English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

In this paper, the Black–Scholes (B-S) equation to price American options is studied which is governed by a partial differential problem. A nonlinear partial differential equation (PDE) is resulted by applying a penalty approach for this problem. To numerically solve this PDE, an equipped finite difference method with variable step size (VSS) in the time direction is designed and implemented, coupled with a boundary value solver based on a multiple shooting method (MSM) in the spatial direction. It is completely proven that the proposed approximate option prices satisfy the early exercise constraint. Moreover, the convergence of the proposed method is analysed. The extracted numerical results indicate the punctuality and effectiveness of the present scheme comparing the previous works.

Efficient numerical pricing of American options based on multiple shooting method: a PDE approach