Generative Models and Time Series Predictions for Financial Applications with Kernels Methods

This numerical study deals with generative and predictive models based on kernel methods. Kernel methods are endowed with error estimates and have natural connections with optimal transport theory. We exploit these connections to describe the sampler, an algorithm allowing to reproduce any continuous random variable based on the observation of its realizations, as well as to quantify the discretization error. We illustrate this algorithm with numerical examples and describe two financial applications based on time series forecasting. The first is pricing using Monte-Carlo methods, the second one is intraday, real time P&L explanation for large derivative portfolios. For these applications, we compute various numerical indicators to check their convergence properties, in accordance with the theoretical analysis