Periodic Reporting for period 1 - ABC-EU-XVA (Valuation Adjustments for Improved Risk Management)
Reporting period: 2018-11-01 to 2020-10-31
ESR2 has worked in the context of WP1 on Credit Valuation Adjustment (CVA), the difference between the risk-free portfolio value and the risky portfolio value, where the risky portfolio value is defined as the portfolio value when taking default risk of the counterparty into account. It is not completely clear how the risky portfolio value should be computed, whether the exercise policy should be adjusted for the fact that the counterparty may default. One consequence is that, in the presence of a netting agreement, the exercise decisions can no longer be made individually, whereas almost all existing algorithms rely on exercise decisions made in isolation. In practice, this means that the counterparty may be paying a CVA which is based on a sub-optimal exercise strategy. ESR2 proposes a neural network-based method for approximating the expected exposures and potential future exposures of Bermudan options.
ESR3 works on counterparty risk, the risk of default by the counterparty in a financial contract.Different techniques for the valuation of derivatives and portfolios under counterparty risk have in common that a partial differential equation (PDE) needs to be solved. The dimension of the PDE depends on the number of stochastic market variables involved in the model. Monte Carlo methods are often appreciated due to their applicability in high dimensions. ESR3 combines these two methods in a hybrid solution approach. In a second piece of research, she included Debt Value Adjustment, connected to a parties’ own default probability) into the modeling.
ESR4 works on the extension of valuation adjustments from a single currency to a multi-currency setting, focussing on the pricing of European options with valuation adjustments. Moreover, stochastic intensities of default are assumed and underlying assets in different currencies are involved. ESR4 solves formulations of the XVA pricing problem by the Monte Carlo Method which is not affected by the curse of dimensionality. The numerical examples help in the analysis of the XVA behavior and its dependence on the underlying assets and the investor’s credit spread.
ESR5 works on collateralization, a market mechanism which efficiently reduces credit risk from over-the-counter derivatives. The optimal choice of collateral securities is known as the cheapest to deliver (CTD) collateral. Under full substitution rights, the entire collateral account can be switched from one collateral security to another at any time. ESR5 considers the case of full substitution rights, assuming an instantaneous exchange of collateral in continuous time. The focus of ESR5’s modeling approach is on a conditionally independent approximation of the involved processes at interpolation points, which leads to improved analytical tractability in a second-order model, while preserving some of the correlation structures observed in the market.
ESR6 analyzed a stochastic version of the Magnus expansion for the solution of linear systems of Ito stochastic differential equations (SDEs). He proved existence and provided a representation formula for the logarithm associated to the solution of the matrix-valued SDEs. The Magnus expansion also provides a novel method for solving stochastic PDEs (SPDEs). He presents some preliminary tests utilizing massive parallelization on a GPU to accelerate the evaluation of such a model. Following this approach, ESR6, in close collaboration with Banco Santander, is working on a novel idea for the introduction of SPDEs in the context of so-called rating triggers, i.e. the consideration of rating changes of a counterparty and not only a direct change to default.
We wish to go beyond the regulatory calculation formulas to better understand the impact of accurately modelling and efficient computation for huge banking portfolios and different stress periods. In a variety of earlier research projects, the academic beneficiaries have developed prototype answers for related research questions appearing in risk management. Together with the industry we aim to generalize these research findings to the real world practice, with data and relevant portfolios from the industrial partners. An innovation of this EID is that industry and academia will work closely together on state-of-the-art methodologies with mathematics and data sciences for real-life XVA problems.