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From microscopic price dynamics to multidimensional rough volatility models

Part of: Stochastic processes Applications Limit theorems

Published online by Cambridge University Press:  01 July 2021

Mathieu Rosenbaum  and
Mehdi Tomas
Mathieu Rosenbaum*
Affiliation:
École Polytechnique
Mehdi Tomas*
Affiliation:
École Polytechnique
*
*Postal address: CMAP, École Polytechnique, Route de Saclay, 91120 Palaiseau, France.
**Postal address: CMAP & LadHyX, École Polytechnique, Route de Saclay, 91120 Palaiseau, France. Email address: mehdi.tomas@polytechnique.edu
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Abstract

Rough volatility is a well-established statistical stylized fact of financial assets. This property has led to the design and analysis of various new rough stochastic volatility models. However, most of these developments have been carried out in the mono-asset case. In this work, we show that some specific multivariate rough volatility models arise naturally from microstructural properties of the joint dynamics of asset prices. To do so, we use Hawkes processes to build microscopic models that accurately reproduce high-frequency cross-asset interactions and investigate their long-term scaling limits. We emphasize the relevance of our approach by providing insights on the role of microscopic features such as momentum and mean-reversion in the multidimensional price formation process. In particular, we recover classical properties of high-dimensional stock correlation matrices.

Keywords

Rough volatilitymultidimensional processesmicrostructureHawkes processeslimit theoremshigh-dimensional correlation matrices

MSC classification

Primary: 60F05: Central limit and other weak theorems
Secondary: 60F17: Functional limit theorems; invariance principles 60G55: Point processes 62P05: Applications to actuarial sciences and financial mathematics
Type
Original Article
Information
Advances in Applied Probability , Volume 53 , Issue 2 , June 2021 , pp. 425 - 462
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Copyright
© The Author(s), 2021. Published by Cambridge University Press on behalf of Applied Probability Trust

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