Academic literature on the topic 'Wrong Way CVA'

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.

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.

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.

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.

Current CVA modeling framework has ignored the impact of stochastic recovery rate. Due to the possible negative correlation between default and recovery rate, stochastic recovery rate could have a doubling effect on wrong-way risk. In the case of a payer CDS, when counterparty defaults, the CDS value could be higher due to default contagion while the recovery rate may also be lower if the economy is in a downturn. Using our recently proposed model of correlated stochastic recovery in the default time Gaussian copula framework, we demonstrate this double impact on wrong-way risk in the CVA calculation for a payer CDS. We also present a new form of Gaussian copula that correlates both default time and recovery rate.

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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A stock swap transaction is an alternative way for a company who want to enter into a long position on its own stocks or who intend to set up a repurchase program without having to dispose of cash or contract a loan, or even hedging against increases on its stock prices. In this swap transaction the company receives the return on its own stock, whilst paying a fixed or floating interest rate. However, this kind of swap presents wrong-way risk, that is, a positive dependence between the underlying asset and the counterparty’s default probability, which must be considered by dealers when pricing this kind of swap contracts. In this work we propose a model for incorporating dependence between default probabilities and the counterparty’s exposure in the calculation of the CVA for these kind of swaps. We use a Cox process to model default times, given that the stochastic default intensity follows a CIR model, and assuming that the factor driving the underlying stock price and the factor driving the default intensity are jointly given by a bivariate standard Gaussian distribution. We analyze the impact on CVA of incorporating wrong-way risk in this kind of swap transaction with different counterparties, and for different maturities and dependence levels.
Uma forma interessante para uma companhia que pretende assumir uma posição comprada em suas próprias ações ou lançar futuramente um programa de recompra de ações, mas sem precisar dispor de caixa ou ter que contratar um empréstimo, ou então se protegendo de uma eventual alta no preço das ações, é através da contratação de um swap de ações. Neste swap, a companhia fica ativa na variação de sua própria ação enquanto paga uma taxa de juros pré ou pós-fixada. Contudo, este tipo de swap apresenta risco wrong-way, ou seja, existe uma dependência positiva entre a ação subjacente do swap e a probabilidade de default da companhia, o que precisa ser considerado por um banco ao precificar este tipo de swap. Neste trabalho propomos um modelo para incorporar a dependência entre probabilidades de default e a exposição à contraparte no cálculo do CVA para este tipo de swap. Utilizamos um processo de Cox para modelar o instante de ocorrência de default, dado que a intensidade estocástica de default segue um modelo do tipo CIR, e assumindo que o fator aleatório presente na ação subjacente e que o fator aleatório presente na intensidade de default são dados conjuntamente por uma distribuição normal padrão bivariada. Analisamos o impacto no CVA da incorporação do riscowrong-way para este tipo de swap com diferentes contrapartes, e para diferentes prazos de vencimento e níveis de correlação.

In questa tesi consideriamo tre diversi problemi finanziari la cui soluzione è correlata alla media aritmetica di alcuni processi stocastici “mean-reverting”, la cui distribuzione è sconosciuta, impedendo calcoli espliciti ed esatti. Proponiamo approssimazioni basate sui momenti ed esaminiamo le applicazioni nell’ambito del pricing di derivati esotici, rischio di credito e simulazione Monte Carlo e dimostriamo che questo tipo di soluzione può essere molto utile in quanto in grado di ridurre il costo computazionale rispetto a metodi numerici alternativi, che sono usati come benchmark in questo lavoro. Il primo capitolo di questa tesi è dedicato a fornire un background teorico sulle approssimazioni basate sui momenti, inclusi alcuni fatti di base sul cosiddetto moment-problem, tecniche di approssimazioni comuni, insieme a una revisione della letteratura sull'uso dei momenti in finanza e illustrazioni numeriche. Nel secondo capitolo, proponiamo formule di approssimazione precise basate sui momenti per il prezzo delle opzioni asiatiche nel caso in cui il prezzo del sottostante sia un processo stocastico mean-reverting (con salti). Nel terzo capitolo introduciamo una metodologia efficiente, basata su moment matching, per la calibrazione dell'intensità di default, che è modellata attraverso un processo esponenziale di Ornstein-Uhlenbeck e applichiamo questo risultato al calcolo del Credit Value Adjustment (CVA) in presenza di Wrong Way Risk, nell’ambito di derivati sui tassi di interesse. Nel quarto capitolo, consideriamo il problema della simulazione dei modelli di volatilità stocastica. In letteratura sono stati proposti schemi di simulazione esatta per vari modelli, ma sono inefficienti dal punto di vista computazionale a causa della loro dipendenza dall'integrale del processo della varianza, che si presume generalmente sia mean reverting e la cui distribuzione è sconosciuta. In questo caso, mostriamo come calcolare i momenti di tale distribuzione sconosciuta e sviluppiamo una nuova metodologia di simulazione che risulta essere molto più veloce, dal punto di vista computazionale, rispetto agli schemi esatti, per un livello di precisione simile. Il capitolo finale è diverso dagli altri poiché i momenti trovano solo un'applicazione marginale. Consideriamo un modello “double exponential jump-diffusion” in cui l'intensità dei salti è un processo stocastico di tipo Hawkes. Questo tipo di dinamica è stata introdotta in letteratura al fine di modellare il fenomeno del “jump clustering”, ampiamente osservato nei mercati finanziari e delle materie prime. Deriviamo la funzione caratteristica dell'integrale dei log-rendimenti e troviamo formula per il pricing di opzioni asiatiche geometriche sotto tale modello.
In this thesis we consider three different financial problems whose solution is related to the arithmetic average of some mean reverting stochastic process, whose distribution is unknown, precluding explicit and exact computations. We propose moment based approximations and examine applications in exotic derivatives pricing, credit risk and Monte Carlo simulation and show that this kind of solution can be very useful as able to reduce the computational cost with respect to alternative numerical methods, which are used as benchmark throughout this work. The first chapter of this thesis is devoted to provide some theoretical background on moment based approximations, including some basic facts on the so-called \textit{moment problem}, common approximations techniques, together with a literature review on the usage of moments in finance and numerical illustrations. In the second chapter, we propose accurate moment based approximation formulas for the price of Asian options in the case where the underlying's price is a mean reverting (with jumps) stochastic process. In the third chapter we introduce an efficient methodology, based on moment matching, for the calibration of the default intensity, which is modeled through an exponential Ornstein-Uhlenbeck process and apply this result to the calculation of Credit Value Adjustment (CVA) in presence of wrong way risk for interest rates derivatives. In the fourth chapter, we consider the problem of simulating stochastic volatility models. Exact simulation schemes have been proposed in literature for various models, but are computationally inefficient due to their dependence on the integral of the variance process, which is generally assumed to be mean reverting and whose distribution is unknown. In this case, we show how to compute the moments of such unknown distribution and develop a new simulation methodology which turns out to be much faster, from a computational point of view, than exact schemes, for a similar level of accuracy. The final chapter is different from the others as moments find only marginal application. We consider a double exponential jump diffusion model where the jump intensity is a stochastic process of Hawkes type. This kind of dynamics has been introduced in literature in order to model jump clustering phenomenon, widely observed in financial and commodity markets. We derive the characteristic function of the integral of log-returns and price geometric Asian options under such model.

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Apesar das recentes turbulências nos mercados, a utilização de derivativos negociados fora de uma câmara de compensação tem apresentado rápido crescimento, constituindo um dos maiores componentes do mercado financeiro global. A correta inclusão da estrutura de dependência entre fatores de crédito e mercado é de suma importância no apreçamento do risco de crédito adjacente a exposições geradas por derivativos. Este é o apreçamento, envolvendo simulações de Monte Carlo, feito por uma instituição negociante para determinar a redução no valor do seu portfólio de derivativos devido a possibilidade de falência da contraparte. Este trabalho apresenta um modelo com abordagem paramétrica para lidar com a estrutura de dependência, intuitivo e de fácil implementação. Ao mesmo tempo, os números são contrastados com os resultados obtidos através de uma abordagem neutra ao risco para um portfólio replicante, sob o mesmo processo estocástico. O modelo é aplicado sobre um contrato a termo de câmbio, e diferentes cópulas e fatores de correlação são utilizados no processo estocástico.
Despite recent turmoils, the use of derivatives traded outside of a clearinghouse has shown rapid growth and is a major component of the global financial market. The correct inclusion of the dependence structure between market and credit factors is of high importance in the pricing of credit risk exposures generated by the adjacent derivatives. This pricing, involving Monte Carlo simulations, is done by a dealer to determine the reduction in the value of its derivatives portfolio because of the bankruptcy of the counterparty. This paper presents a model with parametric approach to deal with the dependence structure, intuitive and easily implemented. Meanwhile, the numbers are contrasted with results obtained using a risk neutral approach for a replicating portfolio under the same stochastic process. The model is applied on a forward exchange contract, and different copulas and correlation factors are used in the stochastic process.

Nous entamons ce rapport de thèse par l’évaluation de l’espérance espérée qui représente une des composantes majeures des ajustements XVA. Sous l’hypothèse d’indépendance entre l’exposition et les coûts de financement et de crédit, nous dérivons dans le chapitre 3 une représentation nouvelle de l’exposition espérée comme la solution d’une équation différentielle ordinaire par rapport au temps d’observation du défaut. Nous nous basons, pour le cas unidimensionnel, sur des arguments similaires à ceux de la volatilité locale de Dupire. Et pour le cas multidimensionnel, nous nous référons à la formule de la Co-aire. Cette représentation permet d’expliciter l’impact de la volatilité sur l’exposition espérée : Cette valeur temps fait intervenir la volatilité des sous-jacents ainsi que la sensibilité au premier ordre du prix, évalués sur un ensemble fini de points. Malgré des limitations numériques, cette méthode est une approche précise et rapide pour la valorisation de la XVA unitaire en dimension 1 et 2.Les chapitres suivants sont dédiés aux aspects du risque de corrélations entre les enveloppes d’expositions et les coûts XVA. Nous présentons une modélisation du risque général de corrélation à travers une diffusion stochastique multivariée, comprenant à la fois les sous-jacents des dérivés et les intensités de défaut. Dans ce cadre, nous exposons une nouvelle approche de valorisation par développements asymptotiques, telle que le prix d’un ajustement XVA correspond au prix de l’ajustement à corrélation nulle, auquel s’ajoute une somme explicite de termes correctifs. Le chapitre 4 est consacré à la dérivation technique et à l’étude de l’erreur numérique dans le cadre de la valorisation de dérivés contingents au défaut. La qualité des approximations numériques dépend uniquement de la régularité du processus de diffusion de l’intensité de crédit, et elle est indépendante de la régularité de la fonction payoff. Les formules de valorisation pour CVA et FVA sont présentées dans le chapitre 5. Une généralisation des développements asymptotiques pour le cadre bilatéral de défaut est adressée dans le chapitre 6.Nous terminons ce mémoire en abordant un cas du risque spécifique de corrélation lié aux contrats de migration de rating. Au-delà des formules de valorisation, notre contribution consiste à présenter une approche robuste pour la construction et la calibration d’un modèle de transition de ratings consistant avec les probabilités de défaut implicites de marché
The point of departure of this thesis is the valuation of the expected exposure which represents one of the major components of XVA adjustments. Under independence assumptions with credit and funding costs, we derive in Chapter 3 a new representation of the expected exposure as the solution of an ordinary differential equation w.r.t the default time variable. We rely on PDE arguments in the spirit of Dupire’s local volatility equation for the one dimensional problem. The multidimensional extension is addressed using the co-area formula. This forward representation gives an explicit expression of the exposure’s time value, involving the local volatility of the underlying diffusion process and the first order Greek delta, both evaluated only on finite set of points. From a numerical perspective, dimensionality is the main limitation of this approach. Though, we highlight high accuracy and time efficiency for standalone calculations in dimensions 1 and 2.The remaining chapters are dedicated to aspects of the correlation risk between the exposure and XVA costs. We start with the general correlation risk which is classically modeled in a joint diffusion process for market variables and the credit/funding spreads. We present a novel approach based on asymptotic expansions in a way that the price of an XVA adjustment with correlation risk is given by the classical correlation-free adjustment to which is added a sum of explicit correction terms depending on the exposure Greeks. Chapter 4 is consecrated to the technical derivation and error analysis of the expansion formulas in the context of pricing credit contingent derivatives. The accuracy of the valuation approach is independent of the smoothness of the payoff function, but it is related to the regularity of the credit intensity model. This finding is of special interest for pricing in a real financial context. Pricing formulas for CVA and FVA adjustments are derived in Chapter 5, along with numerical experiments. A generalization of the asymptotic expansions to a bilateral default risk setting is addressed in Chapter 6.Our thesis ends by tackling the problem of modeling the specific Right-Way Risk induced by rating trigger events within the collateral agreements. Our major contribution is the calibration of a rating transition model to market implied default probabilities

Counterparty credit risk is an important type of financial risk. The importance of proper counterparty risk management became most apparent in the wake of the 2008 series of failures of several large banks. Correlation of market factors is an important issue in the calculation of CVA. A notable case of correlation is wrong-way risk which occurs whenever the probability of default of the counterparty is positively correlated with exposure. The basic formulas for CVA and basic counterparty credit risk models do not account for wrong-way risk because its modeling is nontrivial. This thesis aims to answer how well can the impact of wrong-way risk on CVA be approximated with an add-on which only depends on correlation between the price of the underlying asset and the credit spread of the counterparty. The thesis is supplemented by a fully documented implementation of the model in the Mathematica software.

This chapter focuses on ‘Operation Iraqi Freedom’, the Iraq War, and one of the key justifications, the claim that Saddam was developing weapons of mass destruction and had to be stopped. Intelligence was crucial to this judgement; but it was wrong. This chapter examines why. It focuses on the challenge of analysis, particularly against mysterious and deceptive targets. How was the CIA to determine that Saddam Hussein had nothing to hide when his actions indicated otherwise? Document: Misreading Intentions: Iraq’s Reaction to Inspections Created Picture of Deception Iraq WMD Retrospective Series.