# Math 456

## Topics in Financial Mathematics, Fall 2013

### Basic Information

Instructor: Ari Stern
Email: astern@math.wustl.edu
Office: Cupples I, 211B
Office Hours: TuTh 10:30am-12pm

### Lectures

Lectures will be held MWF 10-11am in Cupples I, 113. The first class will be on Wednesday, August 28, and the last will be on Friday, December 6. Class will be canceled for Labor Day (Monday, September 2), Fall Break (Friday, October 18), and Thanksgiving Break (Wednesday, November 27, and Friday, November 29).

### Homework Assignments

Problem sets will be posted here every one to two weeks, on Wednesday, and will be collected the following Wednesday at the beginning of class. You are encouraged to discuss the homework with your fellow students and to collaborate on problems, but your final write-up must be your own. Please make sure that your solutions are written clearly and legibly.

Ryan Keast (rkeast@math.wustl.edu) is responsible for grading the homework assignments.

• HW1 [pdf]. Due Wednesday, September 11.
• HW2: Exercises 2.36, 2.37, 2.43, 2.44, 2.45. Due Wednesday, September 18.
• HW3: Exercises 3.22, 3.25, 3.26. Due Wednesday, September 25.
Note 1: Here, the "domestic" currency is the Canadian dollar, not the US dollar. Be careful!
Note 2: I have removed Exercise 3.26 due to a possible issue with the problem.
• HW4 [pdf]. Due Wednesday, October 9.
Note: Unlike the previous problem sets, you have two weeks to complete this assignment. Start early, and budget your time wisely!
• HW5: Exercises 6.7, 6.8, 6.9. Due Wednesday, October 16.
Hint: In Exercise 6.8, notice that the assumption implies that R(1) and S(1) have positive covariance.
• HW6: Exercises 7.11, 7.12, 7.14, 7.15. Due Wednesday, October 23.
• HW7: Derive the formulas for vega and rho given in equations (9.17), (9.18), and (9.19), and do Exercises 10.10, 10.12, 10.13. Due Wednesday, November 13.
Note: The exercises have several typos and omissions, so here are some corrections. For Exercise 10.10, the initial price is S=80. For Exercises 10.12 and 10.13, use r=0.1 (not 0.01), σ=0.15, K=80, and N=4; also, "δt" should be "Δt".
• HW8 [pdf]. Due Wednesday, December 4.

### Exams

The midterm exam was held on Monday, October 28. The final exam was held on Monday, December 16, from 10:30am-12:30pm.

Grades will be based on a weighted average of homework (40%, lowest score dropped), midterm exam (20%), and final exam (40%).

### Textbook

The text for this course is Binomial Models in Finance, by John van der Hoek and Robert J. Elliott. Click here to download the book from the publisher in PDF format. If you prefer to have a hard copy, a low-cost paperback version is available for purchase at the same link.

### Catalog Description

An introduction to the principles and methods of financial mathematics, with a focus on discrete-time stochastic models. Topics include no-arbitrage pricing of financial derivatives, risk-neutral probability measures, the Cox-Ross-Rubenstein and Black-Scholes-Merton options pricing models, and implied volatility. Prerequisites: MATH 233 and 3200 or permission of instructor.

### Important Note for Math Majors on the Probability and Statistics Track

This course may not be used as the "additional upper level probability or statistics elective" required for mathematics majors on the probability and statistics track. For the other major tracks, however, it does count as a general "upper level mathematics elective." If you have any questions, please consult the major tracks web page, and speak with your major advisor and/or the Director of Undergraduate Studies, Professor Ron Freiwald.