VARIABLE TIME-STEPPING HYBRID FINITE DIFFERENCE METHODS FOR PRICING BINARY OPTIONS

Title & Authors
VARIABLE TIME-STEPPING HYBRID FINITE DIFFERENCE METHODS FOR PRICING BINARY OPTIONS
Kim, Hong-Joong; Moon, Kyoung-Sook;

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 $\small{{\theta}}$-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;
Language
English
Cited by
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