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

  1. Baxter, Martin., and Andrew Rennie. Financial Calculus: An Introduction to Derivative Pricing. Cambridge: Cambridge University Press, 1996. Available online.

  2. Wilmott, Paul. Paul Wilmott Introduces Quantitative Finance. 2nd ed. Chichester, West Sussex, England: J. Wiley & Sons Ltd., 2007. Available online.



GRADING:



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, Baxter 3.2, 3.3

4

4/19/21

ASSIGNMENT #1 Due @ 400pm

(Derivatives, Binomials)

4/20/21

The Black-Scholes Model

Wilmott 6, Baxter 3.6

4/22/21

Partial Differential Equations

Wilmott 7, Baxter 3.7

5

4/27/21

The Black-Scholes formulae and the Greeks

Wilmott 8, Baxter 3.8

4/29/21

Review


5/1/21

ASSIGNMENT #2 Due @ 1200pm

(PDEs, Black-Scholes)

6

5/4/21

MIDTERM EXAM @ 1020am

 

5/6/21

Volatility Modeling

Wilmott 9

7

5/11/21

Delta Hedging

Wilmott 10

5/13/21

Exotic Options

Wilmott 11

8

5/17/21

ASSIGNMENT #3 Due @ 400pm

(Volatility, Delta)

5/18/21

Bonds, yield, duration, convexity

Wilmott 14

5/20/21

IR Derivatives

Wilmott 18

9

5/25/21

Portfolio Theory

Wilmott 21

5/27/21

VaR

Wilmott 22

5/31/21

ASSIGNMENT #4 Due @ 400pm

(Further Topics)

10

6/1/21

Review

 

6/4/21

FINAL EXAM @ 1130am

 


FURTHER READING

FOUNDATIONAL READING


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.