Fast Valuation of CEV American Options. Issue 75 (January 2015)

• Record Type: Journal Article
• Authors: Thakoor, Nawdha; Tangman, Désiré Yannick; Bhuruth, Muddun
• Is Part Of: Wilmott. Volume 2014:Issue 75(2015:Jan.)
• Page Start: 54
• Page End: 61
• Publication Date: 2015-01
• Subjects: American options -- constant elasticity of variance model -- linear complementarity problem -- finite difference method; Finance -- Periodicals; Financial services industry -- Periodicals; 332
• DOI: 10.1002/wilm.10396
• Languages: English
• ISSNs: 1540-6962

Abstract

Abstract : The semi‐analytical valuation of CEV American options is either computationally expensive when it delivers sufficiently accurate prices, lacks accuracy when computations are faster, or involves functions whose computations can be unstable. Trinomial schemes have the disadvantage that there are no built‐in ways to compute hedging sensitivities and re‐runs are required for the computation of deltas and gammas. We propose a faster computational technique by discretizing the no‐arbitrage partial differential equation using a high‐order three‐point (compact) finite difference approximation combined with a simple extrapolation process in time. This new CEV American option pricing algorithm is simple to implement and is shown to yield prices with high accuracy. The superiority of the procedure over existing schemes is numerically demonstrated.