The path integral representation kernel of evolution operator in Merton-Garman model

Abstract

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.

Keywords

• path integration
• evolution operator kernel
• option pricing
• Black-Scholes formula
• Merton-Garman model