WSEAS Transactions on Business and Economics
Print ISSN: 1109-9526, E-ISSN: 2224-2899
Volume 14, 2017
Numerical Solution of Integral Equation for the Early Exercise Boundary of American Put Option
Author: Ladislav Lukáš
Abstract: The paper is focused on numerical approximation of early exercise boundary within American put option pricing problem. Assuming non-dividend paying, American put option leads to two disjunctive regions, a continuation one and a stopping one, which are separated by an early exercise boundary. We present variational formulation of American option problem with special attention to early exercise action effect. Next, we discuss financially motivated additive decomposition of American option price into a European option price and another part due to the extra premium required by early exercising the option contract. As the optimal exercise boundary is a free boundary, its determination is coupled with the determination of the option price. However, the integral equation is known for determination of early exercise boundary. We propose an iterative procedure for numerical solution of that integral equation. We discuss the construction of initial approximations, and we also describe the steps of our submitted procedure in details. Finally, we present some numerical results of determination of free boundary based upon this approach. All computations are performed by the sw Mathematica, version 11.1.
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Keywords: American put option, early exercise premium, early exercise boundary, pricing problem, integral equation, numerical method
Pages: 235-243
WSEAS Transactions on Business and Economics, ISSN / E-ISSN: 1109-9526 / 2224-2899, Volume 14, 2017, Art. #26