Grant: Discovery Grants Program - Individual

This research program is part of my activities in financial engineering. This time, my research program is articulated around the volatility and the co-movement of asset returns in different markets: commodities, index and stock options, and VIX. All projects have a challenge related to their dimension: we must estimate multivariate models with many latent variables. The methodologies are diverse and adapted to the application: filtering, maximum likelihood and GMM, machine learning, fast Fourier transform, etc. Most market models developed in recent years include unobservable variables, often called latent variables: stochastic volatility, and jumps that must be filtered from market data. Part of this research program aims to estimate this type of model (their parameters and their latent variables) to better manage the risks inherent in these markets. The applications of mathematics to finance have the particularity that there exist many observable quantities that are linked, often in a non-linear manner, with latent variables. In addition to the returns of the underlying security, measures obtained from intraday variations can be incorporated into the sample. There are hundreds, even a thousand derivatives traded daily on certain underlying assets. This raises several research questions that are specific to the applications I explore: (1) How to choose the observable quantities so that the model components are all identified and estimated as precisely as possible; (2) How to develop filters adapted to these higher-dimensional problems; and (3) The options market is by far larger than the underlying asset alone, but noisier. How do we integrate noisy variables in an efficient way. In summary, there is a clear effect of increasing samples on management decisions. Indeed, the addition of information from various sources (the underlying security, its intraday variation, derivatives and their intraday variation) modifies the point estimate and the precision of the parameters and latent variables. It is therefore necessary to better understand the impact of the construction of the sample (choice of the quantities measured) on the inference drawn from these models as well as their ability to predict future evolution. These research questions will be applied to various applications in financial engineering.