Variable time-stepping hybrid finite difference methods for pricing binary options
Bull. Korean Math. Soc. 2011 Vol. 48, No. 2, 413-426
https://doi.org/10.4134/BKMS.2011.48.2.413
Printed March 1, 2011
Hongjoong Kim and Kyoung-Sook Moon
Korea University, Kyungwon University
Abstract : Two types of new methods with variable time steps are proposed in order to valuate binary options efficiently. Type I changes adaptively the size of the time step at each time based on the magnitude of the local error, while Type II combines two uniform meshes. The new methods are hybrid finite difference methods, namely starting the computation with a fully implicit finite difference method for a few time steps for accuracy then performing a $\theta$-method during the rest of computation for efficiency. Numerical experiments for standard European vanilla, binary, and American options show that both Type I and II variable time step methods are much more efficient than the fully implicit method or hybrid methods with uniform time steps.
Keywords : option pricing, variable time steps, hybrid finite difference method, binary options, American options
MSC numbers : 91B28, 65C20
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