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In this article we mainly propose a numerical scheme, based on the novel Stochastic Grid Bundling Method (SGBM), to price American options in the presence of counterparty credit risk. More precisely, we consider the regression techniques (regress later) employed in the SGBM method and take advantage of the bundling structure to develop an efficient parallel strategy that is implemented on a GPU architecture. Also, a novel interpolation-based technique is efficiently applied in the XVA computation. Besides the advantages obtained in the sequential version, when compared with the more classical Least Squares Method, we show the relevant speedup of the parallel GPU-based version with respect to the sequential CPU-based one. [ABSTRACT FROM AUTHOR]

The purpose of the article is to investigate the selected method employed to manage the counterparty credit risk, namely the application of various risk limits. The aim is to recognize utilization schemes of the pre-settlement risk limits in the Polish OTC derivatives market in the relationship between a financial institution and a non-financial counterparty. They are used not only to cover the credit exposure but also to support and enhance the entire market risk management process and day-to-day operations in the financial institutions. Methodology. The research method comprises the analysis of recommendations of the Polish Financial Supervision Authority as well as reports, documents and market risk management principles of selected financial institutions (WSE listed banks). Results of the research. The study indicates two utilization schemes of the pre-settlement limit setup applicable both for daily and credit-related transactions. The first one assumes that the risk requirements remain unchanged during the contract lifetime, the second one considers variable risk requirements over time. Practical implications are discussed (in relation to a notional trade size, risk exposure and margining policy).

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We investigate how market participants price and manage counterparty credit risk using confidential trade repository data on single-name credit default swap (CDS) transactions. We find that counterparty risk has a modest impact on the pricing of CDS contracts but a large impact on the choice of counterparties. For contracts ineligible for central clearing, we show that market participants are significantly less likely to trade with counterparties whose credit risk is highly correlated with the credit risk of the reference entities and with counterparties whose credit quality is low. For clearable contracts, we find that nondealers are more likely to clear during a crisis and less likely to clear when the reference entity is a large U.S. dealer or a sovereign. This paper was accepted by Kay Giesecke, finance. Supplemental Material: The internet appendix and data are available at https://doi.org/10.1287/mnsc.2023.4870. [ABSTRACT FROM AUTHOR]

The computation of credit risk measures such as exposure and Credit Value Adjustments (CVA) requires the simulation of future portfolio prices. Recent metrics, such as dynamic Initial Margin (IM) and Margin Value Adjustments (MVA) additionally require the simulation of future conditional sensitivities. For portfolios with non-linear instruments that do not admit closed-form valuation formulas, this poses a significant computational challenge. This problem is addressed by proposing a static replication algorithm for interest rate options with early-exercise features under an affine term-structure model. Under the appropriate conditions, we can find an equivalent portfolio of vanilla options that replicate these products. Specifically, we decompose the product into a portfolio of European swaptions. The weights and strikes of the portfolio are obtained by regressing the target option value with interpretable, feed-forward neural networks. Once an equivalent portfolio of European swaptions is determined, we can leverage on closed-form expressions to obtain the conditional prices and sensitivities, which serve as an input to exposure and SIMM-driven MVA quantification. For a consistent forward sensitivity estimation, this involves the differentiation of the portfolio-weights. The accuracy and convergence of the method is demonstrated through several representative numerical examples, benchmarked against the established least-square Monte Carlo method. [ABSTRACT FROM AUTHOR]

In this paper we provide an efficient methodology to compute the credit value adjustment of a European contingent claim subject to some default event concerning the issuer solvability, when the underlying and the default event are correlated. In particular, in a Black and Scholes market/CIR intensity-default model, we consider a second order expansion around the origin of a vulnerable call option with respect to a correlation parameter ρ , which may be used to describe the wrong way risk of the contract, measuring the dependence between the underlying asset price and the option's issuer default intensity. Numerical implementations of this approach are compared with the benchmark Monte Carlo simulations. [ABSTRACT FROM AUTHOR]

Theoretical background: The 2008/2009 financial crisis, the COVID-19 pandemic outbreak in 2020 or the Russian invasion of Ukraine in February 2022, all these affected market volatility causing greater interest in counterparty credit risk (CCR) management especially in the OTC derivatives market. This study investigates selected method to mitigate the CCR, namely the application of various risk limits. The research is focused particularly on the pre-settlement risk that financial institutions face after transaction conclusion until the contract’s final settlement. Instead of one single limit there may be a wide range of different treasury limits (a multiple treasury limit setup) applied not only to cover the credit exposure but also to support and enhance the entire market risk management process and day-to-day operations in the financial institutions. Purpose of the article: The paper examines treasury limits employed to manage pre-settlement risk in the Polish OTC derivatives market in the relation between financial institution and non-financial institution. The current literature on this subject includes works on various risk limits, especially in the Polish inter-bank market, however, there is still no broader view on this topic from the analysed perspective. The study indicates different pre-settlement risk limits to be applied in practice both for daily and credit-related transactions considering multiple determinants, such as counterparty and financial instrument type, asset class or collateral form. Research methods: Research methods comprise the analysis of guidelines and recommendations of the Polish Financial Supervision Authority as well as reports, documents and market risk management principles of selected financial institutions. Particular attention is paid to the analysis of legal backgrounds on treasury limits in Poland and bank’s sources, such as master agreements, general conditions of cooperation in the field of treasury products, regulations, information brochures, etc. Selected data from the 2022 Triennial Central Bank Survey of Foreign Exchange and OTC Derivatives Market Activity in Poland is used in the context analysis. Main findings: Different determinants of pre-settlement risk limit setup are identified and on this basis a directory of pre-settlement treasury limits is developed. The paper indicates also some challenges related to their practical application, concerning, for instance, the breaches of contractual terms (events of default), timely renewal of treasury limit or issues regarding the market risk estimation.

In counterparty credit risk complete markets, collateral and capital requirements would be indifferent to banks. The quantification by banks of market incompleteness based on various XVA metrics ([11]) has emerged as the unintended consequence of the FRTB banking reform ([26]) and of the more demanding regulatory capital requirements ([38]). The related risks are in fact reckoned today as the major risks for banks, well ahead market risk ([35, Figure 65 page 67]). The XVA metrics have been introduced and traditionally used by investment banks for pricing and collateral/capital optimization purposes. We demonstrate in this paper that they can be fruitfully used for risk management, suggesting a sound approach to regulatory requirements. We present a one-period cost-of-capital XVA setup encompassing bilateral and centrally cleared trading in a unified framework, with explicit formulas for most quantities at hand. We illustrate possible uses of this framework for running stress test exercises on financial networks with one and two clearinghouses from a clearing member's perspective or for optimizing the porting of the portfolio of a defaulted clearing member using Monte-Carlo technique with corresponding confidence errors in elliptical models. A continuous-time extension of this approach is provided in the companion paper [7]. [ABSTRACT FROM AUTHOR]

Counterparty credit risk (CCR) is a significant risk factor that financial institutions have to consider in today's context, and the COVID-19 pandemic and military conflicts worldwide have heightened concerns about potential default risk. In this work, we investigate the changes in the value of financial derivatives due to counterparty default risk, i.e., total value adjustment (XVA). We perform the XVA for multi-asset option based on the multivariate Carr–Geman–Madan–Yor (CGMY) processes, which can be applied to a wider range of financial derivatives, such as basket options, rainbow options, and index options. For the numerical methods, we use the Monte Carlo method in combination with the alternating direction implicit method (MC-ADI) and the two-dimensional Fourier cosine expansion method (MC-CC) to find the risk exposure and make value adjustments for multi-asset derivatives. [ABSTRACT FROM AUTHOR]

Quantum computing allows a significant speed-up over traditional CPU- and GPU-based algorithms when applied to particular mathematical challenges such as optimisation and simulation. Despite promising advances and extensive research in hard- and software developments, currently available quantum systems are still largely limited in their capability. In line with this, practical applications in quantitative finance are still in their infancy. This paper analyses requirements and concrete approaches for the application to risk management in a financial institution. On the examples of Value-at-Risk for market risk and Potential Future Exposure for counterparty credit risk, the main contribution lies in going beyond textbook illustrations and instead exploring must-have model features and their quantum implementations. While conceptual solutions and small-scale circuits are feasible at this stage, the leap needed for real-life applications is still significant. In order to build a usable risk measurement system, the hardware capacity—measured in number of qubits—would need to increase by several magnitudes from their current value of about 10 2 . Quantum noise poses an additional challenge, and research into its control and mitigation would need to advance in order to render risk measurement applications deployable in practice. Overall, given the maturity of established classical simulation-based approaches that allow risk computations in reasonable time and with sufficient accuracy, the business case for a move to quantum solutions is not very strong at this point. [ABSTRACT FROM AUTHOR]

Theoretical background: The 2008/2009 financial crisis, the COVID-19 pandemic outbreak in 2020 or the Russian invasion of Ukraine in February 2022, all these affected market volatility causing greater interest in counterparty credit risk (CCR) management especially in the OTC derivatives market. This study investigates selected method to mitigate the CCR, namely the application of various risk limits. The research is focused particularly on the pre-settlement risk that financial institutions face after transaction conclusion until the contract’s final settlement. Instead of one single limit there may be a wide range of different treasury limits (a multiple treasury limit setup) applied not only to cover the credit exposure but also to support and enhance the entire market risk management process and day-to-day operations in the financial institutions. Purpose of the article: The paper examines treasury limits employed to manage pre-settlement risk in the Polish OTC derivatives market in the relation between financial institution and non-financial institution. The current literature on this subject includes works on various risk limits, especially in the Polish inter-bank market, however, there is still no broader view on this topic from the analysed perspective. The study indicates different pre-settlement risk limits to be applied in practice both for daily and credit-related transactions considering multiple determinants, such as counterparty and financial instrument type, asset class or collateral form. Research methods: Research methods comprise the analysis of guidelines and recommendations of the Polish Financial Supervision Authority as well as reports, documents and market risk management principles of selected financial institutions. Particular attention is paid to the analysis of legal backgrounds on treasury limits in Poland and bank’s sources, such as master agreements, general conditions of cooperation in the field of treasury products, regulations, information brochures, etc. Selected data from the 2022 Triennial Central Bank Survey of Foreign Exchange and OTC Derivatives Market Activity in Poland is used in the context analysis. Main findings: Different determinants of pre-settlement risk limit setup are identified and on this basis a directory of pre-settlement treasury limits is developed. The paper indicates also some challenges related to their practical application, concerning, for instance, the breaches of contractual terms (events of default), timely renewal of treasury limit or issues regarding the market risk estimation. [ABSTRACT FROM AUTHOR]

In Basel III, the credit valuation adjustment (CVA) was given, and it was discussed that a bank covers mark-to-market losses for expected counterparty risk with a CVA capital charge. The purpose of this study is threefold. Using the logistic distribution, it is shown how the expected exposure can be derived for an interest rate swap. Secondly, the risk measure of VaR is contributed for the CVA under this distribution. Thirdly, generalizations for the CVA VaR and CVA CVaR are given by considering both the credit spread and the expected positive exposure to follow the logistic distributions with different parameters. Finally, several simulations are provided to uphold the theoretical discussions. [ABSTRACT FROM AUTHOR]

This paper proposes an approximate analytical solution method to calculate counterparty credit risk exposures. Compared with the Standard Approach for measuring Counterparty Credit Risk and the Internal Modeling Method provided by Basel Committee, the proposed method significantly improves the calculation efficiency based on sacrificing a little accuracy. Taking Forward Rate Agreement as an example, this article derives the exact expression for Expected Exposure. By approximating the distribution of Forward Rate Agreement's future value to a normal distribution, the approximate analytical expression for Potential Future Exposure is derived. Numerical results show that this method is reliable and is robust under different parameters. [ABSTRACT FROM AUTHOR]

We study how individual banks borrow and lend in the euro unsecured and secured interbank market. We find that banks with lower credit worthiness replace unsecured with secured borrowing, which is consistent with a reduction in the supply of unsecured loans rather than a lower demand for funding. Riskier lenders replace unsecured with secured lending, suggesting that banks take precautionary measures and prefer to lend against safe collateral. Our results highlight the importance of a joint analysis of unsecured and secured funding. Separate analyses only give a partial view and might yield misleading conclusions when banks access both funding sources. [ABSTRACT FROM AUTHOR]

Copyright of Istanbul Medipol Üniversitesi Hukuk Fakültesi Dergisi is the property of Istanbul Medipol University and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

We consider the problem of computing the credit value adjustment (CVA) of a European option in presence of the wrong way risk in a default intensity setting. Namely we model the asset price evolution as solution to a linear equation that might depend on different stochastic factors and we provide an approximate evaluation of the option's price, by exploiting a correlation expansion approach, introduced in Antonelli and Scarlatti (Finance Stoch 13:269–303, 2009). We also extend our theoretical analysis to include some further value adjustments, for instance due to collateralization and funding costs. Finally, in the CVA case, we compare the numerical performance of our method with the one recently proposed by Brigo and Vrins (Eur J Oper Res 269:1154–1164, 2018) and Brigo et al. (Innovations in insurance, risk and asset management, WSPC proceedings, 2018), in the case of a call option driven by a GBM correlated with a CIR default intensity. We additionally compare with the numerical evaluations obtained by other methods. [ABSTRACT FROM AUTHOR]

Counterparty credit risk (CCR), a key driver of the 2007-08 credit crisis, has become one of the main focuses of the major global and U.S. regulatory standards. Financial institutions invest large amounts of resources employing Monte Carlo simulation to measure and pricetheir counterparty credit risk. We develop efficient Monte Carlo CCR frameworks by focusing on the most widely used and regulatory-driven CCR measures: expected positive exposure (EPE), credit value adjustment (CVA), and effective expected positive exposure (eEPE). Our numerical examples illustrate that our proposed efficient Monte Carlo estimators outperform the existing crude estimators of these CCR measures substantially in terms of mean square error (MSE). We also demonstrate that the two widely used sampling methods, the so-called Path Dependent Simulation (PDS) and Direct Jump to Simulation date (DJS), are not equivalent in that they lead to Monte Carlo CCR estimators which are drastically different in terms of their MSE.

A counterparty credit limit (CCL) is a limit that is imposed by a financial institution to cap its maximum possible exposure to a specified counterparty. CCLs help institutions to mitigate counterparty credit risk via selective diversification of their exposures. In this paper, we analyse how CCLs impact the prices that institutions pay for their trades during everyday trading. We study a high-quality data set from a large electronic trading platform in the foreign exchange spot market that allows institutions to apply CCLs. We find empirically that CCLs had little impact on the vast majority of trades in this data set. We also study the impact of CCLs using a new model of trading. By simulating our model with different underlying CCL networks, we highlight that CCLs can have a major impact in some situations. [ABSTRACT FROM AUTHOR]

Considering counterparty credit risk (CCR) for derivatives using valuation adjustments (CVA) is a fundamental and challenging task for entities involved in derivative trading activities. Particularly calculating the expected exposure is time consuming and complex. This paper suggests a fast and simple semi-analytical approach for exposure calculation, which is a modified version of the new regulatory standardized approach (SA-CCR). Hence, it conforms with supervisory rules and IFRS 13. We show that our approach is applicable to multiple asset classes and derivative products, and to single transactions as well as netting sets. [ABSTRACT FROM AUTHOR]

We introduce an arbitrage‐free framework for robust valuation adjustments. An investor trades a credit default swap portfolio with a risky counterparty, and hedges credit risk by taking a position in defaultable bonds. The investor does not know the exact return rate of her counterparty's bond, but she knows it lies within an uncertainty interval. We derive both upper and lower bounds for the XVA process of the portfolio, and show that these bounds may be recovered as solutions of nonlinear ordinary differential equations. The presence of collateralization and closeout payoffs leads to important differences with respect to classical credit risk valuation. The value of the super‐replicating portfolio cannot be directly obtained by plugging one of the extremes of the uncertainty interval in the valuation equation, but rather depends on the relation between the XVA replicating portfolio and the closeout value throughout the life of the transaction. Our comparative statics analysis indicates that credit contagion has a nonlinear effect on the replication strategies and on the XVA. [ABSTRACT FROM AUTHOR]

In recent years, the counterparty credit risk measure, namely the default risk in over-the-counter (OTC) derivatives contracts, has received great attention by banking regulators, specifically within the frameworks of Basel II and Basel III. More explicitly, to obtain the related risk figures, one is first obliged to compute intermediate output functionals related to the mark-to-market position at a given time no exceeding a positive and finite time horizon. The latter implies an enormous amount of computational effort is needed, with related highly time consuming procedures to be carried out, turning out into significant costs. To overcome the latter issue, we propose a smart exploitation of the properties of the (local) time spent by the Brownian motion close to a given value.

Based on Gaussian tail distribution estimates of independent interest, we study the mathematical properties of the default times (or any of their minima) in the dynamic Gaussian copula model. In particular, depending on the value of the correlation parameter ϱ in the model, the so-called invariance property of CrepeySong15c may be satisfied or not. This gives together an example of a model where the invariance property is satisfied but immersion does not hold, for small ϱ and, for larger ϱ an example of a model where the invariance property may not be satisfied.

Abstract 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. Highlights • A counterparty credit risk contagion network evolution model is developed to study counterparty credit risk contagion in the CRT market and its influencing factors. • The preferential and random attachment is considered in the modeling. • A finiteness of assumption is put forwarded that counterparties have "economic man" and "social person" attributes to revise the infection probability of the existing epidemic SIRS model. [ABSTRACT FROM AUTHOR]

According to the Basel Committee’s estimate, three quarters of counterparty credit risk losses during the financial crisis in 2008 originate from credit valuation adjustment’s losses and not from actual defaults. Therefore, from 2015, the Third Basel Accord (EU, 2013a) and (EU, 2013b) instructed banks to calculate the capital requirement for the risk of credit valuation adjustment (CVA). Banks are trying to model CVA to hold the prescribed standards and also reach the lowest possible impact on their profit. In this paper, we try to model CVA using methods that are in compliance with the prescribed standards and also achieve the smallest possible impact on the bank’s earnings. To do so, a data set of interest rate swaps from 2015 is used. The interest rate term structure is simulated using the Hull-White one-factor model and Monte Carlo methods. Then, the probability of default for each counterparty is constructed. A safe level of CVA is reached in spite of the calculated the CVA achieving a lower level than CVA previously used by the bank. This allows a reduction of capital requirements for banks.

Estimating the credit valuation adjustment (CVA) for unlisted companies is a challenging issue because it is not possible to estimate the risk neutral default probability from either the credit default swap (CDS) par spread or equity stock. This paper proposes a calibration method that easily estimates the market risk premium, which is added to the internal rating model of unlisted companies to obtain a risk neutral default probability. The method is applied to price the CVA of a portfolio of swaps for unlisted counterparties using the advanced method approach, and the results are benchmarked using the Bank for International Settlements (BIS) approach for illiquid counterparties. Last, the robustness tests confirm the reliability of the calibration method, both for its use in risk management and accounting. [ABSTRACT FROM AUTHOR]

Over the past few years, the world economy is still in a profound adjustment stage after financial crisis, and it will continue to maintain a “New Mediocre” situation. It is clear that multiple risk factors, such as the issue of Brexit and European refugees, will increase the uncertainty of world economy growth. Under such economic development condition, it is obvious that the development of commercial bank will face a challenge; especially, the development of off-balance sheet business has received more attention from the commercial bank. Therefore, the counterparty credit risk has been brought into focus by the government and regulatory authority. This paper employs the new intuitionistic fuzzy method to improve the score function, and it aims to establish an evaluation mechanism of commercial bank counterparty credit risk management. By selecting the representative Chinese commercial banks, this paper conducts an empirical analysis to verify the validity of the evaluation system and make certain effectiveness evaluation. [ABSTRACT FROM AUTHOR]

With new regulations like the credit valuation adjustment, the assessment of wrong-way-risk is of utter importance. We analyse the effect of a counterparty’s credit risk and its influence on other asset classes (equity, currency, commodity and interest rate) in the event of extreme market movements like the counterparty’s default. With an extreme value approach, we model the tail of the joint distribution of different asset returns belonging to the above asset classes and counterparty credit risk indicated by changes in CDS spreads and calculate the effect on the expected shortfall when conditioning on counterparty credit risk. We find the conditional expected shortfall to be 2 to 440% higher than the unconditional expected shortfall depending on the asset class. Our results give insights both for risk management and for setting an initial margin for non-centrally cleared derivatives which becomes mandatory in the European Market Infrastructure Regulation. [ABSTRACT FROM AUTHOR]

We develop a framework for computing the total valuation adjustment (XVA) of a European claim accounting for funding costs, counterparty credit risk, and collateralization. Based on no-arbitrage arguments, we derive backward stochastic differential equations associated with the replicating portfolios of long and short positions in the claim. This leads to the definition of buyer's and seller's XVA, which in turn identify a no-arbitrage interval. In the case that borrowing and lending rates coincide, we provide a fully explicit expression for the unique XVA, expressed as a percentage of the price of the traded claim, and for the corresponding replication strategies. In the general case of asymmetric funding, repo, and collateral rates, we study the semilinear partial differential equations characterizing buyer's and seller'sXVAand showthe existence of a unique classical solution to it. To illustrate our results, we conduct a numerical study demonstrating how funding costs, repo rates, and counterparty risk contribute to determine the total valuation adjustment. [ABSTRACT FROM AUTHOR]

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.

We present a detailed analysis of interest rate derivatives valuation under credit risk and collateral modeling. We show how the credit and collateral extended valuation framework presented in Pallaviciniet al.[Funding valuation adjustment: FVA consistent with CVA, DVA, WWR, collateral, netting and re-hyphotecation, 2011], and the related collateralized valuation measure, can be helpful in defining the key market rates underlying the multiple interest rate curves that characterize current interest rate markets. A key point is that spot Libor rates are to be treated as market primitives rather than being defined by no-arbitrage relationships. We formulate a consistent realistic dynamics for the different rates emerging from our analysis and compare the resulting model performances to simpler models used in the industry. We include the often neglected margin period of risk, showing how this feature may increase the impact of different rates dynamics on valuation. We point out limitations of multiple curve models with deterministic basis considering valuation of particularly sensitive products such as basis swaps. We stress that a proper wrong way risk analysis for such products requires a model with a stochastic basis and we show numerical results confirming this fact. [ABSTRACT FROM AUTHOR]

Abstract: A credit valuation adjustment (CVA) is an adjustment applied to the value of a derivative contract or a portfolio of derivatives to account for counterparty credit risk. Measuring CVA requires combining models of market and credit risk to estimate a counterparty's risk of default together with the market value of exposure to the counterparty at default. Wrong‐way risk refers to the possibility that a counterparty's likelihood of default increases with the market value of the exposure. We develop a method for bounding wrong‐way risk, holding fixed marginal models for market and credit risk and varying the dependence between them. Given simulated paths of the two models, a linear program computes the worst‐case CVA. We analyze properties of the solution and prove convergence of the estimated bound as the number of paths increases. The worst case can be overly pessimistic, so we extend the procedure by constraining the deviation of the joint model from a baseline reference model. Measuring the deviation through relative entropy leads to a tractable convex optimization problem that can be solved through the iterative proportional fitting procedure. Here, too, we prove convergence of the resulting estimate of the penalized worst‐case CVA and the joint distribution that attains it. We consider extensions with additional constraints and illustrate the method with examples. [ABSTRACT FROM AUTHOR]

We consider two classes of wrong-way risk models in the context of CVA: static (resampling) and dynamic (reduced form). Although both potentially suffer from arbitrage problems, their tractability makes them appealing to the industry and therefore deserve additional study. For example, Gaussian copula-based resampling and reduced-form with 'Hull-White intensities' yield analytical expected positive exposure (EPE) profiles when the portfolio price process (i.e. exposure process) is Gaussian. However, the first approach disregards credit volatility whilst the second can provide default probabilities larger than 1. We therefore enlarge the study by introducing a new dynamic approach for credit risk, consisting in the straight modeling of the survival (Azéma supermartingale) process using the -martingale. This method is appealing in that it helps fixing some drawbacks of the above models. Indeed, it is a dynamic method (it disentangles correlation and credit volatility) that preserves probabilities in without affecting the analytical tractability of the model. In particular, calibration to any valid default probability curve is automatic and the closed-form expression for the EPE profiles remains available under Gaussian exposures. For each approach, we derive analytically the EPE profiles (conditional upon default) associated to prototypical exposure processes of Forward Rate Agreement (FRA) and Interest Rate Swap (IRS) in all cases and provide a comparison and discuss the implied Credit Valuation Adjustment (CVA) figures. [ABSTRACT FROM AUTHOR]