Multilevel Monte Carlo simulation for VIX options in the rough Bergomi model

Florian Bourgey and Stefano De Marco

Journal of Computational Finance

Abstract: In this paper we consider the pricing of Chicago Board Options Exchange Volatility Index (VIX) options in the rough Bergomi model. In this setting, the VIX random variable is defined by the one-dimensional integral of the exponential of a Gaussian process with correlated increments. Hence, approximate samples of the VIX can be constructed via discretization of the integral and simulation of a correlated Gaussian vector. A Monte Carlo estimator of VIX options based on a rectangle discretization scheme and exact Gaussian sampling via the Cholesky method has a computational complexity of order Ο(ε−4) when the mean squared error is set to ε2. We demonstrate that this cost can be reduced to Ο(ε-2ln2(ε)) by combining the scheme above with the multilevel method, and further reduced to the asymptotically optimal cost Ο(ε−2) when using a trapezoidal discretization. We provide numerical experiments highlighting the efficiency of the multilevel approach in the pricing of VIX options in such a rough forward variance setting.

References: Add references at CitEc
Citations:

Downloads: (external link)
https://www.risk.net/journal-of-computational-fina ... -rough-bergomi-model (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:rsk:journ0:7954641

Access Statistics for this article

More articles in Journal of Computational Finance from Journal of Computational Finance
Bibliographic data for series maintained by Thomas Paine ().