We propose operator splitting methods for solving the linear complementarity problems arising from the pricing of American options. The space discretization of the underlying Black-Scholes Scholes equation is done using a central finite-difference scheme. The time discretization as well as the operator splittings are based on the Crank-Nicolson method and the two-step backward differentiation formula. Numerical experiments show that the operator splitting methodology is much more efficient than the projected SOR, while the accuracy of both methods are similar.
Jeong, Da-Rae, Kim, Jun-Seok, Wee, In-Suk 2009. "AN ACCURATE AND EFFICIENT NUMERICAL METHOD FOR BLACK-SCHOLES EQUATIONS" Communications of the Korean Mathematical Society = 대한수학회논문집, 24(4): 617~628
Jeong, Da-Rae, Wee, In-Suk, Kim, Jun-Seok 2010. "AN OPERATOR SPLITTING METHOD FOR PRICING THE ELS OPTION" Journal of the Korean Society for Industrial and Applied Mathematics, 14(3): 175~187
Ahn, Se-Ryoong, Bae, Hyeong-Ohk, Koo, Hyeng-Keun, Lee, Ki-Jung 2011. "A SURVEY ON AMERICAN OPTIONS: OLD APPROACHES AND NEW TRENDS" Bulletin of the Korean Mathematical Society = 대한수학회보, 48(4): 791~812
Lee, Seunggyu, Li, Yibao, Choi, Yongho, Hwang, Hyoungseok, Kim, Junseok 2014. "ACCURATE AND EFFICIENT COMPUTATIONS FOR THE GREEKS OF EUROPEAN MULTI-ASSET OPTIONS" Journal of the Korean Society for Industrial and Applied Mathematics, 18(1): 61~74
Jeong, Darae, Kim, Sungki, Choi, Yongho, Hwang, Hyeongseok, Kim, Junseok 2014. "COMPARISON OF NUMERICAL METHODS (BI-CGSTAB, OS, MG) FOR THE 2D BLACK-SCHOLES EQUATION" Journal of the Korean Society of Mathematical Education. 한국수학교육학회지. Series B, Pure and applied mathematics, 21(2): 129~139
CHOI, YONGHO, JEONG, DARAE, KIM, JUNSEOK, KIM, YOUNG ROCK, LEE, SEUNGGYU, SEO, SEUNGSUK, YOO, MINHYUN 2015. "ROBUST AND ACCURATE METHOD FOR THE BLACK-SCHOLES EQUATIONS WITH PAYOFF-CONSISTENT EXTRAPOLATION" Communications of the Korean Mathematical Society = 대한수학회논문집, 30(3): 297~311