# Math 456

## Topics in Financial Mathematics, Fall 2015

### Basic Information

Instructor: Ari Stern
Email: astern@math.wustl.edu
Office: Cupples I, 211B
Office Hours: TuTh 2-3pm

### Homework Assignments

Problem sets will be posted approximately biweekly, and will be collected at the beginning of class on the due date. 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.

Sasha Tettenhorst (sasha.tettenhorst@wustl.edu) is responsible for grading the homework assignments.

• HW1: handout [pdf]. Due Friday, September 4.
• HW2: handout [pdf]. Due Friday, September 18.
• HW3: Exercises 3.22 and 3.25. Due Friday, September 25.
Note: In the text, the "domestic" currency is the Canadian dollar, not the US dollar. Be careful!
• HW4: handout [pdf]. Due Friday, October 9.
• HW5: Exercises 6.7, 6.8, 6.9. Due Friday, October 30.
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 Friday, November 6.
• HW7: Derive the formulas for rho given in equations (9.18) and (9.19), and do Exercises 10.10, 10.12, 10.13. Due Friday, November 20.
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: handout [pdf]. Due Friday, December 4.

### Lectures

Lectures will be held MWF 1-2pm, in Brown 118. The first class will be on Monday, August 24, and the last will be on Friday, December 4. Class will be canceled for Labor Day (Monday, September 7), Fall Break (Friday, October 16), and Thanksgiving Break (Wednesday, November 25, and Friday, November 27).

### Exams

There was one in-class midterm exam, held on Wednesday, October 21. The final exam was held on Wednesday, December 16, from 1-3pm.

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.