This was the final project for my first-year spring semester Integrated Course Block. ICB is Olin's innovative and constantly evolving introduction to vector calculus and E+M physics that emphasizes numerical simulation, rigorous analysis, and applications of techniques to a wide variety of fields. Thus, in this culminating experience I was able to apply what I had learned about quantitative modeling and PDEs to the financial domain.
Mary Germino, Olin College '10
The Black-Scholes partial differential equation assists financial analysts in assigning fair values to stock options based upon current and projected market trends. In this paper, we discuss basic option valuation theory, provide qualitative motivation for the Black-Scholes model, and present a numerical approach using the FTCS technique to evaluate European-style options. We then offer some analysis of the convergence behavior of this technique under different mesh sizes and provide preliminary error analysis comparing this technique and the closed-form analytical solution. The concepts applied to the development, implementation, and analysis of our numerical model apply to a wide range of other problems that an undergraduate student of mathematics or physics might face.
PDF available for viewing and download below.