Instructor: John W. Welborn
Email: john(dot)w(dot)welborn(at)dartmouth(dot)edu
Office Hours: By Request
Syllabus: Spring 2021
Location: Online via Zoom
Tue/Thu: 10:20AM-11:25AM
Fri X-Hour: 4:00-4:50PM (as needed)
COURSE DESCRIPTION
Financial derivatives can be thought of as wagers on uncertain future financial events. This course will take a mathematically rigorous approach to understanding the Black-Scholes-Merton model and its applications to pricing financial derivatives and risk management. Topics will include arbitrage-free pricing, binomial tree models, measure theory, Ito calculus, the Black-Scholes analysis, Monte Carlo simulation, derivatives pricing, volatility, and hedging.
PREREQUISITES
MATH 20 and MATH 40, or MATH 60; MATH 23; and COSC 1 or the equivalent.
COURSE TEXTBOOKS
Baxter, Martin., and Andrew Rennie. Financial Calculus: An Introduction to Derivative Pricing. Cambridge: Cambridge University Press, 1996. Available online.
Wilmott, Paul. Paul Wilmott Introduces Quantitative Finance. 2nd ed. Chichester, West Sussex, England: J. Wiley & Sons Ltd., 2007. Available online.
GRADING:
Problem Sets: 40%
Midterm Exam: 25% (May 4, 2021 @ 1020am Eastern Time)
Final Exam: 35% (June 4, 2021 @ 1130am Eastern Time.)
PROBLEM SETS
There will be 4 problem sets due throughout the term. Each assignment will be worth 10% of your final grade. For each assignment, you may work in groups of up to 3-4 other students. To complete the assignment, upload a single, clear, and legible PDF document to Canvas.
EXAMS
The midterm and final exams will be online via Canvas. Exams will be open book and open note. Nevertheless, students are expected to do their own work and adhere to the Academic Honor Principle. Students who require testing accommodations must contact me as soon as possible and provide the appropriate documentation. All students must begin and end the exam at the same time, except in the case of pre-approved accommodations.
COURSE SCHEDULE
Week |
Date |
Topic |
Reading(s) |
1 |
3/30/21 |
Introduction |
Joshi |
|
4/1/21 |
Products, Markets, and Derivatives |
Wilmott 1,2 |
2 |
4/6/21 |
The Binomial Branch and Tree Models |
Baxter 2.1, 2.2 |
|
4/8/21 |
Binomial Representation Theorem |
Baxter 2.3, 2.4 |
3 |
4/13/21 |
The Random Behavior of Assets |
Wilmott 4, Baxter 3.1 |
|
4/15/21 |
Elementary Stochastic Calculus |
Wilmott 5 |
4 |
4/19/21 |
ASSIGNMENT #1 Due @ 400pm |
(Derivatives, Binomials) |
|
4/20/21 |
The Black-Scholes Model |
Wilmott 6 |
|
4/22/21 |
Partial Differential Equations |
Wilmott 7 |
5 |
4/27/21 |
The Black-Scholes formulae |
Wilmott 8 |
|
4/29/21 |
Midterm Review |
|
|
4/30/21 |
ASSIGNMENT #2 Due @ 400pm |
(PDEs, Black-Scholes) |
6 |
5/4/21 |
MIDTERM EXAM @ 1020am |
(Ends on 5/6/21) |
|
5/6/21 |
The Greeks |
Wilmott 8 |
7 |
5/11/21 |
Exotic, Path-Dependent and Multi-Asset Options |
Wilmott 11, 12 |
|
5/13/21 |
Barrier Options |
Wilmott 13 |
|
5/14/21 |
PDEs for Barrier Options |
Wilmott (1995) 12 |
8 |
5/18/21 |
ASSIGNMENT #3 Due @ 1020am |
(Greeks and Exotic Options) |
|
5/18/21 |
Change of Measure |
Baxter 3.4 |
|
5/20/21 |
Martingale Representation Theorem |
Baxter 3.5, 3.6 |
9 |
5/25/21 |
Black-Scholes Model and Practice |
Baxter 3.7, 3.8 |
|
5/27/21 |
Final Review |
|
|
5/28/21 |
ASSIGNMENT #4 Due @ 400pm |
(Martingale Measure) |
10 |
6/3/21 |
FINAL EXAM @ 1130am |
(Ends on 6/5/21) |
FURTHER READING
Cox, John C., and Mark. Rubenstein. Options Markets. Englewood Cliffs, N.J: Prentice-Hall, 1985. Print and Online.
Hull, John C. 2018. Options, Futures, and Other Derivatives. 10th ed. Pearson.
Joshi, M. S. The Concepts and Practice of Mathematical Finance. 2nd ed. Cambridge: Cambridge University Press, 2008. Print.
Natenberg, Sheldon. Option Volatility and Pricing: Advanced Trading Strategies and Techniques. McGraw-Hill, 2014. Available online.
Neftci, Salih N. An Introduction to the Mathematics of Financial Derivatives. 2nd ed. San Diego: Academic Press, 2000. Online.
Shreve, Steven. Stochastic Calculus for Finance I: The Binomial Asset Pricing Model. 1st ed. 2004. New York, NY: Springer New York, 2004. Web.
Wilmott, Paul, Sam Howison, and Jeff Dewynne. The Mathematics of Financial Derivatives: A Student Introduction. Cambridge University Press, 2012. Online.
FOUNDATIONAL READING
Bachelier, Louis et al. Louis Bachelier’s Theory of Speculation: The Origins of Modern Finance. Princeton: Princeton University Press, 2006. Online.
Black, E. and M. Scholes. 1973. The valuation of options and corporate liabilities. Journal of Political Economy. 81: 637-54.
Einstein, Albert, R. Fürth, and A. D. Cowper. Investigations on the Theory of the Brownian Movement. London: Methuen & co. ltd., 1926. Print.
Harrison, J. M. and D. M. Kreps. 1979. Martingales and arbitrage in the multi-period securities markets. Journal of Economic Theory 20: 381-408.
Harrison, J. M. and S. R. Pliska. 1981. Martingales and stochastic integration in the theory of continuous trading. Stochastic Processes and Applications. 11: 215-60.
Markowitz, H. 1952. Portfolio selection. Journal of Finance 19: 425-42.
Sharpe, W. 1964. Capital asset prices: a theory of market equilibrium under conditions of risk. Journal of Finance 19: 425-42.
ACADEMIC HONOR PRINCIPLE
Fundamental to the principle of independent learning are the requirements of honesty and integrity in the performance of academic assignments, both in and out of the classroom. Dartmouth operates on the principle of academic honor, without proctoring of examinations. Any student who submits work which is not his or her own, or commits other acts of academic dishonesty, violates the purposes of the college and is subject to disciplinary actions, up to and including suspension or separation. All students must follow the Academic Honor Principle.
MENTAL HEALTH
The academic environment at Dartmouth is challenging, our terms are intensive, and classes are not the only demanding part of your life. There are a number of resources available to you on campus to support your wellness, including your undergraduate dean (http://www.dartmouth.edu/~upperde/), Counseling and Human Development (http://www.dartmouth.edu/~chd/), and the Student Wellness Center (http://www.dartmouth.edu/~healthed/).
STUDENT ACCESSIBILITY NEEDS
Students requesting disability-related accommodations and services for this course must notify me as early in the term as possible. This conversation will help to establish what supports are built into my online course. In order for accommodations to be authorized, students are required to consult with Student Accessibility Services (SAS; student.accessibility.services@dartmouth.edu; SAS website; 603-646-9900) and to email me their SAS accommodation form. We will then work together with SAS if accommodations need to be modified based on the online learning environment. If students have questions about whether they are eligible for accommodations, they should contact the SAS office. All inquiries and discussions will remain confidential.
RELIGIOUS OBSERVANCES
Some students may wish to take part in religious observances that occur during this academic term. If you have a religious observance that conflicts with your participation in the course, please contact me before the end of the second week of the term to discuss accommodations.