Abstract
In this project, we explore several topics in probability theory from a measure-theoretic perspective in order to arrive at a comprehensive explanation of the Black-Scholes formula. No knowledge of financial mathematics or economic theory is assumed, however, basic knowledge of continuity and properties of integration over continuous intervals is required. Earlier chapters provide the necessary background in finance to understand the goal of the project, while several introductory probability topics are covered in the appendices. We then transition to the introduction of Borel sets and the Borel-Cantelli lemma, which evolves into an account of discrete martingale processes and martingale convergence. This allows us to define a geometric Brownian motion using the central limit theorem, which we use to model the price evolution of the underlying security of a call option. Our results combine to provide a theoretical approach to the Black-Scholes formula and ultimately present a solution to the arbitrage-free price of a European call option.
Advisor
Hartman, Jim
Department
Mathematics
Recommended Citation
Manfrediz, Daniel T., "Behind Black-Scholes: Probability and Measure Theory in Finance" (2018). Senior Independent Study Theses. Paper 12839.
https://openworks.wooster.edu/independentstudy/12839
Disciplines
Finance | Probability | Set Theory
Keywords
Black-Scholes, Borel Sets, Martingales, Brownian Motion, Sigma Algebra
Publication Date
2018
Degree Granted
Bachelor of Arts
Document Type
Senior Independent Study Thesis
© Copyright 2018 Daniel T. Manfrediz