TY - JOUR
T1 - Spectral Method for the Black-Scholes Model of American Options Valuation
AU - Song , Haiming
AU - Zhang , Ran
AU - Tian , Wenyi
JO - Journal of Mathematical Study
VL - 1
SP - 47
EP - 64
PY - 2014
DA - 2014/03
SN - 47
DO - http://doi.org/10.4208/jms.v47n1.14.03
UR - https://global-sci.org/intro/article_detail/jms/9949.html
KW - American option pricing, Black-Scholes model, optimal exercise boundary, front-fixing, Chebyshev spectral method, Runge-Kutta method.
AB - <p style="text-align: justify;">In this paper, we devote ourselves to the research of numerical methods
for American option pricing problems under the Black-Scholes model. The optimal
exercise boundary which satisfies a nonlinear Volterra integral equation is resolved by
a high-order collocation method based on graded meshes. For the other spatial domain
boundary, an artificial boundary condition is applied to the pricing problem for the
effective truncation of the semi-infinite domain. Then, the front-fixing and stretching
transformations are employed to change the truncated problem in an irregular domain
into a one-dimensional parabolic problem in [−1,1]. The Chebyshev spectral method
coupled with fourth-order Runge-Kutta method is proposed for the resulting parabolic
problem related to the options. The stability of the semi-discrete numerical method is
established for the parabolic problem transformed from the original model. Numerical
experiments are conducted to verify the performance of the proposed methods and
compare them with some existing methods.</p>