Asymptotic approximation of the free boundary for the American Put near expiry
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 is given. The valuation of commodity options is then discussed. Partial differential equations as free boundary problems are then applied to valuation of the American Put option. A method of solution to this problem close to expiry is investigated.
Bales, Walter, "Asymptotic approximation of the free boundary for the American Put near expiry" (2009). ETD Collection for University of Texas, El Paso. AAI1465237.