Condensed Matter Physics, 2011, vol. 14, No. 2, 23001:1-16
The path integral representation kernel of evolution operator in Merton-Garman model
(Department for Theoretical Physics, Ivan Franko National University of Lviv, 12 Drahomanov Str., 79005 Lviv, Ukraine )
(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 Merton-Garman Hamiltonian is constructed. Based on this kernel option formula is obtained, which generalizes the well-known Black-Scholes result. Possible approximation numerical schemes for path integral calculations are proposed.
path integration, evolution operator kernel, option pricing, Black-Scholes formula, Merton-Garman model
03.65.-w., 89.65.Gh, 89.65.s, 02.50.r, 02.50.Cw