**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)ucla.edu

**Office Hours:** Fridays, 10AM-12PM, MS
5634

**Lecture Meeting Time/Location:** Monday, Wednesday and Friday,
2PM-250PM, MS 5138

**TA:** Adam Azzam, adamazzam(@-symbol)math.ucla.edu

**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:**

- My email address for this course is heilman(@-symbol)ucla.edu
- It is your responsibility to make sure you are receiving emails from heilman(@-symbol)ucla.edu , and they are not being sent to your spam folder.
- Do NOT email me with questions that can be answered from the syllabus.

- Late homework is not accepted.
- If you still want to turn in late homework, then the number of minutes late, divided by ten, will be deducted from the score. (The time estimate is not guaranteed to be accurate.)
- The lowest two homework scores will be dropped. This policy is meant to account for illnesses, emergencies, etc.
- Do not submit homework via email.
- There will be 8 homework assignments, assigned weekly on Tuesday and
turned
in at the
**beginning**of the discussion section on the following Tuesday. - A random subset of the homework problems will be graded each week. However, it is strongly recommended that you try to complete the entire homework assignment.
- You may use whatever resources you want to do the homework, including computers, textbooks, friends, the TA, etc. However, I would discourage any over-reliance on search technology such as Google, since its overuse could degrade your learning experience. By the end of the quarter, you should be able to do the entire homework on your own, without any external help..
- All homework assignments must be
**written by you**, i.e. you cannot copy someone else's solution verbatim. - Homework solutions will be posted on Friday after the homework is turned in.

- The final grade is weighted as the larger of the following two schemes. Scheme 1: homework (15%), the first midterm (20%), the second midterm (25%), and the final (40%). Scheme 2: homework (15%), largest midterm grade (35%), final (50%). The grade for the semester will be curved. However, anyone who exceeds my expectations in the class by showing A-level performance on the exams and homeworks will receive an A for the class.
- We will use the MyUCLA gradebook.
- If you cannot attend one of the exams, you must notify me within the first two weeks of the start of the quarter. Later requests for rescheduling will most likely be denied.
- You must attend the final exam to pass the course.

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

Week | Monday | Tuesday | Wednesday | Thursday | Friday |

1 | Apr 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 |

**Advice on succeeding in a math class:**

- Review the relevant course material
**before**you come to lecture. Consider reviewing course material a week or two before the semester starts. - When reading mathematics, use a pencil and paper to sketch the calculations that are performed by the author.
- Come to class with questions, so you can get more out of the
lecture. Also, finish your homework at
least
**two days**before it is due, to alleviate deadline stress. - Write a rough draft and a separate final draft for your homework. This procedure will help you catch mistakes. Also, consider typesetting your homework. Here is a template .tex file if you want to get started typesetting.
- If you are having difficulty with the material or a particular homework problem, review Polya's Problem Solving Strategies, and come to office hours.