Instructor: Steven Heilman, heilman(@-symbol)
Office Hours: Fridays, 10AM-12PM, MS 5634
Lecture Meeting Time/Location: Monday, Wednesday and Friday, 2PM-250PM, MS 5138
TA: Adam Azzam, adamazzam(@-symbol)
TA Office Hours: Mondays 315PM-445PM, MS 6139
Discussion Session Meeting Time/Location: Tuesday, 2PM-250PM, MS 5138
Recommended Textbook: John C. Hull, Options, Futures and Other Derivatives, 8th Ed. (I will not be following this textbook very closely, since this book is not very mathematical. So I will not require you to have this textbook. On the other hand, the textbook has a wealth of examples to demonstrate the concepts we will discuss. So, if you are really interested in math finance, you should probably read this textbook.)
Other Textbooks (not required): I will be drawing on various sources in the course; for example, I will be drawing on some lecture notes here. These notes are definitely more concise and mathematical than the Hull book.
Sheldon M. Ross, An Elementary Introduction to Mathematical Finance. This book is essentially a condensed version of the Hull book, sometimes with more mathematical detail.
Ruth J. Williams, Introduction to the Mathematics of Finance. This book is similar to the Ross book with more mathematical detail. Also, the presentation is a bit more advanced.
Some math finance websites

First Midterm: Monday, April 24, 2PM-250PM, MS 5138
Second Midterm: Friday, May 19, 2PM-250PM, Dodd 175
Final Exam:Monday, June 12, 3PM-6PM, Boelter 5436
Other Resources: Supplemental Problems from the textbook. An introduction to mathematical arguments, Michael Hutchings, An Introduction to Proofs, How to Write Mathematical Arguments
Email Policy:

Exam Procedures: Students must bring their UCLA ID cards to the midterms and to the final exam. Phones must be turned off. Cheating on an exam results in a score of zero on that exam. Exams can be regraded at most 15 days after the date of the exam. This policy extends to homeworks as well. All students are expected to be familiar with the UCLA Student Guide to Academic Integrity. If you are an OSD student, I would encourage you to discuss with me ways that I can improve your learning experience; I would also encourage you to contact the OSD office to confirm your exam arrangements at the beginning of the quarter.
Exam Resources: Here are the exams I used when I taught the 171 class in previous quarters. The 171 class, as I taught it, will have some overlap with our 174E class: Exam 1 Exam 1 Solutions Exam 2 Exam 2 Solutions Final Final Solutions. Exam 1 Exam 1 Solutions Exam 2 Exam 2 Solutions Final Final Solutions. Also, here ia a sample MFE Actuarial Exam (with solutions, and more than 30 questions), which might be good practice for our final exam. Also, for the final, it might be helpful to study some QFICore morning session exams here Occasionally these exams will cover slightly different material than this class, or the material will be in a slightly different order, but generally, the concepts should be close.

Homework Policy: Grading Policy:

Tentative Schedule: (This schedule may change slightly during the course.)

Week Monday Tuesday Wednesday Thursday Friday
1Apr 3: Law of Large Numbers Apr 4: Homework 0 (ungraded) Apr 5: Central Limit Theorem Apr 7: Modeling, Hypothesis Testing
2 Apr 10: Random Walk (Binomial) Model of Stocks Apr 11: Homework 1 due Apr 12: Stopping Times (Options) Apr 14: Hitting Times
3 Apr 17: Review of Conditional Expectation Apr 18: Homework 2 due Apr 19: Martingales Apr 21: Optional Stopping Theorem
4 Apr 24: Midterm #1 Apr 25: No homework due Apr 26: Gambler's Ruin Apr 28: Review of Lagrange Multipliers
5 May 1: Arbitrage Pricing Theory May 2: Homework 3 due May 3: Arbitrage Pricing Theory May 5, Capital Asset Pricing Model
6 May 8: Regression Models May 9, Homework 4 due May 10: Continuous Time Models May 12: Review of Differential Equations
7 May 15, Wiener Processes May 16: Homework 5 due May 17: 13, Brownian Motion May 19: Midterm #2
8 May 22: 13, Geometric Brownian Motion May 23: Homework 6 due May 24: 13, Ito's Lemma May 26: 14, Black-Scholes-Merton Model
9 May 29: No class May 30: Homework 7 due May 31: 14, Black-Scholes-Merton Model Jun 3: 14, Solving Stochastic Differential Equations
10 Jun 5: Greeks Jun 6: Homework 8 due Jun 7: Binomial Models Revisited Jun 9, Review of Course

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Homework Exam Solutions Supplementary Notes