Path integral Monte Carlo method for option pricing
Path integral Monte Carlo method for option pricing
The Markov chain Monte Carlo (MCMC) method, in conjunction with the Metropolis–Hastings algorithm, is used to simulate the path integral for the Black–Scholes–Merton model of option pricing. After a brief derivation of the path integral solution of this model, we develop the MCMC method by discretizing the path integral on a time lattice and evaluating this discretized form for various scenarios. Particular attention is paid to the existence of autocorrelations, their decay with the number of sweeps, and the resulting estimate of the corresponding errors. After testing our approach against closed-form solutions, we demonstrate the utility and flexibility of our method with applications to non-Gaussian models.
Capuozzo, Pietro
bbefa561-1775-4b73-941f-59524a103d68
Panella, Emanuele
a267a404-f5cc-4358-995d-d2088e17d166
Schettini Gherardini, Tancredi
3e21560e-6d9c-4e1d-b28f-40be1d44e4f6
Vvedensky, Dimitri D.
d155c436-68a5-47c2-8be3-ccc4a1c044ca
6 July 2021
Capuozzo, Pietro
bbefa561-1775-4b73-941f-59524a103d68
Panella, Emanuele
a267a404-f5cc-4358-995d-d2088e17d166
Schettini Gherardini, Tancredi
3e21560e-6d9c-4e1d-b28f-40be1d44e4f6
Vvedensky, Dimitri D.
d155c436-68a5-47c2-8be3-ccc4a1c044ca
Capuozzo, Pietro, Panella, Emanuele, Schettini Gherardini, Tancredi and Vvedensky, Dimitri D.
(2021)
Path integral Monte Carlo method for option pricing.
Physica A: Statistical Mechanics and its Applications, 581, [126231].
(doi:10.1016/j.physa.2021.126231).
Abstract
The Markov chain Monte Carlo (MCMC) method, in conjunction with the Metropolis–Hastings algorithm, is used to simulate the path integral for the Black–Scholes–Merton model of option pricing. After a brief derivation of the path integral solution of this model, we develop the MCMC method by discretizing the path integral on a time lattice and evaluating this discretized form for various scenarios. Particular attention is paid to the existence of autocorrelations, their decay with the number of sweeps, and the resulting estimate of the corresponding errors. After testing our approach against closed-form solutions, we demonstrate the utility and flexibility of our method with applications to non-Gaussian models.
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e-pub ahead of print date: 1 July 2021
Published date: 6 July 2021
Identifiers
Local EPrints ID: 484264
URI: http://eprints.soton.ac.uk/id/eprint/484264
ISSN: 0378-4371
PURE UUID: b7758acc-169d-4f19-8fdf-a30cbe284ebc
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Date deposited: 13 Nov 2023 18:53
Last modified: 18 Mar 2024 04:04
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Contributors
Author:
Emanuele Panella
Author:
Tancredi Schettini Gherardini
Author:
Dimitri D. Vvedensky
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