EP30.FSF1103 — Option Pricing

This course covers the mathematical foundations and advanced techniques required for the pricing and implementation of options. The course begins with discrete-time Binomial tree models to build intuition before transitioning to continuous-time models. Students will revisit the Black-Scholes-Merton framework and risk-neutral pricing through the rigorous lens of stochastic calculus. Some of the pricing models considered are the European, Barrier, Asian and American options. These problems are either solved analytically by the martingale approach or numerically, using finite difference schemes for solving partial differential equations (PDEs) derived from option pricing models. The curriculum concludes with a modern module on computational finance, applying recent Machine Learning and Deep Learning techniques to option pricing and calibration, bridging classical quantitative finance with modern AI applications.

Requirements for Final Examination

Attendance score must be at least 5 (according to University regulations).

See Appendix 2, Rubric 1 for attendance evaluation.

Requirements for Class Attendance

Students are responsible for attending all scheduled classes.

In case of absence due to force majeure, students must actively acquire the knowledge through the materials provided by the lecturer and other assigned readings.

Requirements for In-class Behaviour

The course is conducted on the principle of mutual respect between lecturers and students.

Students are required to take full notes and participate in answering questions.

Students must read assigned materials in advance.

Homework assignments must be completed as required.

Students must not make noise and disturb others.

Laptops, tablets, and mobile phones may only be used for note-taking, calculations, or learning purposes, and must not be used for any other activities.

The course content includes

• Discrete-Time Models: Binomial Trees
• The Black-Scholes Framework
• Greeks and Hedging
• Exotic Options (Analytical)
• American Derivative Securities
• Introduction to Finite Differences (FD)
• Solving PDEs for Option Pricing
• Supervised Learning for Option Pricing
• Model Calibration with AI