Numerical Study of the Convexity of the Exercise Boundary of the American Put Option on a Dividend-Paying Asset

[摘要] Numerical evidence is provided to show that the optimal exercise boundary for American put options with continuous dividend rate d is convex for values d less than or equal to r, where r is the risk-free rate. For d greater than r, the boundary is not convex. As d increases beyond r, the non-convex region moves away from expiry and increases in size. A front-fixing method has been used to transform the American put problem into a nonlinear parabolic differential equation posed on a fixed domain. Explicit and implicit finite-difference methods are used to simulate the problem numerically. As a test, both the explicit and implicit method has been compared and the finite-difference methods give stable results.

[发布机构] the University of Pittsburgh

[效力级别] black-scholes equation