Constructing positive reliable numerical solution for American call options: A new front-fixing approach

• R. Company ^[1] ; V.N. Egorova ^[1] ; L. Jódar ^[1]
  1. [1] Universidad Politécnica de Valencia

     Universidad Politécnica de Valencia

     Valencia, España

     
• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 291, Nº 1 (1 January 2016), 2016, págs. 422-431
• Idioma: inglés
• DOI: 10.1016/j.cam.2014.09.013
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• Resumen

  • A new front-fixing transformation is applied to the Black–Scholes equation for the American call option pricing problem. The transformed non-linear problem involves homogeneous boundary conditions independent of the free boundary. The numerical solution by an explicit finite-difference method is positive and monotone. Stability and consistency of the scheme are studied. The explicit proposed method is compared with other competitive implicit ones from the points of view accuracy and computational cost.