The Schedule

Abstract: We propose neo-classical alternatives to NNs for financial applications. Financial applications are often characterized by a limited amount of data to fit, and require explainability (properties of the approximator should be understandable from parameters) and predictability (no local minimum uncertainty). Deep NNs, as a rule, do not satisfy one or more of these requirements. Our solution combines a linear regression against a well-defined set of basis functions derived from the spectral information about the approximated function with a low-dimensional solver. The solver easily extends to higher dimensions and has a controlled guess and bounds. Importantly, our regression basis is efficient for high-dimensional problems.

Abstract: In this talk, we present a novel computational framework for portfolio-wide risk management problems where the presence of a potentially large number of risk factors makes traditional numerical techniques ineffective.
The new method utilises a coupled system of BSDEs for the valuation adjustments (xVA) and solves these by a recursive application of a neural network based BSDE solver. This not only makes the computation of xVA for high-dimensional problems feasible, but also produces hedge ratios and dynamic risk measures for xVA, and allows simulations of the collateral account.

Abstract:

Signature methods represent a non-parametric way for extracting characteristic features from time series data which is essential in machine learning tasks. This explains why these techniques become more and more popular in Econometrics and Mathematical Finance. Indeed, signature based approaches allow for data-driven and thus more robust model selection mechanisms, while first principles like no arbitrage can still be easily guaranteed. In view of option pricing the key quantity that one needs to compute in these models is the expected signature of some underlying process. Surprisingly this can be achieved for generic classes of jump diffusions (with possibly path dependent characteristics) via techniques from affine and polynomial processes. More precisely, we show how the signature process of these jumps diffusions can be embedded in the framework of affine and polynomial processes, which have been -- due to their tractability -- the dominating process class prior to the new era of highly over-parametrized dynamic models. In other words, this means that the infinite dimensional Feynman Kac PIDE of the signature process can be reduced to ODEs either of Riccati or linear type. We illustrate our findings by means of one dimensional diffusion processes with analytic characteristics.

Abstract: Multivariate time series exhibit two types of dependence: across variables and across time points. Vine copulas are graphical models for the dependence and can conveniently capture both types of dependence in the same model. We derive the maximal class of graph structures that guarantee stationarity under a natural and verifiable condition called translation invariance. We propose computationally efficient methods for estimation, simulation, prediction, and uncertainty quantification and show their validity by asymptotic results and simulations. The talk is based on the joint work with Thomas Nagler and Daniel Krüger