Credit Valuation Adjustment Research Articles

Calculation of Sensitivities for FRTB Standardized Approach

Sensitivities are the core inputs to the Standardized Approach of the Fundamental Review of the Trading Book (FRTB) and are costly to implement and calculate for large portfolios and complex products. The internally calculated sensitivities by institutions may not be directly applicable for FRTB purpose due to different choices of risk factors. This paper introduces a new framework of defining and deriving FRTB sensitivities from the internally calculated sensitivities while keeping consistent risk measurement under the Standardized Approach framework, which will significantly improve efficiency of implementation, validation and model risk management for FRTB Standardized Approach and other similar regulatory programs, including SA-CVA (Credit Valuation Adjustment) VaR and ISDA-Standard Initial Margin Model (SIMM) etc.

CVA AND VULNERABLE OPTIONS IN STOCHASTIC VOLATILITY MODELS

This work aims to provide an efficient method to evaluate the Credit Value Adjustment (CVA) for a vulnerable European option, which is an option subject to some default event concerning the issuer solvability. Financial options traded in OTC markets are of this type. In particular, we compute the CVA in some popular stochastic volatility models such as SABR, Hull et al., which have proven to fit quite well market derivatives prices, admitting correlation with the default event. This choice covers the relevant case of Wrong Way Risk (WWR) when a credit deterioration determines an increase in the claim value. Contrary to the structural modeling adopted in [G. Wang, X. Wang & K. Zhu (2017) Pricing vulnerable options with stochastic volatility, Physica A 485, 91–103; C. Ma, S. Yue & Y. Ma (2020) Pricing vulnerable options with Stochastic volatility and Stochastic interest rate, Computational Economics 56, 391–429], we use the reduced-form intensity-based approach to provide an explicit representation formula for the vulnerable option price and related CVA. Later, we specialize the evaluation formula and construct its approximation for the three models mentioned above. Assuming a CIR model for the default intensity process, we run a numerical study to test our approximation, comparing it with Monte Carlo simulations. The results show that for moderate values of the correlation and maturities not exceeding one year, the approximation is very satisfactory as of accuracy and computational time.

Counterparty risk valuation on credit-linked notes under a Markov Chain framework

A credit-linked note (CLN) is a note paying an enhanced coupon to investors for bearing the credit risk of a reference entity. In this paper, we study the counterparty risk on CLNs under a Markov chain framework, and introduce a Markov copula model to describe joint defaults between the reference entity underlying the CLN and CLN issuer. Assuming that the respective default intensities are directly and inversely proportional to the interest rate, which follows a CIR process, we obtain the explicit formulae for CLN values through a PDE approach. Finally, credit valuation adjustment (CVA) formula is derived to price counterparty credit risk.

An Analytical Expression for Credit Valuation Adjustment Pricing with Wrong-Way Risk

Recently, financial institutions were required to provide the financial derivatives instrument level credit valuation adjustment (CVA) by the new accounting standard. CVA trading desks are facing difficulties to calculate a netting-set level CVA with wrong-way risk (WWR) since the dynamics of the exposures and probability of default (PD) are separated and calculated by different counterparty credit risk (CCR) computing systems. Another difficult work is that the netting-set level CVA mixed the pricing models for all trades under a netting-set. It is significant to develop a new CVA model that is based on the credit adjustment to the existing pricing model under one risk-neutral framework. This paper presents the work on CVA with WWR under the credit deterioration dynamics in both normal and stressed economic conditions. In terms of the double-correlation structure that is constructed based on the Gaussian latent variable models we propose an analytical expression of CVA for the fundamental financial derivatives such as futures or forwards contracts. The double-correlation structure captures the market- and asset-credit correlations. The proposed CVA pricing framework is based on the credit deterioration dynamics rather than default dynamics. The credit deterioration index (CDI) is defined as the limit of the credit deterioration variable and calculated using the rating agency credit rating transition data. The proposed CVA with WWR model is a function of the correlations, CDI, counterparty probability of default, loss given default, interest rate and volatility of the traded derivatives. The market- and asset-credit correlation parameters are calibrated to either the normal or stressed market. Under the stressed market, the scenario design, shock variable selection and shock magnitude are discussed. The numerical results show that the CVA is an increasing function of the market-credit correlation and a decreasing function of the credit rating. The stressed CVA is about four times higher than the normal CVA.

Consistent Spread Dynamics for CVA Risk Charge and Historical Value-at-Risk by Means of Cross Sectional / Consolidated Bucket Link Copula Simulation

This paper describes the modelling of spread risk, in case of missing or illiquid market data, by using a subset of good quality liquid bond/credit default swap (CDS) spread time series. The proposed method links copula simulation to the actual historical spread dynamics. This is important when calculating credit valuation adjustment (CVA) risk charge and Value-at-Risk (VaR) with historical simulation. The methodology center around buckets of similar spreads. Buckets with good data, are straight forward, whereas buckets without data rely on a cross sectional model spread based on other buckets with good data. Residuals from regression of the bucket spread returns against market index returns are used to derive a link for each bucket. The link is subsequently used for simulating the spread dynamics in case of missing or illiquid spreads, using a modified one factor copula. A link between the actual and simulated residuals maintaining the risk dynamics is thus ensured. The result of the copula simulation is transformed into quantiles that are plugged into residual distributions from actual quality data, thereby maintaining the properties of actual market data such that the choice of copula only affects the risk dynamics, not the distributions of the risk factors.

Distributionally Robust XVA via Wasserstein Distance: Wrong Way Counterparty Credit and Funding Risk

This paper investigates calculations of robust X-Value adjustment (XVA), in particular, credit valuation adjustment (CVA) and funding valuation adjustment (FVA), for over-the-counter derivatives under distributional ambiguity using Wasserstein distance as the ambiguity measure. Wrong way counterparty credit risk and funding risk can be characterized (and indeed quantified) via the robust XVA formulations. The simpler dual formulations are derived using recent Lagrangian duality results. Next, some computational experiments are conducted to measure the additional XVA charges due to distributional ambiguity under a variety of portfolio and market configurations. Finally some suggestions for further work are discussed.

A computational approach to hedging Credit Valuation Adjustment in a jump-diffusion setting

This study contributes to understanding Valuation Adjustments (xVA) by focussing on the dynamic hedging of Credit Valuation Adjustment (CVA), corresponding Profit & Loss (P&L) and the P&L explain. This is done in a Monte Carlo simulation setting, based on a theoretical hedging framework discussed in existing literature. We look at hedging CVA market risk for a portfolio with European options on a stock, first in a Black-Scholes setting, then in a Merton jump-diffusion setting. Furthermore, we analyze the trading business at a bank after including xVAs in pricing. We provide insights into the hedging of derivatives and their xVAs by analyzing and visualizing the cash-flows of a portfolio from a desk structure perspective. The case study shows that not charging CVA at trade inception results in an expected loss. Furthermore, hedging CVA market risk is crucial to end up with a stable trading strategy. In the Black-Scholes setting this can be done using the underlying stock, whereas in the Merton jump-diffusion setting we need to add extra options to the hedge portfolio to properly hedge the jump risk. In addition to the simulation, we derive analytical results that explain our observations from the numerical experiments. Understanding the hedging of CVA helps to deal with xVAs in a practical setting.

An Accurate Solution for Credit Value Adjustment and Wrong Way Risk

An Accurate Solution for Credit Value Adjustment and Wrong Way Risk

Basel IV implementation: a review of the case of the European Union

PurposeIntroducing radical changes to the methodologies for the determination of capital requirements, the final stage of the Basel III standards, which is referred to as “Basel IV” by the industry, will be a significant challenge for the global banking sector. This article reviews the main components of the new framework, analyses its ongoing implementation in the European Union and discusses its potential impact on banks, putting forward policy recommendations.Design/methodology/approachThis article uses primary sources such as the publications by the Basel Committee for Banking Supervision and the European Commission. It also reviews the secondary sources, including both academic articles and analyses by various stakeholders. However, this article does not undertake any empirical analysis.FindingsThis article discusses that Basel IV will introduce strategic, operational and regulatory challenges for banks in scope. It also identifies a number of areas which are subject to further debate in the European Union such as the enhanced due diligence requirements under the new credit risk framework; governance, reporting and control rules under the operational risk framework; exemptions for certain derivative transactions under the credit valuation adjustment framework and the level of application of the capital floors within banking groups. This article concludes that the global implementation of the reforms by all jurisdictions and transposition into national banking laws concurrently with the European Union in line with the Basel Committee's implementation timeline is important from a financial stability standpoint.Originality/valueThe article presents an up-to-date and comprehensive review of the practical implications of Basel IV standards. It analyses the implementation of the standards in the case of the European Union, reviews the potential policy implications and presents recommendations for risk management practitioners.

Accelerating CVA and CVA Sensitivities Using Quasi‐Monte Carlo Methods

We analyze the efficiency of the quasi Monte Carlo method (QMC) when used to compute credit valuation adjustment (CVA) and CVA sensitivities for various portfolios of interest rate swaps using a multi-currency extension to the Hull-White model. We find that QMC with Sobol’ sequences and the Brownian bridge discretization produces results as accurate as classical MC with 10,000 simulations when using roughly 800 simulations: a factor of 12 acceleration. The acceleration varies significantly across portfolios (increasing with moneyness and usually, but not always, decreasing with number of factors), calculation types (order from highest to lowest, usually, but not always, CVA, CR Deltas, IR and FX Deltas, and IR and FX Vegas), and the choice of model (local models usually outperform global models). QMC without the Brownian bridge discretization results in a more modest factor of 4 acceleration. Classical MC with antithetic sampling results in a factor of 2 acceleration. Randomized QMC (linear permutation of digits) with the Brownian bridge discretization improved the efficiency over the non-randomized sequences for smaller in-the-money portfolios. Randomization in combination with a direct and independent simulation approach of the risk factors produced extraordinary results in the limited tests we performed (CVA on a single currency swap), offering an additional factor of 6 acceleration over the pathwise simulation.

Gaussian process regression for derivative portfolio modeling and application to credit valuation adjustment computations

Modeling counterparty risk is computationally challenging because it requires the simultaneous evaluation of all trades between each counterparty under both market and credit risk. We present a multi-Gaussian process regression approach, which is well suited for the over-the-counter derivative portfolio valuation involved in credit valuation adjustment (CVA) computation. Our approach avoids nested simulation or simulation and regression of cashflows by learning a Gaussian metamodel for the mark-to-market cube of a derivative portfolio. We model the joint posterior of the derivatives as a Gaussian process over function space, imposing the spatial covariancestructure on the risk factors. Monte Carlo simulation is then used to simulate the dynamics of the risk factors. The uncertainty in portfolio valuation arising from the Gaussian process approximation is quantified numerically. Numerical experiments demonstrate the accuracy and convergence properties of our approach for CVA computations, including a counterparty portfolio of interest rate swaps.

Computing credit valuation adjustment solving coupled PIDEs in the Bates model

Credit Value Adjustment is the charge applied by financial institutions to the counter-party to cover the risk of losses on a counterpart default event. In this paper we estimate such a premium under the Bates stochastic model (Bates in The Review of Financial Studies 9(1): 69–107, 1996), which considers an underlying affected by both stochastic volatility and random jumps. We propose an efficient method which improves the Finite-Difference Monte Carlo (FDMC) approach introduced by de Graaf et al. (Journal of Computational Finance 21, 2017) In particular, the method we propose consists in replacing the Monte Carlo step of the FDMC approach with a finite difference step and the whole method relies on the efficient solution of two coupled partial integro-differential equations which is done by employing the Hybrid Tree-Finite Difference method developed by Briani et al. ( arXiv:1603.07225 2016;IMA Journal of Management Mathematics 28(4): 467–500, 2017;The Journal of Computational Finance 21(3): 1–45, 2017). Moreover, the direct application of the hybrid techniques in the original FDMC approach is also considered for comparison purposes. Several numerical tests prove the effectiveness and the reliability of the proposed approach when both European and American options are considered. Subject classification numbers as needed.

Model Independent WWR for Regulatory CVA and for Accounting CVA and FVA

Wrong way risk (WWR) is a consideration for regulatory capital for credit valuation adjustment (CVA). WWR is also of interest for pricing and accounting and in these cases must include funding as well as exposure and default in CVA and FVA calculation. Here we introduce a model independent approach to WWR for regulatory CVA and also for accounting CVA and FVA. This model independent approach is extremely simple: we just re-write the CVA and FVA integral expressions in terms of their components and then calibrate these components. This provides transparency between component calibration and CVA/FVA effect because there is no model interpretation in between. Including funding in WWR means that there are now two WWR terms rather than the usual one. Using a regulatory inspired calibration from MAR50 we investigate WWR effects for vanilla interest rate swaps and show that the WWR effects for FVA are significantly more material than for CVA. This model independent approach can also be used to compare any WWR model by simply calibrating to it for a portfolio and counterparty, to demonstrate the effects of the model under investigation in terms of components of CVA/FVA calculations.

The Implications of Tail Dependency Measures for Counterparty Credit Risk Pricing

This paper investigates the counterparty credit risk of interest rate swaps positions using the credit valuation adjustment (CVA) measure, and examines the potential dependency relationships between the probability of default (PD) and exposure at default (EAD). We empirically tested, using interest rate swaption implied market volatilities, three tail dependency models: a Basel III Committee independent model, a Gaussian copula dependent model, and a Wrong Way Risk (WWR) with copula dependency approach. The results show that the CVA underestimation when using a Gaussian copula for modelling the dependence of PD and EAD is about 51%–362% compared to using WWR, and the underestimation between using the standardised Basel independent model and using the Gaussian copula is about 527%–1609%, including the period of the 2007/2008 crisis. This has important implications for regulators, financial institutions, and credit risk managers when calculating counterparty risk.

Semi-analytic pricing formulas for basket credit-linked notes with and without counterparty risks

This paper discusses the pricing of basket credit linked notes (BCLN) under the reduced model. Three types of BCLNs are discussed: the first, the second and the mth-to-default BCLNs with and without counterparty risks. Based on conditional independence, the joint distribution of default times can be calculated and thus the price problems are transformed into partial differential equation (PDE) forms. Then the semi-analytical pricing formulas for the above BCLNs are obtained with PDE method and the calculation of credit valuation adjustments are also obtained. Finally, numerical test results show the high precision of the derived pricing formulas.

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.

Failing Faithful Representations of Financial Statements: Issues in Reporting Financial Instruments

Both the International Financial Reporting Standards (IFRS) and the codified accounting standards (ASC) for the US GAAP categorize hedging relationships as falling into several buckets. The two buckets of relevance in this paper are (i) hedging the volatility of fair values, and (ii) hedging the volatility of future cash flow. In this paper, I argue that at least three accounting treatments of derivatives and hedging lead to creating serious distortion of reporting actual transactions, to combining hard and plastic valuations, and to violating adherence to the principle of ‘faithful representation’. The three accounting treatments are as follows: (1) creating the fictional Hypothetical Derivatives Method; (2) allowing for the establishment of purely discretionary valuation adjustments for all over‐the‐counter derivative assets (Credit Valuation Adjustment) and liabilities (Debt Valuation Adjustment) without any guides or constraints; (3) requiring subjective metaphysical separation of embedded derivatives with the main guide being the management's own perception of the instrument's embodiment of unrelated value and risk generators. To remedy the resulting distortion in financial reporting, significant revisions of certain accounting standards are sorely needed.

Credit Valuation Adjustment Compression by Genetic Optimization

Since the 2008–2009 financial crisis, banks have introduced a family of X-valuation adjustments (XVAs) to quantify the cost of counterparty risk and of its capital and funding implications. XVAs represent a switch of paradigm in derivative management, from hedging to balance sheet optimization. They reflect market inefficiencies that should be compressed as much as possible. In this work, we present a genetic algorithm applied to the compression of credit valuation adjustment (CVA), the expected cost of client defaults to a bank. The design of the algorithm is fine-tuned to the hybrid structure, both discrete and continuous parameter, of the corresponding high-dimensional and nonconvex optimization problem. To make intensive trade incremental XVA computations practical in real-time as required for XVA compression purposes, we propose an approach that circumvents portfolio revaluation at the cost of disk memory, storing the portfolio exposure of the night so that the exposure of the portfolio augmented by a new deal can be obtained at the cost of computing the exposure of the new deal only. This is illustrated by a CVA compression case study on real swap portfolios.

CVA and vulnerable options pricing by correlation expansions

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.

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.