The Black-Scholes Model: For Proprietary Trading (edX)

This course is organized into three stages; beginners, intermediate, and professional.
The beginner’s level (Section 1), using a simple binomial model, explains why you can make money using what you have learned about the Black-Scholes theory in a basic finance course. This is sufficient to use for a personal winning experience.
At the intermediate level (Sections 2-3), we review the Black-Scholes model in an alternative way as a preparation for more advanced applications. We give closed-form solutions for futures and European options in Section 3. Especially futures formula is general and can be used even when the underlying has jumps in the valuation process.
At the professional level (Section 4), it is not possible to lay down the entire propriety system design in a single lecture. We point in the direction of the core design.

Prerequisites:
Mathematics knowledge is required.

• For the beginner’s level (Section 1), Linear algebra; two-variable simultaneous equations, vectors, matrices, and determinants.
• For the intermediate level (Sections 2-3), Advanced calculus, probability and statistics (normal distribution and change of probability measure), basic stochastic calculus, and familiarity with the Black-Scholes model.
• For the advanced professional level (Section 4), Lie algebra and Lie group, operational calculus, product (Feynman path) integration, advanced probability modeling with Levy process in cumulant generating form.

What you'll learn

• Use the Black-Scholes model professionally.
• Use the simple binomial model, and price an option precisely fitting your hedging requirements, the core idea for a layperson.
• Design concepts needed for proprietary trading of sophisticated tailor-made derivative products using the Black-Scholes model and multi-risk-factors extension, used for professionals.