From microscopic price dynamics to multidimensional rough volatility models
- 1 June 2021
- journal article
- research article
- Published by Cambridge University Press (CUP) in Advances in Applied Probability
- Vol. 53 (2), 425-462
- https://doi.org/10.1017/apr.2020.60
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
This publication has 21 references indexed in Scilit:
- Deep Learning VolatilitySSRN Electronic Journal, 2019
- Volatility of volatility is (also) roughJournal of Futures Markets, 2019
- Volatility is roughQuantitative Finance, 2017
- Dissecting cross-impact on stock markets: an empirical analysisJournal of Statistical Mechanics: Theory and Experiment, 2017
- Pricing under rough volatilityQuantitative Finance, 2015
- Hawkes Processes in FinanceMarket Microstructure and Liquidity, 2015
- Limit theorems for nearly unstable Hawkes processesThe Annals of Applied Probability, 2015
- Principal regression analysis and the index leverage effectPhysica A: Statistical Mechanics and its Applications, 2011
- Noise Dressing of Financial Correlation MatricesPhysical Review Letters, 1999
- Spectra of some self-exciting and mutually exciting point processesBiometrika, 1971