Optimal convergence rate of the explicit finite difference scheme for American option valuation

✍ Scribed by Bei Hu; Jin Liang; Lishang Jiang

• Publisher: Elsevier Science
• Year: 2009
• Tongue: English
• Weight: 897 KB
• Volume: 230
• Category: Article
• ISSN: 0377-0427
• DOI: 10.1016/j.cam.2008.12.018

✦ Synopsis

An optimal convergence rate O(∆x) for an explicit finite difference scheme for a variational inequality problem is obtained under the stability condition σ 2 ∆t ∆x 2 1 using completely PDE methods. As a corollary, a binomial tree scheme of an American put option (where σ 2 ∆t ∆x 2 = 1) is convergent unconditionally with the rate O((∆t) 1/2 ).