Course Number
Next Offered
Spring 2022
Primary Program
Applied and Computational Mathematics
Applied Physics Laboratory
Mode of Study
Face to Face, Virtual Live

The concept of options stems from the inherent human desire and need to reduce risks. This course starts with a rigorous mathematical treatment of options pricing, and related areas by developing a powerful mathematical tool known as Ito calculus. We introduce and use the well-known field of stochastic differential equations to develop various techniques as needed, as well as discuss the theory of martingales. The mathematics will be applied to the arbitrage pricing of financial derivatives, which is the main topic of the course. We treat the Black-Scholes theory in detail and use it to understand how to price various options and other quantitative financial instruments. Topics covered in the course include options strategies, binomial pricing, Weiner processes and Ito’s lemma, the Black-Scholes-Merton Model, futures options and Black’s Model, option Greeks, numerical procedures for pricing options, the volatility smile, the value at risk, exotic options, martingales and risk measures. Course Note(s): This class is distinguished from EN.625.641 Mathematics of Finance: Investment Science (formerly 625.439) and EN.625.714 Introductory Stochastic Differential Equations with Applications, as follows: EN.625.641 Mathematics of Finance: Investment Science gives a broader and more general treatment of financial mathematics, and EN.625.714 Introductory Stochastic Differential Equations with Applications provides a deeper (more advanced) mathematical understanding of stochastic differential equations, with applications in both finance and non-finance areas.

Course Prerequisite(s)

Multivariate calculus, linear algebra and matrix theory (e.g., EN.625.609 Matrix Theory), and a graduate-level course in probability and statistics (such as EN.625.603 Statistical Methods and Data Analysis).

Course Offering(s)


01/26/2022 - 05/04/2022
Wed 7:20 p.m. - 10:00 p.m.
Notes: Students who wish to enroll and attend in Virtual Live (3VL only) courses in-person/on-site at Homewood or the Applied Physics Lab in the Spring 2022 term must upload their proof of COVID-19 and flu vaccination or receive an approve medical/religious exemption in the Vaccine Management System (VMS) system prior to their enrollment. Students who plan to attend Virtual Live (3VL) courses remotely must email [email protected] to indicate their status to “Off-campus" prior to their enrollment. For these courses, direct enrollment is not permitted for this term. Instead students must email [email protected] with their registration request, and our registration team will complete the enrollment once vaccination compliance has been verified. Note: Students will have until November 19, 2021 to become flu vaccine compliant.
Spring 2022
Mode of Study
Virtual Live
Applied Physics Laboratory