Physical Sciences and Mathematics Commons^™

Asymptotic Approximation Of The Free Boundary For The American Put Near Expiry, Walt E. Bales

Open Access Theses & Dissertations

An introduction to boundary value problems for the heat operator will focus on the Dirichlet and Neumann problems in bounded domains. Following an overview of the basic financial principles of derivative securities, a derivation of the Black-Scholes formulae will be given. Partial differential equations as free boundary problems will then be discussed and applied to modeling the American Put option. A method of solution close to expiry will then be investigated.