OJM  Vol.3 No.2 , May 2013
Darboux Transformation in Quantum Black-Scholes Hamiltonian and Supersymmetry
ABSTRACT
In this paper, we consider the Black-Scholes (BS) equation for option pricing with constant volatility. Here, we construct the first-order Darboux transformation and the real valued condition of transformed potential for BS corresponding equation. In that case we also obtain the transformed of potential and wave function. Finally, we discuss the factorization method and investigate the supersymmetry aspect of such corresponding equation. Also we show that the first order equation is satisfied by commutative algebra.

Cite this paper
J. Sadeghi, M. Rostami, A. Pourdarvish and B. Pourhassan, "Darboux Transformation in Quantum Black-Scholes Hamiltonian and Supersymmetry," Open Journal of Microphysics, Vol. 3 No. 2, 2013, pp. 43-46. doi: 10.4236/ojm.2013.32008.
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