Counterparty Credit Risk Research Articles

Credit valuation adjustment wrong-way risk in a Gaussian copula model

The credit valuation adjustment (CVA) is currently calculated in financial institutions to measure counterparty credit risk (CCR) on over-the-counter derivatives. A key factor in CVA is wrong-way risk (WWR): the correlation between counterparty exposures and credit qualities. In this paper, we present an analytical expression for CVA with WWR under the assumption of the lognormally distributed trade value. Using a Gaussian latent variable to drive market–credit correlation, the calculation of WWR is easily incorporated into the existing exposure simulation process in a CCR system. The proposed CVA with WWR model is used to find the CVA alpha that is a function of the market–credit correlation and the counterparty credit quality. The CVA alpha is used to study general WWR and specific WWR. The numerical results show that the entity’s rating downgrade has more of an impact on specific WWR than on general WWR.

Machine learning in risk measurement: Gaussian process regression for value-at-risk and expected shortfall

While machine learning and its many variants are becoming established tools in quantitative finance, their application in a risk measurement context is less developed. This paper uses a scheme from probability theory and statistics — Gaussian processes — and applies the corresponding non-parametric technique of Gaussian process regression (GPR) to ‘train’ a system suitable for revaluing instruments, as required, to determine a portfolio’s value-at-risk and expected shortfall. Time series of historical valuation parameters and prices of the portfolio’s constituents serve as the only inputs. On the example of a variety of portfolios comprising vanilla and barrier options, it is demonstrated that, even with limited training sets, GPR leads to risk figures identical to those from full revaluation and outperforms Taylor expansion. Applications for risk management and regulatory capital calculations are apparent. Research into an extension to related areas such as counterparty credit risk measurement is promising. JEL classification: C10; G13; G18.

A simulation analysis of systemic counterparty risk in over-the-counter derivatives markets

In this paper, we propose a simulation framework to assess systemic risk in over-the-counter derivatives markets. We incorporate credit valuation adjustment (CVA), a mark-to-market estimate of counterparty credit risk booked on a bank’s balance sheet, into an otherwise standard structural model of credit risk. In this model, banks optimally hedge CVA by trading a credit default swap (CDS). The model aims to capture a possible adverse effect called “CDS–CVA feedback loop” from CVA hedging, which could increase CDS spreads due to a lack of liquidity in CDS markets and even further increase CVA because CVA is valued using the default probability extracted from CDS spreads. In order to measure systemic counterparty credit risk, we aggregate CVA across banks and examine how the distribution of systemic counterparty credit risk changes depending on underlying model parameters. We document that the tail risk of CVA increases nonlinearly when the liquidity of CDS markets declines. As an extension, we also model cost of posting collateral and discuss the trade-off between reducing systemic counterparty credit risk, stability of CDS markets and collateral cost.

CCAR Consistent WWR for CVA and Capital

Wrong way risk (WWR) phenomena in counterparty credit risk value adjustment (CVA) and capital is well understood. It arises from level correlation or cointegration of counterparty default and exposure. There is very limited trading available in CVA space and therefore different banks take quite different assumptions for computing CVA. It is well known that using historical daily correlation of changes between market variables and counterparty hazard rate is not sufficient to produce significant correlation of levels of defaults and exposure. Since WWR comes from correlation of levels and non daily changes of market variables WWR may be easily underestimated. Under risk neutral measure it is generally difficult to correlate levels of market variables through common drifts, which generally do not exist. On the other hand simple way to create level correlation under risk neutral measure would be by global synchronized jump of all market variables. We argue in this note that such jump is already available and is prescribed in CCAR stress testing, so using those jumps will produce WWR exposure comparable between different banks and would reflects regulators consistent WWR in CVA.

The Role of the Standardized Approach to Measuring the Counterparty Credit Risk Exposures (Basel III) in Order to Create Conditions for Russia’s Economic Growth

The subject of the researchis the Standardized Approach to measuring the Counterparty Credit Risk (SA-CCR) exposures according to the reform of the international standards of macroprudential regulation to ensure a breakthrough in the scientific, technological and socio-economic development of Russia. The purposeof the research was to assess the introduction and use of the post-crisis Basel III standard until 2021 to create financially sound credit and banking institutions as the main triggers of the system risk in order to maintain public confidence in the financial system and ensure sustainable economic growth. The paper examines the prospects for the implementation of the Basel III standard, taking into account the standardized approach to measuring the counterparty credit risk to meet the challenges of Russia’s entry into the top five world economies.Given the global financial market conditions, the economic growth is ensured by the economies of scale as well as by harmonization of structural macroprudential rules in different countries, which requires an international standardized approach to system risk management when macro-prudential policies are aimed at alleviating credit risks thereby having a positive impact on the economic growth.The effectiveness of the macro-prudential policy for banks is reduced when less regulated financial intermediaries increase the market share and openness allowing organizations and households to receive money from foreign financial sources.The paper concludesthat in shaping the country’s macro-prudential policies, it is necessary to assess the relative importance of each channel of manifestation and transformation of the system risk and its impact on the economic growth in the national economy.

KVA, Mind Your P's and Q's!

There is an increasing consensus within banks on the need to recognize the impact of rising capital requirements on their derivative business in the form of capital valuation adjustment (KVA). There are still concerns over how exactly KVA should be calculated, charged, and managed. We analyze the aspects of the costs arising due to holding of counterparty credit risk capital. This study demonstrates that banks which are careless with their KVA method and ignore actively managing it, can rake a significant loss and will eventually increase uncertainty in the shareholders' return on capital.

Applying Machine Learning for Troubleshooting Credit Exposure and xVA Profiles

We explore the possibility of applying machine learning techniques to characterizing and troubleshooting problem in credit exposure profiles used in counterparty credit risk management and XVA. Machine learning models are trained to identify characteristics from the daily credit exposure profiles generated through Monte Carlo simulation and identify anomalies due to either counterparty behavioral changes or errors in inputs or calculation. In the paper, we have trained both K-means clustering and Convolutional Neural Network to a training data set containing more than 400,000 credit exposure profiles. The performance of models is satisfactory and we believe this is a promising area for further exploration. Identifying anomalies provides credit analysts early insight into emerging credit risk and errors in the data lineage.

Risk Factor Evolution for Counterparty Credit Risk under a Hidden Markov Model

One of the key components of counterparty credit risk (CCR) measurement is generating scenarios for the evolution of the underlying risk factors, such as interest and exchange rates, equity and commodity prices, and credit spreads. Geometric Brownian Motion (GBM) is a widely used method for modeling the evolution of exchange rates. An important limitation of GBM is that, due to the assumption of constant drift and volatility, stylized facts of financial time-series, such as volatility clustering and heavy-tailedness in the returns distribution, cannot be captured. We propose a model where volatility and drift are able to switch between regimes; more specifically, they are governed by an unobservable Markov chain. Hence, we model exchange rates with a hidden Markov model (HMM) and generate scenarios for counterparty exposure using this approach. A numerical study is carried out and backtesting results for a number of exchange rates are presented. The impact of using a regime-switching model on counterparty exposure is found to be profound for derivatives with non-linear payoffs.

An Artificial Intelligence Approach to Regulating Systemic Risk.

We apply an artificial intelligence approach to simulate the impact of financial market regulations on systemic risk—a topic vigorously discussed since the financial crash of 2007–09. Experts often disagree on the efficacy of these regulations to avert another market collapse, such as the collateralization of interbank (counterparty) derivatives trades to mitigate systemic risk. A limiting factor is the availability of proprietary bank trading data. Even if this hurdle could be overcome, however, analyses would still be hampered by segmented financial markets where banks trade under different regulatory systems. We therefore adapt a simulation technology, combining advances in graph theoretic models and machine learning to randomly generate entire financial systems derived from realistic distributions of bank trading data. We then compute counterparty credit risk under various scenarios to evaluate and predict the impact of financial regulations at all levels—from a single trade to individual banks to systemic risk. We find that under various stress testing scenarios collateralization reduces the costs of resolving a financial system, yet it does not change the distribution of those costs and can have adverse effects on individual participants in extreme situations. Moreover, the concentration of credit risk does not necessarily correlate monotonically with systemic risk. While the analysis focuses on counterparty credit risk, the method generalizes to other risks and metrics in a straightforward manner.

Counterparty Credit Risk and American Options

This paper analyzes the effect of counterparty credit risk on optimal early exercise policy and value of American options. In contrast with the existing literature we find that the price of the underlying asset at which it is optimal to exercise an American option can be significantly different when there is counterparty credit risk. We show that it is not always optimal to exercise when a credit event is likely yet it is sometimes optimal to exercise for credit reasons even when the risk of a credit event is fairly remote. Further, we find that discounting the expected payoff on American options at a higher credit-risk-adjusted rate may lead to inaccurate valuation results. Numerical examples illustrate that early exercise can mitigate only approximately one third of the expected credit loss for American options. This result conflicts with the existing literature that claims early exercise can largely eliminate such expected credit loss. The remaining expected credit loss can be attributed to two sources: the write-down of the payoff if financial distress occurs; and the loss of time value if early exercise was motivated by credit concerns.

Interest Rate Swap Credit Value Adjustment

The credit valuation adjustment (CVA) of OTC derivatives is an important part of the Basel III credit risk capital requirements and current accounting rules. Its calculation is not an easy task - not only it is necessary to model the future value of the derivative, but also the probability of default of a counterparty. Another complication arises in the calculation when the exposure to a counterparty is adversely correlated with the credit quality of that counterparty, i.e. when it is needed to incorporate the wrong-way risk. A semi-analytical CVA formula simplifying the interest rate swap (IRS) valuation with the counterparty credit risk including the wrong-way risk is derived and analyzed in the paper. The formula is based on the fact that the CVA of an IRS can be expressed using swaption prices. The link between the interest rates and the default time is represented by a Gaussian copula with constant correlation coefficient.Finally, the results of the semi-analytical approach are compared with the results of a complex simulation study.

Valuing Interest Rate Swaps Using OIS Discounting

The financial crisis of 2007-09 precipitated a significant change in the practice of interest rate swap valuation. Going from traditional LIBOR to OIS (overnight indexed swap) discounting might not seem to be a profound event but it is more than just another method to calculate fair values for over-the-counter derivative contracts. It embodies newfound appreciation of counterparty credit risk and the role of collateral and central clearing. Implementation of OIS discounting has created a cottage industry for risk management consultants and trainers to deal with the technicalities of the new approach. From my academic perspective, it is clear that many of our finance textbooks that cover interest rate swaps need to be revised.The first section of this note reviews interest rate swap valuation in principle, the reasons for the move from LIBOR to OIS discounting, the implications for swap rates, and the 'winners and losers' that arise from the transition. The second section works through a numerical example to illustrate the calculations. This entails bootstrapping a sequence of discount factors that are consistent with interest rate swaps that have a market value of zero. The implied LIBOR forward curve is derived (or, in general, the forward curve for the money market reference rate). This curve becomes particularly important under OIS discounting when valuing a swap as a combination of fixed-rate and floating-rate bonds.Fortunately for risk managers, OIS discounting uses the same types of analytic techniques as the traditional approach. However, there are some differences that are beyond the scope of this note, for instance, calculating the sensitivities of swap values to changes in OIS rates and the LIBOR-OIS spread (i.e., working with dual curves rather than a single curve for risk measurement) and dealing with cross-currency swaps. Also, LIBOR is an interest rate that reasonably can be assumed to vary day by day in the interbank market whereas OIS rates are more directly a tool of monetary policy, suggesting that rate volatility depends on the pattern and timing of policy meetings and actions.

Counterparty credit risk and derivatives pricing

We derive a model with qualitative implications for options pricing under counterparty credit risk and provide empirical evidence using the data from the Hong Kong derivatives market during 2005–2014. We find that the log-price difference between a derivative warrant with counterparty credit risk and an otherwise identical option without counterparty credit risk is significantly and negatively associated with the credit default swap spread on the warrant issuer. We also find that the prices of out-of-the-money put warrants are more sensitive to credit risk than those of other warrants. Our results show counterparty credit risk matters for derivative pricing.

Initial Margin Simulation with Deep Learning

Regulatory initial margin (IM) for non-cleared OTC derivatives is currently being implemented in the financial industry per BCBS-IOSCO requirements. To incorporate IM into counterparty credit risk (CCR) measurements and xVA calculations (especially MVA), it is necessary to simulate future IM requirements inside a CCR/xVA system. However, this is an extremely challenging task because the two readily available approaches – brute force simulation and regression-based approximation – are either prohibitively expensive in terms of computational cost, or extremely difficult for large and diverse portfolios due to the high dimensionality of the problem. In this paper, a practical deep learning approach to IM simulation is proposed, with a proof-of-concept implementation and test results demonstrating fast and accurate portfolio-level simulation of scenario-dependent IM through multiple time steps. Model training is shown to converge quickly, and model performance is robust under practical conditions. This approach separates offline training from online simulation, so that it can be implemented in production without significant system overhaul. Conceptually, since training data are generated by a deterministic function (in this case the sensitivity-based SIMM model), data noise is not a concern and overfitting can be avoided, assuming portfolio turnovers occur gradually during periods of time much longer than model training cycles. Model output can also be explained or validated by the underlying data-generating function for transparency. Other potential applications of this deep learning approach are also discussed, including collateral optimization.

CVA for Cliquet options under Heston model

Credit value adjustment (CVA) is an important pricing component in the counterparty credit risk (CCR) management. Cliquet options are a popular volatility product with protection against downside risk as well as significant upside potential. This paper aims to study the CVA for Cliquet options under stochastic volatility models. A partial differential equation (PDE) is first derived to price Cliquet options under the Heston model. Numerical schemes are then provided to solve the PDE and calculate exposure and CVA. Numerical tests are also carried out to examine the scheme accuracy and impacts of wrong way risk to CVA. Test results show that the numerical schemes are accurate. Wrong way risk plays an important role in pricing CVA for Cliquet options and the impact is crucial from the perspective of CCR management.

Optimální způsob sjednání derivátu za přítomnosti rizika protistrany

The paper deals with the optimal strategy for entering a derivative contract under existence of counterparty credit risk. Derivative contracts can be traded in three ways - bilaterally without any collateral agreement, bilaterally with collateral agreement or through a central counterparty. Our goal is to define rules for determining the most efficient way of trading. We take into account credit value adjustment, funding costs and capital costs related to regulatory requirements. In our empirical research, we focus on interest rate swaps with different maturities, specifically we analyse the impact of own and counterparty credit spreads on the overall costs. The results show higher efficiency of central clearing for investors with high creditworthiness. The costs of central clearing are very sensitive with respect to own credit spread and, therefore, the final decision depends on the actual relation with counterparty spread.

Artificial Neural Network Approach to Counterparty Credit Risk and XVA

Novel approaches employing an Artificial Neural Networks to enhance the infrastructure of existing Monte Carlo Risk engines are presented. An Artificial Neural Network is utilized to retrieve trade- and market data from existing Expected Exposure profiles of interest rate swaps which enables its usage as part of data control frameworks and exposure explain applications. An Artificial Neural Network is also utilized to predict Expected Exposure mimicking a Monte Carlo Risk engine showing similar accuracy at faster speeds of execution.

Contagion model on counterparty credit risk in the CRT market by considering the heterogeneity of counterparties and preferential-random mixing attachment

This article constructs a SIRS model on counterparty credit risk contagion in the CRT market by considering the characteristics of preferential-random mixing attachment and heterogeneity of counterparties. It theoretically analyzes the effects, mechanisms, and evolution characteristics of the structure of counterparty credit network and its heterogeneity, counterparty behavior preference, fitness of counterparties, and regulatory rescue strategy on counterparty credit risk contagion in the CRT market. With the help of computer numerical simulation, the evolution of counterparty credit risk contagion in the CRT market are intuitively analyzed and depicted. The following main conclusions are obtained: (1) Counterparty credit risk contagion threshold in the CRT market is a monotone decreasing convex function on the counterparty risk preference and counterparty fitness and a monotone increasing convex function on the supervision and rescue probability (2) Counterparty credit risk contagion scale in the CRT market is a monotone decreasing concave function on the counterparty risk preference and counterparty fitness, a monotone decreasing convex function on the supervision and rescue probability, and a monotone increasing concave function on the counterparty degree. (3)The greater the heterogeneity of the network, the greater the counterparty credit risk contagion threshold and the lower the counterparty credit risk contagion scale. (4)The degree distribution of counterparty credit network in the CRT market significantly affects the credit risk contagion threshold and scale in the CRT market.

The efficiency of the Anderson–Darling test with a limited sample size: an application to backtesting counterparty credit risk internal models

This work presents a theoretical and empirical evaluation of Anderson-Darling test when the sample size is limited. The test can be applied in order to backtest the risk factors dynamics in the context of Counterparty Credit Risk modelling. We show the limits of such test when backtesting the distributions of an interest rate model over long time horizons and we propose a modified version of the test that is able to detect more efficiently an underestimation of the model’s volatility. Finally we provide an empirical application. JEL: C19. C22

Assessing qualitative similarities between financial reporting frameworks using visualization and rules: COREP vs. pillar 3

SummaryFinancial institutions are struggling with larger volume, more specific and greater frequency of regulatory reporting after the global financial crisis in 2008, especially those that need to report to multiple jurisdictions. To help to improve reporting efficiency, this paper aims to assess the existence of similarities between templates related to credit and counter party credit risk of COREP and Pillar 3 regulatory reporting frameworks by applying Correspondence Analysis and Association Rules Mining. Our results suggest a high degree of overlap between these reporting frameworks, more prominently the three business functions as Front office, Finance and Risk. These patterns can be used as guidance for financial institutions to reshape their reporting architecture.