Back
 JAMP  Vol.3 No.9 , September 2015
On the Interconnectedness of Schrodinger and Black-Scholes Equation
Abstract: The following paper tries to derive a Black-Scholes equation by using tools of quantum physics pertaining in that sense to Hamiltonian operator, path integrals, completeness equation, introducing ket and bra vectors. Schrodinger Hamiltonian is presented and compared to Black-Scholes-Schrodinger Hamiltonian. Similarity was demonstrated and it was proved that Schrodinger Hamiltonian was Hermitian while Black-Scholes Hamiltonian was anti-Hermitian. By using Schrodinger equation, price of option was implemented in the Schrodinger equation and by using Black-Scholes Hamiltonian. Black-Scholes equation was derived and a new and really powerful approach was demonstrated that could have immense application in the quantitative analysis and asset pricing.
Cite this paper: Vukovic, O. (2015) On the Interconnectedness of Schrodinger and Black-Scholes Equation. Journal of Applied Mathematics and Physics, 3, 1108-1113. doi: 10.4236/jamp.2015.39137.
References

[1]   Baaquie, B.E. (2004) Quantum Finance: Path Integrals and Hamiltonians for Options and Interest Rates. Cambridge University Press, Cambridge.
http://dx.doi.org/10.1017/cbo9780511617577

[2]   Baaquie, B.E. (2009) Interest Rates and Coupon Bonds in Quantum Finance. Cambridge University Press, Cambridge.
http://dx.doi.org/10.1017/cbo9780511808715

[3]   Baaquie, B.E. (2010) Interest Rates in Quantum Finance: Caps, Swaptions and Bond Options. Physica A: Statistical Mechanics and Its Applications, 389, 296-314.
http://dx.doi.org/10.1016/j.physa.2009.09.031

[4]   Haven, E. and Khrennikov, A. (2013) Quantum Social Science. Cambridge University Press, Cambridge.
http://dx.doi.org/10.1017/cbo9781139003261

[5]   Contreras, M., Pellicer, R., Villena, M. and Ruiz, A. (2010) A Quantum Model of Option Pricing: When Black-Scholes meets Schrödinger and Its Semi-Classical Limit. Physica A: Statistical Mechanics and Its Applications, 389, 5447-5459.

 
 
Top