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Exact solution of a generalized version of the Black-Scholes equation

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  • Liviu-Adrian Cotfas
  • Camelia Delcea
  • Nicolae Cotfas

Abstract

We analyze a generalized version of the Black-Scholes equation depending on a parameter $a\!\in \!(-\infty,0)$. It satisfies the martingale condition and coincides with the Black-Scholes equation in the limit case $a\nearrow 0$. We show that the generalized equation is exactly solvable in terms of Hermite polynomials and numerically compare its solution with the solution of the Black-Scholes equation.

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  • Liviu-Adrian Cotfas & Camelia Delcea & Nicolae Cotfas, 2014. "Exact solution of a generalized version of the Black-Scholes equation," Papers 1411.2628, arXiv.org.
    • Handle: RePEc:arx:papers:1411.2628
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    References listed on IDEAS

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    1. Fabio Bagarello, 2009. "A quantum statistical approach to simplified stock markets," Papers 0907.2531, arXiv.org.
    2. Bagarello, F., 2009. "A quantum statistical approach to simplified stock markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(20), pages 4397-4406.
    3. Jana, T.K. & Roy, P., 2011. "Supersymmetry in option pricing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(12), pages 2350-2355.
    4. Cotfas, Liviu-Adrian, 2013. "A finite-dimensional quantum model for the stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(2), pages 371-380.
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