Journal articles: 'Credit valuation adjustment (cva)'

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YI, CHUANG. "DANGEROUS KNOWLEDGE: CREDIT VALUE ADJUSTMENT WITH CREDIT TRIGGERS." International Journal of Theoretical and Applied Finance 14, no. 06 (September 2011): 839–65. http://dx.doi.org/10.1142/s0219024911006395.

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We generalize the arbitrage-free valuation framework for counterparty credit risk (CCR) adjustments when credit triggers are allowed in the contract. The settlement of the deal for the investor could be either obliged or optional to execute when the counterparty hits the credit trigger before any default events from the two parties. General formulas for credit value adjustment (CVA) are given for all four cases: obliged unilateral, obliged bilateral, optional unilateral and optional bilateral. The unilateral CVA with an optional credit trigger is found to be the same as the unilateral CVA with an analogous obliged credit trigger. We show that adding credit triggers will decrease the unilateral CVA for both obliged and optional cases, which are in line with the motivation of investors to reduce CCR. However, adding credit triggers may not necessarily reduce bilateral CVA. Counter-intuitively, we show that the bilateral CVA may actually increase by adding credit triggers. Moreover, the increased amount of bilateral CVA due to credit triggers for one party is exactly the same amount of bilateral CVA reduced for the other party. The CVA calculation is subjected to large uncertainty of model risks, mostly due to the lack of data for calibrating jump-to-default probabilities. Some explicit models for obliged unilateral CVA are discussed with special caveats on the model assumptions. Numerical examples are also given to illustrate the model risk of CVA calculation due to the uncertainty of jump sizes, even though pure jump models are assumed.

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Van Vuuren, Gary Wayne, and Ja'nel Esterhuysen. "A primer on counterparty valuation adjustments in South Africa." South African Journal of Economic and Management Sciences 17, no. 5 (November 28, 2014): 584–600. http://dx.doi.org/10.4102/sajems.v17i5.648.

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Counterparty valuation adjustment (CVA) risk accounts for losses due to the deterioration in credit quality of derivative counterparties with large credit spreads. Of the losses attributed to counterparty credit risk incurred during the financial crisis of 2008-9 were due to CVA risk; the remaining third were due to actual defaults. Regulatory authorities have acknowledged and included this risk in the new Basel III rules. The capital implications of CVA risk in the South African milieu are explored, as well as the sensitivity of CVA risk components to market variables. Proposed methodologies for calculating changes in CVA are found to be unstable and unreliable at high average spread levels.

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Chataigner, Marc, and Stéphane Crépey. "Credit Valuation Adjustment Compression by Genetic Optimization." Risks 7, no. 4 (September 29, 2019): 100. http://dx.doi.org/10.3390/risks7040100.

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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.

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BIELECKI, TOMASZ R., IGOR CIALENCO, and ISMAIL IYIGUNLER. "COLLATERALIZED CVA VALUATION WITH RATING TRIGGERS AND CREDIT MIGRATIONS." International Journal of Theoretical and Applied Finance 16, no. 02 (March 2013): 1350009. http://dx.doi.org/10.1142/s021902491350009x.

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In this paper we discuss the issue of computation of the bilateral credit valuation adjustment (CVA) under rating triggers, and in presence of ratings-linked margin agreements. Specifically, we consider collateralized OTC contracts, that are subject to rating triggers, between two parties — an investor and a counterparty. Moreover, we model the margin process as a functional of the credit ratings of the counterparty and the investor. We employ a Markovian approach for modeling of the rating transitions of the two parties to the contract. In this framework, we derive the representation for bilateral CVA. We also introduce a new component in the decomposition of the counterparty risky price: namely the rating valuation adjustment (RVA) that accounts for the rating triggers. We give two examples of dynamic collateralization schemes where the margin thresholds are linked to the credit ratings of the parties. Our results are illustrated via computation of various counterparty risk adjustments for a CDS contract and for an IRS contract.

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FENG, QIAN, and CORNELIS W. OOSTERLEE. "COMPUTING CREDIT VALUATION ADJUSTMENT FOR BERMUDAN OPTIONS WITH WRONG WAY RISK." International Journal of Theoretical and Applied Finance 20, no. 08 (December 2017): 1750056. http://dx.doi.org/10.1142/s021902491750056x.

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We study the impact of wrong way risk (WWR) on credit valuation adjustment (CVA) for Bermudan options. WWR is modeled by a dependency between the underlying asset and the intensity of the counterparty’s default. Two WWR models are proposed, based on a deterministic function and a CIR-jump (CIRJ) model, respectively. We present a nonnested Monte Carlo approach for computing CVA–VaR and CVA–expected shortfall (ES) for Bermudan options. By varying correlation coefficients, we study the impact of credit quality and WWR on the optimal exercise boundaries and CVA values of Bermudan products. Stress testing is performed.

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Křivánková, Lenka, and Silvie Zlatošová. "Modelling Counterparty Credit Risk in Czech Interest Rate Swaps." Acta Universitatis Agriculturae et Silviculturae Mendelianae Brunensis 65, no. 3 (2017): 1015–22. http://dx.doi.org/10.11118/actaun201765031015.

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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.

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BRIGO, DAMIANO, CRISTIN BUESCU, and MASSIMO MORINI. "COUNTERPARTY RISK PRICING: IMPACT OF CLOSEOUT AND FIRST-TO-DEFAULT TIMES." International Journal of Theoretical and Applied Finance 15, no. 06 (September 2012): 1250039. http://dx.doi.org/10.1142/s0219024912500392.

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In the absence of a universally accepted procedure for the credit valuation adjustment (CVA) calculation, we compare a number of different bilateral counterparty valuation adjustment (BVA) formulas. First we investigate the impact of the choice of the closeout convention used in the formulas. Important consequences on default contagion manifest themselves in a rather different way depending on which closeout formulation is used (risk-free or replacement), and on default dependence between the two entities in the deal. Second we compare the full bilateral formula with an approximation that is based on subtracting two unilateral credit valuation adjustment (UCVA) formulas. Although the latter might be attractive for its instantaneous implementation once one has a unilateral CVA system, it ignores the impact of the first-to-default time, when closeout procedures are ignited. We illustrate in a number of realistic cases both the contagion effect due to the closeout convention, and the CVA pricing error due to ignoring the first-to-default time.

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Yang, Yifan, Frank J. Fabozzi, and Michele Leonardo Bianchi. "Bilateral counterparty risk valuation adjustment with wrong way risk on collateralized commodity counterparty." Journal of Financial Engineering 02, no. 01 (March 2015): 1550001. http://dx.doi.org/10.1142/s2345768615500014.

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Basel III requires banks to include a credit value adjustment (CVA) into capital charges. Both CVA and debt value adjustment (DVA) must be included for derivatives using mark-to-market accounting. An effective method to calculate bilateral-CVA (BR-CVA) by incorporating wrong-way risk (WWR) for a collateralized counterparty is proposed which handles WWR — defined as when counterparty credit exposure increases as default probability increases — by building a trivariate Gaussian copula between the aggregate market risk exposure factor and default quality of the financial institution and counterparty. This paper extends the ordered-scenario copula model proposed in the literature. It links BR-CVA pricing and WWR, which is close to the current regulatory requirement and useful for managing a financial institution's risk. A practical example is provided. Numerical results suggest that the proposed method is efficient and robust and can easily stress test the impact of WWR in BR-CVA pricing.

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Liu, Qian. "Calculation of Credit Valuation Adjustment Based on Least Square Monte Carlo Methods." Mathematical Problems in Engineering 2015 (2015): 1–6. http://dx.doi.org/10.1155/2015/959312.

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Counterparty credit risk has become one of the highest-profile risks facing participants in the financial markets. Despite this, relatively little is known about how counterparty credit risk is actually priced mathematically. We examine this issue using interest rate swaps. This largely traded financial product allows us to well identify the risk profiles of both institutions and their counterparties. Concretely, Hull-White model for rate and mean-reverting model for default intensity have proven to be in correspondence with the reality and to be well suited for financial institutions. Besides, we find that least square Monte Carlo method is quite efficient in the calculation of credit valuation adjustment (CVA, for short) as it avoids the redundant step to generate inner scenarios. As a result, it accelerates the convergence speed of the CVA estimators. In the second part, we propose a new method to calculate bilateral CVA to avoid double counting in the existing bibliographies, where several copula functions are adopted to describe the dependence of two first to default times.

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Singh, Derek, and Shuzhong Zhang. "Distributionally Robust XVA via Wasserstein Distance: Wrong Way Counterparty Credit and Funding Risk." Applied Economics and Finance 7, no. 6 (October 27, 2020): 70. http://dx.doi.org/10.11114/aef.v7i6.5060.

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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.

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CRÉPEY, STÉPHANE, RÉMI GERBOUD, ZORANA GRBAC, and NATHALIE NGOR. "COUNTERPARTY RISK AND FUNDING: THE FOUR WINGS OF THE TVA." International Journal of Theoretical and Applied Finance 16, no. 02 (March 2013): 1350006. http://dx.doi.org/10.1142/s0219024913500064.

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The credit crisis and the ongoing European sovereign debt crisis have highlighted the native form of credit risk, namely the counterparty risk. The related credit valuation adjustment (CVA), debt valuation adjustment (DVA), liquidity valuation adjustment (LVA) and replacement cost (RC) issues, jointly referred to in this paper as total valuation adjustment (TVA), have been thoroughly investigated in the theoretical papers [8, 9]. The present work provides an executive summary and numerical companion to these papers, through which the TVA pricing problem can be reduced to Markovian pre-default TVA BSDEs. The first step consists in the counterparty clean valuation of a portfolio of contracts, which is the valuation in a hypothetical situation where the two parties would be risk-free and funded at a risk-free rate. In the second step, the TVA is obtained as the value of an option on the counterparty clean value process called contingent credit default swap (CCDS). Numerical results are presented for interest rate swaps in the Vasicek, as well as in the inverse Gaussian Hull-White short rate model, which allows also to assess the related model risk issue.

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Wu, Lixin, and Chonhong Li. "FVA and CVA under margining." Studies in Economics and Finance 32, no. 3 (August 3, 2015): 298–321. http://dx.doi.org/10.1108/sef-08-2014-0162.

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Purpose – The purpose of this paper is to provide a framework of replication pricing of derivatives and identify funding valuation adjustment (FVA) and credit valuation adjustments (CVA) as price components. Design/methodology/approach – The authors propose the notion of bilateral replication pricing. In the absence of funding cost, it reduces to unilateral replication pricing. The absence of funding costs, it introduces bid–ask spreads. Findings – The valuation of CVA can be separated from that of FVA, so-called split up. There may be interdependence between FVA and the derivatives value, which then requires a recursive procedure for their numerical solution. Research limitations/implications – The authors have assume deterministic interest rates, constant CDS rates and loss rates for the CDS. The authors have also not dealt with re-hypothecation risks. Practical implications – The results of this paper allow user to identify CVA and FVA, and mark to market their derivatives trades according to the recent market standards. Originality/value – For the first time, a line between the risk-neutral pricing measure and the funding risk premiums is drawn. Also, the notion of bilateral replication pricing extends the unilateral replication pricing.

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BRIGO, DAMIANO, ANDREA PALLAVICINI, and VASILEIOS PAPATHEODOROU. "ARBITRAGE-FREE VALUATION OF BILATERAL COUNTERPARTY RISK FOR INTEREST-RATE PRODUCTS: IMPACT OF VOLATILITIES AND CORRELATIONS." International Journal of Theoretical and Applied Finance 14, no. 06 (September 2011): 773–802. http://dx.doi.org/10.1142/s0219024911006759.

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The purpose of this paper is introducing rigorous methods and formulas for bilateral counterparty risk credit valuation adjustment (CVA) on interest-rate portfolios. In doing so, we summarize the general arbitrage-free valuation framework for counterparty risk adjustments in presence of bilateral default risk, including the default of the investor. We illustrate the symmetry in the valuation and show that the adjustment involves a long position in a put option plus a short position in a call option, both with zero strike and written on the residual net present value of the contract at the relevant default times. We allow for correlation between the default times of the investor and counterparty, and for correlation of each with the underlying risk factor, namely interest rates. We also analyze the often neglected impact of credit spread volatility. We include close-out netting rules in our examples, although other agreements, such as periodic margining or collateral posting, are left for future work.

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WU, LIXIN. "CVA AND FVA TO DERIVATIVES TRADES COLLATERALIZED BY CASH." International Journal of Theoretical and Applied Finance 18, no. 05 (July 28, 2015): 1550035. http://dx.doi.org/10.1142/s0219024915500351.

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In this paper, we consider replication pricing of derivatives that are partially collateralized by cash. We let issuer replicate the derivatives payout using shares and cash, and let buyer replicate the loss given the counterparty default using credit default swaps. The costs of funding for replication and collateral posting are taken into account in the pricing process. A partial differential equation (PDE) for the derivatives price is established, and its solution is provided in a Feynman–Kac formula, which decomposes the derivatives value into the risk-free value of the derivative plus credit valuation adjustment (CVA) and funding valuation adjustment (FVA). For most derivatives, we show that CVAs can be evaluated analytically or semi-analytically, while FVAs as well as the derivatives values can be solved recursively through numerical procedures due to their interdependence. In numerical demonstrations, continuous and discrete margin revisions are considered, respectively, for an equity call option and a vanilla interest-rate swap.

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Brigo, Damiano, and Andrea Pallavicini. "Nonlinear consistent valuation of CCP cleared or CSA bilateral trades with initial margins under credit, funding and wrong-way risks." Journal of Financial Engineering 01, no. 01 (March 2014): 1450001. http://dx.doi.org/10.1142/s2345768614500019.

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The introduction of Central Clearing Counterparties (CCPs) in most derivative transactions will dramatically change the landscape of derivatives pricing, hedging and risk management, and, according to the TABB Group, will lead to an overall liquidity impact of about USD 2 trillions. In this paper, we develop for the first time a comprehensive approach for pricing under CCP clearing, including variation and initial margins, gap credit risk and collateralization, showing concrete examples for interest rate swaps. This framework stems from our 2011 framework on credit, collateral and funding costs in Pallavicini et al. (Pallavicini, A., D. Perini and D. Brigo, 2011, Funding Valuation Adjustment: FVA consistent with CVA, DVA, WWR, Collateral, Netting and Re-hypothecation, arxiv.org, ssrn.com). Mathematically, the inclusion of asymmetric borrowing and lending rates in the hedge of a claim, and a replacement closeout at default, lead to nonlinearities showing up in claim dependent pricing measures, aggregation dependent prices, nonlinear Partial Differential Equations (PDEs) and Backward Stochastic Differential Equations (BSDEs). This still holds in presence of CCPs and CSA. We introduce a modeling approach that allows us to enforce rigorous separation of the interconnected nonlinear risks into different valuation adjustments where the key pricing nonlinearities are confined to a funding costs component that is analyzed through numerical schemes for BSDEs. We present a numerical case study for Interest Rate Swaps that highlights the relative size of the different valuation adjustments and the quantitative role of initial and variation margins, of liquidity bases, of credit risk, of the margin period of risk and of wrong-way risk correlations.

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Viljanen, Mika Veli-Pekka. "CVA: the first sign of BCBS strategic change?" Journal of Financial Regulation and Compliance 23, no. 3 (July 13, 2015): 230–51. http://dx.doi.org/10.1108/jfrc-05-2014-0021.

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Purpose – The purpose of this paper is to aid understanding of the changes in Basel Committee on Banking Supervision (BCBS) regulatory strategies after the global financial crisis. Design/methodology/approach – The author uses the credit valuation adjustment (CVA) charge reform as a test case for inquiring whether BCBS has departed from its pre-crisis facilitative regulatory strategy path. The regulatory strategy of the CVA charge is discussed. Findings – The charge exhibits a new regulatory strategy that BCBS has adopted. It seeks to manipulate market structures by imposing risk-insensitive capital charge methodologies. Originality/value – The paper offers a new heuristic to analyse regulatory initiatives and their significance. The CVA charge has not been subject to a regulatory theory-based analysis in prior literature.

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ALBANESE, CLAUDIO, DAMIANO BRIGO, and FRANK OERTEL. "RESTRUCTURING COUNTERPARTY CREDIT RISK." International Journal of Theoretical and Applied Finance 16, no. 02 (March 2013): 1350010. http://dx.doi.org/10.1142/s0219024913500106.

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We introduce an innovative theoretical framework for the valuation and replication of derivative transactions between defaultable entities based on the principle of arbitrage freedom. Our framework extends the traditional formulations based on credit and debit valuation adjustments (CVA and DVA). Depending on how the default contingency is accounted for, we list a total of ten different structuring styles. These include bi-partite structures between a bank and a counterparty, tri-partite structures with one margin lender in addition, quadri-partite structures with two margin lenders and, most importantly, configurations where all derivative transactions are cleared through a central counterparty clearing house (CCP). We compare the various structuring styles under a number of criteria including consistency from an accounting standpoint, counterparty risk hedgeability, numerical complexity, transaction portability upon default, induced behavior and macro-economic impact of the implied wealth allocation.

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Hesp, Elise, Bert-Jan Bout, and Ralph ter Hoeven. "Toelichting op tegenpartijrisico in de jaarrekening van Europese banken." Maandblad Voor Accountancy en Bedrijfseconomie 89, no. 4 (April 15, 2015): 122–33. http://dx.doi.org/10.5117/mab.89.31276.

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In dit artikel wordt ingegaan op de kwaliteit van de toelichting over het op derivaten gelopen kredietrisico. In de kredietcrisis is nadrukkelijk gebleken dat dit kredietrisico, ook wel tegenpartijrisico genoemd, zeker niet verwaarloosbaar is. Bij de waardering van derivaten wordt met het kredietrisico rekening gehouden door aanpassingen op de reële waarde die met de termen ‘credit valuation adjustments’ en ‘debit valuation adjustments’ (CVA/DVA) worden aangeduid. In ons onderzoek worden achttien jaarrekeningen (boekjaar 2013) van Europese banken, verdeeld over zes landen, onderzocht. Met name wordt de kwaliteit van de toelichting op CVA/DVA onderzocht aan de hand van een zelf ontwikkelde disclosure-index bestaande uit relevant gebleken informatie-elementen. Verder worden beschrijvende statistieken gepresenteerd. Uit ons onderzoek blijkt dat de kwaliteit van de toelichting op CVA/DVA sterk varieert. De grotere banken in de onderzoekspopulatie blijken meer relevante informatie te geven in hun jaarrekening over CVA/DVA dan de relatief kleinere banken, hetgeen verklaard kan worden door de meer prominente rol die grootbanken innemen in het aangaan en tegensluiten van de derivatenposities.

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DE GRAAF, CORNELIS S. L., QIAN FENG, DRONA KANDHAI, and CORNELIS W. OOSTERLEE. "EFFICIENT COMPUTATION OF EXPOSURE PROFILES FOR COUNTERPARTY CREDIT RISK." International Journal of Theoretical and Applied Finance 17, no. 04 (June 2014): 1450024. http://dx.doi.org/10.1142/s0219024914500241.

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Three computational techniques for approximation of counterparty exposure for financial derivatives are presented. The exposure can be used to quantify so-called Credit Valuation Adjustment (CVA) and Potential Future Exposure (PFE), which are of utmost importance for modern risk management in the financial industry, especially since the recent credit crisis. The three techniques all involve a Monte Carlo path discretization and simulation of the underlying entities. Along the generated paths, the corresponding values and distributions are computed during the entire lifetime of the option. Option values are computed by either the finite difference method for the corresponding partial differential equations, or the simulation-based Stochastic Grid Bundling Method (SGBM), or by the COS method, based on Fourier-cosine expansions. In this research, numerical results are presented for early-exercise options. The underlying asset dynamics are given by either the Black–Scholes or the Heston stochastic volatility model.

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VRINS, FRÉDÉRIC. "WRONG-WAY RISK CVA MODELS WITH ANALYTICAL EPE PROFILES UNDER GAUSSIAN EXPOSURE DYNAMICS." International Journal of Theoretical and Applied Finance 20, no. 07 (November 2017): 1750045. http://dx.doi.org/10.1142/s0219024917500455.

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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 [Formula: see text]-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 [Formula: see text] 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.

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VAN BAKEL, SJOERD, SVETLANA BOROVKOVA, and MATTEO MICHIELON. "CONIC CVA AND DVA FOR OPTION PORTFOLIOS." International Journal of Theoretical and Applied Finance 23, no. 05 (August 2020): 2050032. http://dx.doi.org/10.1142/s0219024920500326.

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In this paper, we propose a framework for credit and debit valuation adjustments (CVA and DVA, respectively) for options and option portfolios which is based on conic finance, that is, where the positions are valued at their bid or ask prices depending on whether they are assets or liabilities. This can be achieved by transforming the pricing measure via appropriate distortion functions, depending on (at least) one parameter. We apply our methodology, which is based on the Wang transform, to portfolios of European commodity futures options, and we show that both CVA and DVA are significantly impacted by bid-ask spreads, when compared to their traditional risk-neutral counterparts. In particular, we show that DVA decreases when computed under conic finance settings, which is in line with the regulatory efforts to rein in DVA gains for financial institutions resulting from their own credit quality deterioration. Finally, we investigate the robustness of our approach with respect to the calibrated parameters, and we show that the calibrated distortion parameter is an excellent explanatory variable for the observed bid-ask spreads.

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STEIN, HARVEY J. "FIXING RISK NEUTRAL RISK MEASURES." International Journal of Theoretical and Applied Finance 19, no. 03 (April 21, 2016): 1650021. http://dx.doi.org/10.1142/s0219024916500217.

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In line with regulations and common risk management practice, the credit risk of a portfolio is managed via its potential future exposures (PFEs), expected exposures (EEs), and related measures, the expected positive exposure (EPE), effective expected exposure (EEE), and the effective expected positive exposure (EEPE). Notably, firms use these exposures to set economic and regulatory capital levels. Their values have a big impact on the capital that firms need to hold to manage their risks. Due to the growth of credit valuation adjustment (CVA) computations, and the similarity of CVA computations to exposure computations, firms find it expedient to compute these exposures under the risk neutral measure. Here, we show that exposures computed under the risk neutral measure are essentially arbitrary. They depend on the choice of numéraire, and can be manipulated by choosing a different numéraire. The numéraire can even be chosen in such a way as to pass backtests. Even when restricting attention to commonly used numéraires, exposures can vary by a factor of two or more. As such, it is critical that these calculations be carried out under the real world measure, not the risk neutral measure. To help rectify the situation, we show how to exploit measure changes to efficiently compute real world exposures in a risk neutral framework, even when there is no change of measure from the risk neutral measure to the real world measure. We also develop a canonical risk neutral measure that can be used as an alternative approach to risk calculations.

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MBAYE, CHEIKH, and FRÉDÉRIC VRINS. "A SUBORDINATED CIR INTENSITY MODEL WITH APPLICATION TO WRONG-WAY RISK CVA." International Journal of Theoretical and Applied Finance 21, no. 07 (November 2018): 1850045. http://dx.doi.org/10.1142/s0219024918500450.

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Credit valuation adjustment (CVA) pricing models need to be both flexible and tractable. The survival probability has to be known in closed form (for calibration purposes), the model should be able to fit any valid credit default swap (CDS) curve, should lead to large volatilities (in line with CDS options) and finally should be able to feature significant wrong-way risk (WWR) impact. The Cox–Ingersoll–Ross (CIR) model combined with independent positive jumps and deterministic shift (JCIR[Formula: see text]) is a very good candidate : the variance (and thus covariance with exposure, i.e. WWR) can be increased with the jumps, whereas the calibration constraint is achieved via the shift. In practice however, there is a strong limit on the model parameters that can be chosen, and thus on the resulting WWR impact. This is because only non-negative shifts are allowed for consistency reasons, whereas the upwards jumps of the JCIR[Formula: see text] need to be compensated by a downward shift. To limit this problem, we consider the two-side jump model recently introduced by Mendoza-Arriaga and Linetsky, built by time-changing CIR intensities. In a multivariate setup like CVA, time-changing the intensity partly kills the potential correlation with the exposure process and destroys WWR impact. Moreover, it can introduce a forward looking effect that can lead to arbitrage opportunities. In this paper, we use the time-changed CIR process in a way that the above issues are avoided. We show that the resulting process allows to introduce a large WWR effect compared to the JCIR[Formula: see text] model. The computation cost of the resulting Monte Carlo framework is reduced by using an adaptive control variate procedure.

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WU, LIXIN, and DAWEI ZHANG. "xVA: DEFINITION, EVALUATION AND RISK MANAGEMENT." International Journal of Theoretical and Applied Finance 23, no. 01 (February 2020): 2050006. http://dx.doi.org/10.1142/s0219024920500065.

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xVA is a collection of valuation adjustments made to the classical risk-neutral valuation of a derivative or derivatives portfolio for pricing or for accounting purposes, and it has been a matter of debate and controversy. This paper is intended to clarify the notion of xVA as well as the usage of the xVA items in pricing, accounting or risk management. Based on bilateral replication pricing using shares and credit default swaps, we attribute the P&L of a derivatives trade into the compensation for counterparty default risks and the costs of funding. The expected present values of the compensation and the funding costs under the risk-neutral measure are defined to be the bilateral CVA and FVA, respectively. The latter further breaks down into FCA, MVA, ColVA and KVA. We show that the market funding liquidity risk, but not any idiosyncratic funding risks, can be bilaterally priced into a derivative trade, without causing price asymmetry between the counterparties. We call for the adoption of VaR or CVaR methodologies for managing funding risks. The pricing of xVA of an interest-rate swap is presented.

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Černý, Jakub, and Jiří Witzany. "Interest Rate Swap Credit Valuation Adjustment." Journal of Derivatives 23, no. 2 (November 30, 2015): 24–35. http://dx.doi.org/10.3905/jod.2015.23.2.024.

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JOSHI, MARK, and OH KANG KWON. "LEAST SQUARES MONTE CARLO CREDIT VALUE ADJUSTMENT WITH SMALL AND UNIDIRECTIONAL BIAS." International Journal of Theoretical and Applied Finance 19, no. 08 (December 2016): 1650048. http://dx.doi.org/10.1142/s0219024916500485.

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Credit value adjustment (CVA) and related charges have emerged as important risk factors following the Global Financial Crisis. These charges depend on uncertain future values of underlying products, and are usually computed by Monte Carlo simulation. For products that cannot be valued analytically at each simulation step, the standard market practice is to use the regression functions from least squares Monte Carlo method to approximate their values. However, these functions do not necessarily provide accurate approximations to product values over all simulated paths and can result in biases that are difficult to control. Motivated by a novel characterization of the CVA as the value of an option with an early exercise opportunity at a stochastic time, we provide an approximation for CVA and other credit charges that rely only on the sign of the regression functions. The values are determined, instead, by pathwise deflated cash flows. A comparison of CVA for Bermudan swaptions and cancellable swaps shows that the proposed approximation results in much smaller errors than the standard approach of using the regression function values.

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27

EL HAJJAJI, OMAR, and ALEXANDER SUBBOTIN. "CVA WITH WRONG WAY RISK: SENSITIVITIES, VOLATILITY AND HEDGING." International Journal of Theoretical and Applied Finance 18, no. 03 (May 2015): 1550017. http://dx.doi.org/10.1142/s021902491550017x.

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We propose a Credit Value Adjustment (CVA) model capturing the Wrong Way Risk (WWR) that is not product-specific and is suitable for large-scale computations. The model is based on a doubly stochastic default process with the default intensities proxied by credit spreads. For different exposure structures, we show how credit–market correlation affects the CVA level, its sensitivities to credit and market factors, its volatility and the quality of hedging. The WWR is most significant for exposures highly sensitive to the market volatility in a situation when credit spreads are at moderate levels but both the market factors and credit spreads are volatile. In such conditions, ignoring credit–market correlations results in important CVA mispricing. While the benefits from hedging are always magnified in the situation of the WWR, the right way exposure case is more delicate: only a well-designed mix of credit and market hedges can bring volatility down. Our results raise doubts on the Basel III policy of recognizing credit but not market hedges for computing the CVA volatility capital charge.

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28

Bo, Lijun, and Agostino Capponi. "Bilateral credit valuation adjustment for large credit derivatives portfolios." Finance and Stochastics 18, no. 2 (November 20, 2013): 431–82. http://dx.doi.org/10.1007/s00780-013-0217-4.

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29

Cherubini, Umberto. "Credit valuation adjustment and wrong way risk." Quantitative Finance Letters 1, no. 1 (December 2013): 9–15. http://dx.doi.org/10.1080/21649502.2013.808029.

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Baviera, Roberto, Gaetano La Bua, and Paolo Pellicioli. "A note on CVA and wrong way risk." International Journal of Financial Engineering 03, no. 02 (June 2016): 1650012. http://dx.doi.org/10.1142/s2424786316500122.

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Hull and White approach to Wrong Way Risk in the computation of Credit Value Adjustment (CVA) is considered the most straightforward generalization of the standard Basel approach. The model is financially intuitive and it can be implemented by a slight modification of existing algorithms for CVA calculation. However, path dependency in the key quantities has non-elementary consequences in the calibration of model parameters. We propose a simple and fast approach for computing these quantities via a recursion formula. We show in detail the calibration methodology on market data and CVA computations in two relevant cases: a FX forward and an interest rate swap.

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31

Xiao, Tim. "An Accurate Solution for Credit Value Adjustment (CVA) and Wrong Way Risk." Journal of Fixed Income 25, no. 1 (June 30, 2015): 84–95. http://dx.doi.org/10.3905/jfi.2015.25.1.084.

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32

BRIGO, DAMIANO, and KYRIAKOS CHOURDAKIS. "COUNTERPARTY RISK FOR CREDIT DEFAULT SWAPS: IMPACT OF SPREAD VOLATILITY AND DEFAULT CORRELATION." International Journal of Theoretical and Applied Finance 12, no. 07 (November 2009): 1007–26. http://dx.doi.org/10.1142/s0219024909005567.

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We consider counterparty risk for Credit Default Swaps (CDS) in presence of correlation between default of the counterparty and default of the CDS reference credit. Our approach is innovative in that, besides default correlation, which was taken into account in earlier approaches, we also model credit spread volatility. Stochastic intensity models are adopted for the default events, and defaults are connected through a copula function. We find that both default correlation and credit spread volatility have a relevant impact on the positive counterparty-risk credit valuation adjustment to be subtracted from the counterparty-risk free price. We analyze the pattern of such impacts as correlation and volatility change through some fundamental numerical examples, analyzing wrong-way risk in particular. Given the theoretical equivalence of the credit valuation adjustment with a contingent CDS, we are also proposing a methodology for valuation of contingent CDS on CDS.

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33

Breton, Michele, and Oussama Marzouk. "Counterparty risk: credit valuation adjustment variability and value-at-risk." Journal of Risk 21, no. 5 (2019): 1–28. http://dx.doi.org/10.21314/jor.2019.411.

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34

Harb, Etienne, and Wael Louhichi. "Pricing CDS spreads with Credit Valuation Adjustment using a mixture copula." Research in International Business and Finance 39 (January 2017): 963–75. http://dx.doi.org/10.1016/j.ribaf.2016.02.003.

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35

Goudenège, Ludovic, Andrea Molent, and Antonino Zanette. "Computing credit valuation adjustment solving coupled PIDEs in the Bates model." Computational Management Science 17, no. 2 (June 2020): 163–78. http://dx.doi.org/10.1007/s10287-020-00365-6.

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36

SCHERER, MATTHIAS, and THORSTEN SCHULZ. "EXTREMAL DEPENDENCE FOR BILATERAL CREDIT VALUATION ADJUSTMENTS." International Journal of Theoretical and Applied Finance 19, no. 07 (November 2016): 1650042. http://dx.doi.org/10.1142/s0219024916500424.

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Recognizing counterparty default risk as integral part of the valuation process of financial derivatives has changed the classical view on option pricing. Calculating the bilateral credit valuation adjustment (BCVA) including wrong way risk (WWR) requires a sound model for the dependence structure between three quantities: the default times of the two contractual parties and the derivative/portfolio value at the first of the two default times. There exist various proposals, but no market consensus, on how this dependence structure should be modeled. Moreover, available mathematical tools depend strongly on the marginal models for the default times and the model for the underlying of the derivative. In practice, independence between all (or some) quantities is still a popular (over-)simplification, which completely misses the root of WWR. In any case, specifying the dependence structure imposes one to model risk and even within some parametric model one typically obtains a considerable interval of BCVA values when the parameters are taken to the extremes. In this work, we present a model-free approach to identify the dependence structure that implies the extremes of BCVA. This is achieved by solving a mass-transportation problem using tools from optimization.

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DURAND, CYRIL, and MAREK RUTKOWSKI. "CVA UNDER ALTERNATIVE SETTLEMENT CONVENTIONS AND WITH SYSTEMIC RISK." International Journal of Theoretical and Applied Finance 16, no. 07 (November 2013): 1350039. http://dx.doi.org/10.1142/s0219024913500398.

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We propose a fairly general framework which allows one to perform Credit Value Adjustment (CVA) computations for a contract with bilateral counterparty risk in the presence of (a) systemic risk and (b) wrong-way or right-way risks. Our methodology focuses on the role of alternative settlement clauses, but it also aims to cover various features of margin agreements. We present a comparative analysis of numerical results that supports our initial conjecture that alternative specifications of settlement values have a nonnegligible impact on CVA computations for contracts with bilateral counterparty risk. Our conclusions emphasize the practical importance of more sophisticated models that are capable of fully reflecting the actual features of financial contracts, as well as the influence of the market environment.

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ALÒS, E., F. ANTONELLI, A. RAMPONI, and S. SCARLATTI. "CVA AND VULNERABLE OPTIONS IN STOCHASTIC VOLATILITY MODELS." International Journal of Theoretical and Applied Finance 24, no. 02 (March 2021): 2150010. http://dx.doi.org/10.1142/s0219024921500102.

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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.

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39

Pykhtin, Michael, and Dan Rosen. "Pricing counterparty risk at the trade level and credit valuation adjustment allocations." Journal of Credit Risk 6, no. 4 (December 2010): 3–38. http://dx.doi.org/10.21314/jcr.2010.116.

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40

BRIGO, Damiano, and Frédéric VRINS. "Disentangling wrong-way risk: pricing credit valuation adjustment via change of measures." European Journal of Operational Research 269, no. 3 (September 2018): 1154–64. http://dx.doi.org/10.1016/j.ejor.2018.03.015.

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41

NG, LESLIE. "NUMERICAL PROCEDURES FOR A WRONG WAY RISK MODEL WITH LOGNORMAL HAZARD RATES AND GAUSSIAN INTEREST RATES." International Journal of Theoretical and Applied Finance 16, no. 08 (December 2013): 1350049. http://dx.doi.org/10.1142/s0219024913500490.

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In this work, we present some numerical procedures for a wrong way risk model that can be used for credit value adjustment (CVA) calculations. We look at a model that uses a multi-factor Hull–White model for interest rates and a single-factor lognormal Black–Karasinski default intensity model for counterparty credit, where the default intensity driver is correlated with all interest rate drivers. We describe how a trinomial tree-based approach for implementing single factor short rate models by Hull and White (1994) can be modified and used to calibrate the intensity model to credit default swaps (CDSs) in the presence of correlation. We also provide approximate pricing methods for CDS options and single swap contingent CDS contracts. The latter methods could also be used for model calibration purposes subject to data availability.

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42

Shiraya, Kenichiro, and Akihiko Takahashi. "Price impacts of imperfect collateralization." International Journal of Financial Engineering 03, no. 01 (March 2016): 1650004. http://dx.doi.org/10.1142/s2424786316500043.

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This paper studies impacts of imperfect collateralization on derivatives values. Particularly, we investigate option prices in no collateral posting and time-lagged collateral posting cases with stochastic volatility, interest rate, and default intensity models, where a stochastic collateral asset value may depend on the values of the assets different from the underlying contract. We also derive an approximation of the credit value adjustment (CVA)’s density function in pricing forward contract with bilateral counter party risk, which seems useful in evaluation of the CVA’s Value-at-Risk (VaR).

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43

van der Zwaard, Thomas, Lech A. Grzelak, and Cornelis W. Oosterlee. "A computational approach to hedging Credit Valuation Adjustment in a jump-diffusion setting." Applied Mathematics and Computation 391 (February 2021): 125671. http://dx.doi.org/10.1016/j.amc.2020.125671.

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44

ANTONELLI, F., A. RAMPONI, and S. SCARLATTI. "RANDOM TIME FORWARD-STARTING OPTIONS." International Journal of Theoretical and Applied Finance 19, no. 08 (December 2016): 1650050. http://dx.doi.org/10.1142/s0219024916500503.

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We introduce a natural generalization of the forward-starting options. The main feature of the contract presented here is that the strike-determination time is not fixed ex-ante, but allowed to be random, usually related to the occurrence of some event, either of financial nature or not. We will call these options random time forward-starting (RTFS). We show that, under an appropriate “martingale preserving” hypothesis, we can exhibit arbitrage free prices, which can be explicitly computed in many classical market models, at least under independence and in absence of simultaneous jumps between the random time and the assets' prices. Practical implementations of the pricing methodologies are also provided. Finally, a credit value adjustment (CVA) formula for these over the counter (OTC) options is computed for the unilateral counterparty credit risk.

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45

SHEN, YANBIN, J. H. M. ANDERLUH, and J. A. M. VAN DER WEIDE. "ALGORITHMIC COUNTERPARTY CREDIT EXPOSURE FOR MULTI-ASSET BERMUDAN OPTIONS." International Journal of Theoretical and Applied Finance 18, no. 01 (February 2015): 1550001. http://dx.doi.org/10.1142/s0219024915500016.

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For an efficient computation of the counterparty credit exposure profiles of the multi-asset options, a simulation-based method, named the Stochastic Grid Bundling Method (SGBM), is applied. The method is based on a 'regression later' technique used for the conditional expectation approximation and a bundling (or 'binning') technique used for state space partitioning. In the case of high-dimensional underlying asset processes, by using the bundling technique, the accuracy of exposure profiles is improved significantly, and the computation speed is reasonably fast. A detailed analysis for the bundling technique and regression approximation technique used in SGBM is given via various numerical examples. We provide an efficiency comparison of SGBM, the Standard Regression Method (SRM), and the Standard Regression Bundling Method (SRBM). We also show that for discontinuous payoffs, such as digital options, by using the bundling technique appropriately, SGBM can get accurate and stable results of option prices and exposure profiles. Compared with the benchmark results of one-dimensional European and Bermudan options, the SGBM has high accuracy in the computation of exposure profiles. The efficient calculation of the expected exposure (EE) by using SGBM forms the basis of the credit value adjustment (CVA) for multi-asset portfolios.

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46

Han, Meng, Yeqi He, and Hu Zhang. "A note on discounting and funding value adjustments for derivatives." Journal of Financial Engineering 01, no. 01 (March 2014): 1450008. http://dx.doi.org/10.1142/s2345768614500081.

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In this paper, valuation of a derivative partially collateralized in a specific foreign currency defined in its credit support annex traded between default-free counterparties is studied. Two pricing approaches — by hedging and by expectation — are presented to obtain similar valuation formulae which are equivalent under certain conditions. Our findings show that the current marking-to-market value of such a derivative consists of three components: the price of the perfectly collateralized derivative (a.k.a. the price by collateral rate discounting), the value adjustment due to different funding spreads between the payoff currency and the collateral currency, and the value adjustment due to funding requirements of the uncollateralized exposure. These results generalize previous works on discounting for fully collateralized derivatives and on funding value adjustments for partially collateralized or uncollateralized derivatives.

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47

Kao, Lie-Jane. "Credit valuation adjustment of cap and floor with counterparty risk: a structural pricing model for vulnerable European options." Review of Derivatives Research 19, no. 1 (July 22, 2015): 41–64. http://dx.doi.org/10.1007/s11147-015-9114-7.

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TAKINO, KAZUHIRO. "AN EQUILIBRIUM MODEL FOR AN OTC DERIVATIVE MARKET UNDER A COUNTERPARTY RISK CONSTRAINT." Journal of Financial Management, Markets and Institutions 06, no. 02 (December 2018): 1850007. http://dx.doi.org/10.1142/s2282717x1850007x.

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In this study, we develop an equilibrium pricing model for an option contract with a counterparty risk, a collateral agreement, a counterparty risk constraint, and a threshold. Since we consider the option market to be an example of the derivatives market, we suppose that the buyer of an option has only countertparty risk of a seller defaulting. In addition, we consider a model where the buyer is allowed to enter into an option contract within an allocated amount of risk capital for counterparty risk, and requires (cash) collateral to the seller if the exposure exceeds the threshold. The counterparty risk is measured as a credit valuation adjustment. We provide an equilibrium pricing rule and an equilibrium volume formula by solving participants’ static utility-maximization problems. Based on numerical simulations, we verify the mechanisms through which collateralization, risk capital, and the threshold affect the size of the over-the-counter (OTC) option market. Finally, we analyze the influence of the buyer’s risk-aversion on the market, without collateralization. The results imply that the risk constraint might be a proxy for an investor’s attitude towards risk.

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Feridun, Mete, and Alper Özün. "Basel IV implementation: a review of the case of the European Union." Journal of Capital Markets Studies 4, no. 1 (July 13, 2020): 7–24. http://dx.doi.org/10.1108/jcms-04-2020-0006.

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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.

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Alavian, Shahram, Jie Ding, Peter Whitehead, and Leonardo Laudicina. "Credit Valuation Adjustment (CVA)." SSRN Electronic Journal, 2008. http://dx.doi.org/10.2139/ssrn.1310226.

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Journal articles on the topic 'Credit valuation adjustment (cva)'

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