Darboux Transformation in Quantum Black-Scholes Hamiltonian and Supersymmetry

Copyright © 2013 Jafar Sadeghi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. In this paper, we consider the Black-Scholes (BS) equation for option pricing with constant volatility. Here, we con-struct the first-order Darboux transformation and the real valued condition of transformed potential for BS correspond-ing equation. In that case we also obtain the transformed of potential and wave function. Finally, we discuss the factori-zation method and investigate the supersymmetry aspect of such corresponding equation. Also we show that the first order equation is satisfied by commutative algebra