TITLE:
Darboux Transformation in Quantum Black-Scholes Hamiltonian and Supersymmetry
AUTHORS:
Jafar Sadeghi, Mohammad Rostami, Ahmad Pourdarvish, Behnam Pourhassan
KEYWORDS:
Black-Scholes Hamiltonian; Darboux Transformation; Supersymmetry
JOURNAL NAME:
Open Journal of Microphysics,
Vol.3 No.2,
May
24,
2013
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.