The Black-Scholes model stands as a cornerstone in the field of financial mathematics, revolutionizing the way options are priced and opening new avenues for risk management and investment strategies. Developed by Fischer Black and Myron Scholes in 1973, with subsequent contributions by Robert Merton, the model provides a powerful framework for valuing European-style options in an efficient market environment. At its core, the model rests on the assumption of a frictionless market with constant volatility, where the price of the underlying asset follows a geometric Brownian motion. Through the model’s differential equation, options pricing becomes a tractable problem, yielding analytical solutions for option prices and the associated Greek parameters: delta, gamma, theta, vega, and rho. Despite its widespread adoption and effectiveness in many scenarios, the Black-Scholes model does have limitations. Its assumptions of constant volatility and frictionless markets may not always hold true in real-world conditions, leading to discrepancies between theoretical prices and observed market values.
Black Scholes Model in Pricing Options
by Gloria Uwizeye | Mar 12, 2024 | Math Seminar, Spring 2024 | 4 comments
4 Comments
Submit a Comment Cancel reply
You must be logged in to post a comment.
Your topic seems very complex. I do not have any prior knowledge on this topic, but I am excited to learn about it. Gloria, I am very excited about this talk, I truly want to know what you have to say about Black Scholes Model in Pricing Options!
That Black-Scholes model sounds very interesting! I am very excited to see how differential equations can tie into finance and economics. I think it is a great topic to look at with your knowledge of economics and mathematics.
This seems like a great topic. I do not have any previous knowledge on this material but I enjoyed learning about this model and how it impacts option pricing. I felt that you were really interested in this topic and I enjoyed your presentation. Great Job!
I really enjoyed your presentation! I do not have any prior knowledge in finance and economics, so it was interesting to hear about a branch of math that I am unfamiliar with. You were very knowledgable about your topic and answered questions very well to help others understand!