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Quantum mechanics approach to option pricing

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posted on 07.11.2018, 11:21 by Wenyan Hao
Options are financial derivatives on an underlying security. The Schrodinger and Heisenberg approach to the quantum mechanics together with the Dirac matrix approaches are applied to derive the Black-Scholes formula and the quantum Cox- Rubinstein formula. The quantum mechanics approach to option pricing is based on the interpretation of the option price as the Schrodinger wave function of a certain quantum mechanics model determined by Hamiltonian H. We apply this approach to continuous time market models generated by Levy processes. In the discrete time formulization, we construct both self-adjoint and non selfadjoint quantum market. Moreover, we apply the discrete time formulization and analyse the quantum version of the Cox-Ross-Rubinstein Binomial Model. We find the limit of the N-period bond market, which convergences to planar Brownian motion and then we made an application to option pricing in planar Brownian motion compared with Levy models by Fourier techniques and Monte Carlo method. Furthermore, we analyse the quantum conditional option price and compare for the conditional option pricing in the quantum formulization. Additionally, we establish the limit of the spectral measures proving the convergence to the geometric Brownian motion model. Finally, we found Binomial Model formula and Path integral formulization gave are close to the Black-Scholes formula.



Utev, Sergey; Gorban, Alexander

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Department of Mathematics

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University of Leicester

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