Course: MATH 174E, Mathematics of Finance, Lecture 3, Spring
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
Last update: 14 June 2017
Instructor: Steven Heilman, heilman(@-symbol)ucla.edu
Office Hours: Fridays, 10AM-12PM, MS
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
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
Other Textbooks (not required): I will be drawing on various
sources in the course; for example, I will be drawing on some lecture
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.
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
Supplemental Problems from the textbook.
introduction to mathematical
arguments, Michael Hutchings,
An Introduction to Proofs,
How to Write Mathematical Arguments
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
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.
- My email address for this course is heilman(@-symbol)ucla.edu
- It is your responsibility to make sure you are receiving emails from
, and they are not being sent to your spam folder.
- Do NOT email me with questions that can be answered from the syllabus.
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
Exam 1 Solutions
Exam 2 Solutions
Exam 1 Solutions
Exam 2 Solutions
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
slightly different material than this class, or the material will be in a slightly
different order, but generally, the concepts should be close.
- 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
in at the beginning of the discussion section on the following
- 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
- 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|
||Apr 10: Random Walk (Binomial) Model of Stocks
||Apr 11: Homework 1 due
||Apr 12: Stopping Times (Options)
||Apr 14: Hitting Times
||Apr 17: Review of Conditional Expectation
||Apr 18: Homework 2 due
||Apr 19: Martingales
||Apr 21: Optional Stopping Theorem
||Apr 24: Midterm #1
||Apr 25: No homework due
||Apr 26: Gambler's Ruin
||Apr 28: Review of Lagrange Multipliers
||May 1: Arbitrage Pricing Theory
||May 2: Homework 3 due
||May 3: Arbitrage Pricing Theory
||May 5, Capital Asset Pricing Model
||May 8: Regression Models
||May 9, Homework 4 due
||May 10: Continuous Time Models
||May 12: Review of Differential Equations|
||May 15, Wiener Processes
||May 16: Homework 5 due
||May 17: 13, Brownian Motion
||May 19: Midterm #2
||May 22: 13, Geometric Brownian Motion
||May 23: Homework 6 due
||May 24: 13, Ito's Lemma
||May 26: 14, Black-Scholes-Merton Model|
||May 29: No class
||May 30: Homework 7 due
||May 31: 14, Black-Scholes-Merton Model
||Jun 3: 14, Solving Stochastic Differential Equations|
||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.
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
Strategies, and come to office hours.