| Title: | The Black-Scholes- Merton Equation and Option Pricing |
| Speaker: | Darren E. Mason Professor Mathematics and Computer Science Albion College Albion, Michigan |
| Abstract: | The Black-Scholes option pricing formula is a 1997 Nobel Prize winning result in economics (& mathematical finance) that provides a framework for rational pricing of a large class of stock options. In this talk we will discuss the basic idea of an option on an asset as well as the problem of fair valuation of such a financial object. Then, assuming that the stock price St follows a geometric Brownian motion, we will discuss a rough hedging argument that results in the Black-Scholes partial differential equation as a necessary condition for risk-free portfolio evolution. Using changes of coordinate systems and integrating factors, the Black-Scholes partial differential equation will be transformed into the classic heat (or diffusion) equation, for which a standard integral solution form is known. Finally, we will use this integral solution to derive the celebrated Black-Scholes option pricing formula. Some limitations of this model will also be discussed. |
| Location: | Palenske 227 |
| Date: | 9/28/2017 |
| Time: | 3:30 PM |
@abstract{MCS:Colloquium:DarrenEMason:2017:9:28,
author = "{Darren E. Mason}",
title = "{The Black-Scholes- Merton Equation and Option Pricing}",
address = "{Albion College Mathematics and Computer Science Colloquium}",
month = "{28 September}",
year = "{2017}"
}