DOI: https://doi.org/10.30970/jps.18.1005
OPTION PRICE DYNAMICS EQUATION AND MODELS OF QUANTUM MECHANICS
V. Yanishevsky
National University "Lvivska polytechnika",
12, Bandery St., Lviv, UA-79013, Ukraine
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Journal of Physical Studies 18(1), Article 1005 [7 pages] (2014)
DOI: https://doi.org/10.30970/jps.18.1005 OPTION PRICE DYNAMICS EQUATION AND MODELS OF QUANTUM MECHANICSV. Yanishevsky
National University "Lvivska polytechnika", |
|
On the basis of model problems of quantum mechanics partial cases of Merton-Garman equations for the option price dynamics were analyzed. It was shown that the Heston model is equivalent with the one-dimensional problem of quantum-mechanical oscillator. A formula for the option price was derived basing on the evolution operator's kernel (propagator) of radial oscillator. By analogy with one dimensional Schrödinger equation for a particle in external field, a complexity of other partial cases of the Merton-Garman equation was shown and the parameter values, for which its exact solution exists, were defined.
PACS number(s): 03.65.-w, 89.65.Gh, 89.65.-s, 02.50.-r, 02.50.Cw