Multilevel Monte Carlo Methods for Simulated Maximum Likelihood Inference in Multivariate Diffusions
(2016) WORLD CONGRESS OF THE BACHELIER FINANCE SOCIETY- Abstract
- Multilevel Monte Carlo is a novel method for reducing the computational cost when computing conditional expectations of stochastic processes. This paper considers the transition density for diffusion processes. It is known that the transition density can be written as an expectation by utilizing the law of total probability combined with the Markov property. This idea is combined with the multilevel Monte Carlo framework to derive a new estimator. Both the theoretical derivation and the simulations show that the proposed method is able to reduce the variance of the estimates substantially, when keeping the bias and computational cost fixed, relative to the standard approximations.
- Abstract (Swedish)
- Multilevel Monte Carlo is a novel method for reducing the computational cost
when computing conditional expectations of stochastic processes. This paper considers
the transition density for diffusion processes. It is known that the transition
density can be written as an expectation by utilizing the law of total probability
combined with the Markov property. This idea is combined with the multilevel
Monte Carlo framework to derive a new estimator.
Both the theoretical derivation and the simulations show that the proposed
method is able to reduce the variance of the estimates substantially, when keeping
the bias and computational cost fixed, relative to the standard approximations.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/e0ebfbe0-b6b3-4b74-9e19-169448425e9b
- author
- Lindström, Erik
LU
and Åkerlindh, Carl LU
- organization
- publishing date
- 2016
- type
- Contribution to conference
- publication status
- published
- subject
- conference name
- WORLD CONGRESS OF THE BACHELIER FINANCE SOCIETY
- conference location
- New York, United States
- conference dates
- 2016-07-15 - 2016-07-19
- language
- English
- LU publication?
- yes
- id
- e0ebfbe0-b6b3-4b74-9e19-169448425e9b
- date added to LUP
- 2017-10-26 16:38:03
- date last changed
- 2019-03-08 03:24:08
@misc{e0ebfbe0-b6b3-4b74-9e19-169448425e9b, abstract = {{Multilevel Monte Carlo is a novel method for reducing the computational cost when computing conditional expectations of stochastic processes. This paper considers the transition density for diffusion processes. It is known that the transition density can be written as an expectation by utilizing the law of total probability combined with the Markov property. This idea is combined with the multilevel Monte Carlo framework to derive a new estimator. Both the theoretical derivation and the simulations show that the proposed method is able to reduce the variance of the estimates substantially, when keeping the bias and computational cost fixed, relative to the standard approximations.<br/><br/><br/><br/><br/><br/><br/><br/><br/><br/>}}, author = {{Lindström, Erik and Åkerlindh, Carl}}, language = {{eng}}, title = {{Multilevel Monte Carlo Methods for Simulated Maximum Likelihood Inference in Multivariate Diffusions}}, year = {{2016}}, }