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Darboux Transformation in Quantum Black-Scholes Hamiltonian and Supersymmetry
Department of Physics, Islamic Azad University—Ayatollah Amoli Branch, Amol, Iran
Department of Physics, Islamic Azad University—Ayatollah Amoli Branch, Amol, Iran
Department of Statistics, Mazandaran University, Babolsar, Iran
Department of Physics, Imam Hossein University, Tehran, Iran
- 1 Department of Physics, Islamic Azad University—Ayatollah Amoli Branch, Amol, Iran
- 2 Department of Physics, Islamic Azad University—Ayatollah Amoli Branch, Amol, Iran
- 3 Department of Statistics, Mazandaran University, Babolsar, Iran
- 4 Department of Physics, Imam Hossein University, Tehran, Iran
Open Journal of Microphysics·Volume 03 (2013)·Pages 43–46·Published 22 May 2013·DOI10.4236/ojm.2013.32008
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Abstract
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 satisfie d by commutative algebra.
KeywordsBlack-Scholes HamiltonianDarboux TransformationSupersymmetry
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