Condensed Matter Physics, 2011, vol. 14, No. 2, 23001:116
DOI:10.5488/CMP.14.23001
arXiv:1106.5143
Title:
The path integral representation kernel of evolution operator in MertonGarman model
Author(s):

L.F. Blazhyevskyi
(Department for Theoretical Physics, Ivan Franko National University of Lviv, 12 Drahomanov Str., 79005 Lviv, Ukraine )
,


V.S. Yanishevsky
(Department for Economical Cybernetics and Innovations, Drohobych Ivan Franko State Pedagogical University, 46 Lesja Ukrajinka Str., 82100 Drohobych, Ukraine)

In the framework of path integral the evolution operator kernel for the MertonGarman Hamiltonian is constructed. Based on this kernel option formula is obtained, which generalizes the wellknown BlackScholes result. Possible approximation numerical schemes for path integral calculations are proposed.
Key words:
path integration, evolution operator kernel, option pricing, BlackScholes formula, MertonGarman model
PACS:
03.65.w., 89.65.Gh, 89.65.s, 02.50.r, 02.50.Cw
