The multivariate mixture dynamics model: shifted dynamics and correlation skew

Damiano Brigo, Camilla Pisani () and Francesco Rapisarda ()
Additional contact information
Camilla Pisani: Nordea Bank
Francesco Rapisarda: Bloomberg LP

Annals of Operations Research, 2021, vol. 299, issue 1, No 56, 1435 pages

Abstract: Abstract The multi variate mixture dynamics model is a tractable, dynamical, arbitrage-free multivariate model characterized by transparency on the dependence structure, since closed form formulae for terminal correlations, average correlations and copula function are available. It also allows for complete decorrelation between assets and instantaneous variances. Each single asset is modelled according to a lognormal mixture dynamics model, and this univariate version is widely used in the industry due to its flexibility and accuracy. The same property holds for the multivariate process of all assets, whose density is a mixture of multivariate basic densities. This allows for consistency of single asset and index/portfolio smile. In this paper, we generalize the MVMD model by introducing shifted dynamics and we propose a definition of implied correlation under this model. We investigate whether the model is able to consistently reproduce the implied volatility of FX cross rates once the single components are calibrated to univariate shifted lognormal mixture dynamics models. We consider in particular the case of the Chinese Renminbi FX rate, showing that the shifted MVMD model correctly recovers the CNY/EUR smile given the EUR/USD smile and the USD/CNY smile, thus highlighting that the model can also work as an arbitrage free volatility smile extrapolation tool for cross currencies that may not be liquid or fully observable. We compare the performance of the shifted MVMD model in terms of implied correlation with those of the shifted simply correlated mixture dynamics model where the dynamics of the single assets are connected naively by introducing correlation among their Brownian motions. Finally, we introduce a model with uncertain volatilities and correlation. The Markovian projection of this model is a generalization of the shifted MVMD model.

Keywords: MVMD model; Mixture of densities; Multivariate local volatility; Correlation skew; Random correlation; Calibration; Cross exchange rates; FX smile; Index volatility smile; Renminbi–USD smile; Renminbi–EUR smile; CNY–USD smile; CNY–EUR smile; SCMD model; 60H10; 60J60; 62H20; 91B28; 91B70 (search for similar items in EconPapers)
JEL-codes: G13 (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10479-019-03239-6 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
Working Paper: The Multivariate Mixture Dynamics Model: Shifted dynamics and correlation skew (2018)
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:spr:annopr:v:299:y:2021:i:1:d:10.1007_s10479-019-03239-6

Ordering information: This journal article can be ordered from
http://www.springer.com/journal/10479

DOI: 10.1007/s10479-019-03239-6

Access Statistics for this article

Annals of Operations Research is currently edited by Endre Boros

More articles in Annals of Operations Research from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().