Skip to main content

Valuation Adjustments for Improved Risk Management

Periodic Reporting for period 1 - ABC-EU-XVA (Valuation Adjustments for Improved Risk Management)

Reporting period: 2018-11-01 to 2020-10-31

"This EID project aims to address a number of significant challenges arising from the mathematical modelling, numerical computation and risk management, in the form of valuation adjustments, of financial contracts. Valuation adjustments represent a major focus of the ongoing regulatory reform related to the recent global financial crisis. Over-the-counter (OTC) financial derivatives form a significant part of global finance, with the notional outstanding of approximately over 550 billion US dollars in 2016. They are typically traded bilaterally, and each party takes counterparty default risk with respect to the other party. Since the global financial crisis, a number of new regulations have been introduced to improve the stability, robustness and resilience, where aspects such as counterparty risk and liquidity risk were shown to be significant. As a result of these changes, banks are required to apply and report on account books various valuation adjustments of the OTC derivatives to reflect the risk management costs of the associated risks. X-Value Adjustment (XVA) refers generally to these valuation adjustments. The purpose of XVA is twofold: to hedge possible losses due to a counterparty default event, and to determine the amount of capital required by the bank under the new regulations. The ""X"" in XVA can be many different letters nowadays, as financial industry has to deal with CVA (credit value adjustment), CollVA (collateral value adjustment), DVA (debt value adjustments), FVA (funding value adjustment), KVA (capital value adjustment), MVA (margin value adjustment), amongst others."
ESR1 works on the modeling of wrong way risk (WWR), a cutting-edge topic is the joint modelling of the probability of default (PD) and the loss given default (LGD). ESR1 models the dependence between PD and LGD, and take into consideration the discrepancies between risk-neutral and physical measures. ESR1’s work is novel in the sense that reinforcement urn processes are being considered for the modeling. In many applications, data is only available in an incomplete form. ESR1 proposes an extension of the Expectation-Maximization (EM) algorithm for RUPs, both in the univariate and the bivariate case. Furthermore, a new methodology combining EM and the prior elicitation mechanism of RUPs is developed: the Expectation-Reinforcement algorithm.

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.
This project lies at the intersection of financial risk management, numerical mathematics and data science, commonly referred to as Quantitative Risk Management. The objective is to perform multi-disciplinary research and gain deep insight into a variety of aspects of financial counterparty risk and their consequences. Moreover, we incorporate (big) data and machine learning techniques into the modelling and computation of XVA. From their projects, the ESRs will gain expertise in counterparty risk, modern valuation adjustments and how to include these in the financial mathematical models, in algorithms, software, (big) data.

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.
ICCF conference, July 2019
Python crash course, June 2019
The 6 ESRs in the Bologna Risk Management School, May 2019
Kick-Off Meeting, Amsterdam, Febr. 2019