Semismooth Newton methods with domain decomposition for American options
The authors consider a class of parallel semismooth Newton algorithms for the numerical solution of the American option under the Black-Scholes-Merton pricing framework. A nonlinear function is used to transform the complementarity problem, which arises from the discretization of the pricing model, into a nonlinear system. More precisely, the authors consider a more general class of semismooth Newton methods and some highly parallel domain decomposition methods for the American option. In addition, an adaptive time stepping technique, which adjusts the time step size according to the initial residual of Newton iterations is applied to improve the performance of the proposed numerical method. The effectiveness and scalability of the proposed algorithm depend heavily on the design of the preconditioner. It is shown that the class of additive Schwarz method works well, and is more attractive than the traditional preconditioners. Numerical results for several test cases showed that the proposed algorithm is robust and superior to the classical methods.
scientific article; zbMATH DE number 6866620