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.

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