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Quantum harmonic oscillator in option pricing

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  • Liviu-Adrian Cotfas
  • Nicolae Cotfas

Abstract

The Black-Scholes model anticipates rather well the observed prices for options in the case of a strike price that is not too far from the current price of the underlying asset. Some useful extensions can be obtained by an adequate modification of the coefficients in the Black-Scholes equation. We investigate from a mathematical point of view an extension directly related to the quantum harmonic oscillator. In the considered case, the solution is the sum of a series involving the Hermite-Gauss functions. A finite-dimensional version is obtained by using a finite oscillator and the Harper functions. This simplified model keeps the essential characteristics of the continuous one and uses finite sums instead of series and integrals.

Suggested Citation

  • Liviu-Adrian Cotfas & Nicolae Cotfas, 2013. "Quantum harmonic oscillator in option pricing," Papers 1310.4142, arXiv.org, revised Oct 2013.
    • Handle: RePEc:arx:papers:1310.4142
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    References listed on IDEAS

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    1. Jana, T.K. & Roy, P., 2011. "Supersymmetry in option pricing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(12), pages 2350-2355.
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    Cited by:

    1. Pineiro-Chousa, Juan & Vizcaíno-González, Marcos, 2016. "A quantum derivation of a reputational risk premium," International Review of Financial Analysis, Elsevier, vol. 47(C), pages 304-309.

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