In this paper, we develop a class of parallel semismooth Newton algorithms for the numerical solution of the American option under the Black–Scholes–Merton pricing framework. In the approach, a nonlinear function is used to transform the complementarity problem, which arises from the discretization of the pricing model, into a nonlinear system. Then, a generalized Newton method with a domain decomposition type preconditioner is applied to solve this nonlinear system. 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 method. Numerical experiments show that the proposed semismooth method has a good accuracy and scalability.
Journal of Computational and Applied Mathematics – Elsevier
Published: Aug 1, 2018
It’s your single place to instantly
discover and read the research
that matters to you.
Enjoy affordable access to
over 12 million articles from more than
10,000 peer-reviewed journals.
All for just $49/month
Read as many articles as you need. Full articles with original layout, charts and figures. Read online, from anywhere.
Keep up with your field with Personalized Recommendations and Follow Journals to get automatic updates.
It’s easy to organize your research with our built-in tools.
Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.
All the latest content is available, no embargo periods.
“Hi guys, I cannot tell you how much I love this resource. Incredible. I really believe you've hit the nail on the head with this site in regards to solving the research-purchase issue.”Daniel C.
“Whoa! It’s like Spotify but for academic articles.”@Phil_Robichaud
“I must say, @deepdyve is a fabulous solution to the independent researcher's problem of #access to #information.”@deepthiw
“My last article couldn't be possible without the platform @deepdyve that makes journal papers cheaper.”@JoseServera