The path integral representation kernel of evolution operator in Merton-Garman model
L. F. Blazhyevskyi, V. S. Yanishevsky
TL;DR
This paper constructs a path integral kernel for the Merton-Garman model's evolution operator, leading to a generalized option pricing formula and proposing numerical approximation schemes.
Contribution
It introduces a path integral kernel for the Merton-Garman Hamiltonian and derives a generalized option formula beyond Black-Scholes, with numerical schemes for calculations.
Findings
Kernel construction for Merton-Garman model
Generalized option pricing formula
Proposed numerical approximation schemes
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.
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Taxonomy
TopicsNumerical methods in inverse problems · Spectral Theory in Mathematical Physics · Differential Equations and Boundary Problems