A new predictor-corrector scheme for valuing American puts. (English) Zbl 1237.91236

Zhu, Song-Ping; Zhang, Jin

Appl. Math. Comput. 217, No. 9, 4439-4452 (2011).

Summary: We present a new numerical scheme, based on the finite difference method, to solve American put option pricing problems. Upon applying a Landau transform or the so-called front-fixing technique [H. G. Landau, Q. Appl. Math. 8, 81–94 (1950; Zbl 0036.13902)] to the Black-Scholes partial differential equation, a predictor-corrector finite difference scheme is proposed to numerically solve the nonlinear differential system. Through the comparison with S.-P. Zhu’s analytical solution [Quant. Finance 6, No. 3, 229–242 (2006; Zbl 1136.91468)], we shall demonstrate that the numerical results obtained from the new scheme converge well to the exact optimal exercise boundary and option values. The results of our numerical examples suggest that this approach can be used as an accurate and efficient method even for pricing other types of financial derivative with American-style exercise.

MSC:

91G60	Numerical methods (including Monte Carlo methods)
91G20	Derivative securities (option pricing, hedging, etc.)
65M06	Finite difference methods for initial value and initial-boundary value problems involving PDEs

Keywords:

American put options; predictor-corrector; finite difference method; free boundary problem

Citations:

Zbl 0036.13902; Zbl 1136.91468

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