American Options and Wiener Processes Asynchronous Lecture

Finance 4366 will not meet in person tomorrow, Thursday, March 21, due to ongoing health-related issues in my family.  Therefore, tomorrow’s “American Options and Wiener Processes” lecture will be delivered asynchronously. As in past asynchronous lectures, class participation credit will be awarded to students who write and upload a lecture synopsis to Canvas, the deadline for which is Friday, March 22 by 5 pm.

In my March 19th lecture, we learned that the early exercise of an American call option may be optimal when the underlying asset pays dividends.  In this lecture, we finish our coverage of discrete-time financial modeling in which the passage of time is measured over distinct and separate intervals (ranging from seconds to days, months, or even years), and consider financial modeling in the more realistic continuous-time framework in which the passage of time occurs over infinitesimally small time intervals.  Hull’s “Wiener Processes and Ito’s Lemma” textbook chapter (the teaching note for which is available at http://fin4366.garven.com/spring2024/lecture10.pdf) is named after the two math/stat-based methods required to understand continuous-time finance, particularly the groundbreaking (and Nobel prize-winning) Black-Scholes-Merton model, which revolutionized the pricing of options and derivatives.

Tomorrow, I plan to be available for office hours via Zoom from 3:30-5, if any of my students would like to come by.

American Options, Part 2 Asynchronous Lecture

Finance 4366 will not meet in person tomorrow, Tuesday, March 19, due to ongoing health-related issues in my family.  Therefore, tomorrow’s “American Options, Part 2” lecture will be delivered asynchronously. As in last week’s asynchronous lectures, class participation credit will be awarded to students who write and upload a lecture synopsis to Canvas.

In my March 14th lecture, I showed how Cox-Ross-Rubinstein (CRR) binomial option pricing model prices and probabilities converge toward Black-Scholes-Merton (BSM) continuous-time model prices and probabilities. Additionally, I began the first of two discussions on American option pricing. Unlike European options, which can only be exercised on their expiration date, American options can be exercised anytime between the contract’s start and expiration. We focused on American options for stocks that don’t pay dividends and observed that while it might be optimal to exercise an in-the-money put option early, it will never be optimal to exercise an American call option written against a non-dividend-paying stock.

In American Options, Part 2, we’ll explore scenarios where the early exercise of an American call option may be optimal when the underlying asset does pay dividends. It draws heavily from the Effects of Dividends on the Pricing of European and American Options teaching note.

Friendly reminder about turning in Problem Set 1

Apologies for the submission error on Canvas for problem set 1. As outlined in the course syllabus, please ensure that all problem-set assignments are submitted in PDF format through Canvas at the dates and times listed in Canvas.

I have rectified the Assignments section on Canvas to exclusively accept problem sets in PDF format from now on. The deadline for uploading problem set 1 is tomorrow (Wednesday, January 24) at 2 p.m. You can submit it here.