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Quantum harmonic oscillator in option pricing

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  • Liviu-Adrian Cotfas
  • Nicolae Cotfas
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    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.

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    File URL: http://arxiv.org/pdf/1310.4142
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    Paper provided by arXiv.org in its series Papers with number 1310.4142.

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    Date of creation: Oct 2013
    Date of revision: Oct 2013
    Handle: RePEc:arx:papers:1310.4142

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    Web page: http://arxiv.org/

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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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