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We show that the non Hermitian Black-Scholes Hamiltonian and its various generalizations are pseudo Hermitian. The metric operator is explicitly constructed for this class of Hamitonians.It is also s...
Appraisal of a contour integral method for the Black-Scholes and Heston equations
matrix exponential Laplace transform numerical contour integration financial option pricing
2010/11/3
A contour integral method recently proposed by Weideman [IMA J. Numer. Anal., to appear] for
integrating semi-discrete advection-diffusion PDEs, is extended for application to some of the important e...
Laplace transformation method for the Black-Scholes equation
Black-Scholes equation basket option Laplace inversion parallel method transparent boundary condition
2010/10/29
In this paper we apply the innovative Laplace transformation method introduced by Sheen, Sloan, and Thom´ee (IMA J. Numer. Anal., 2003)to solve the Black-Scholes equation. The algorithm is of ar...
Optimal systems of subalgebras for a nonlinear Black-Scholes equation
Black - Scholes model nonlinearity optimal system
2010/10/29
The main object of our study is a four dimensional Lie algebra which describes the symmetry properties of a nonlinear Black-Scholes model. This model implements a feedback effect which is typical for ...