Disentangling Wrong-Way Risk: Pricing CVA via Change of Measures and Drift Adjustment

Brigo, Damiano; Vrins, Frédéric

doi:10.2139/ssrn.3366804

Cited by 8 publications

(23 citation statements)

References 25 publications

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“…Hence, τ is a G-stopping time, but not an F-stopping time. In such a case, one can replace G s by F s in the expression providing the time-s price of the risk-free ZCB: It is originally due to Dellacherie and Meyer Dellacherie and Meyer (1980), although its use in financial applications have been put forward by Bielecki, Jeanblanc and Rutkowski Bielecki and Rutkowski (2002) (see, e.g., Bielecki et al (2011) for numerous examples in credit risk and Brigo and Vrins (2018) for a specific application in counterparty credit risk). Applying the Key lemma to the risky ZCB formula above yields, with X ← e − t s rudu , P r…”

Section: Discounting In a Defaultable Marketmentioning

confidence: 99%

See 1 more Smart Citation

Affine Term-Structure Models: A Time-Changed Approach with Perfect Fit to Market Curves

Mbaye

Vrins²

2019

SSRN Journal

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We address the so-called calibration problem which consists of fitting in a tractable way a given model to a specified term structure like, e.g., yield, prepayment or default probability curves. Time-homogeneous jump-diffusions like Vasicek or Cox-Ingersoll-Ross (possibly coupled with compound Poisson jumps, JCIR, a.k.a. SRJD), are tractable processes but have limited flexibility; they fail to replicate actual market curves. The deterministic shift extension of the latter, Hull-White or JCIR++ (a.k.a. SSRJD) is a simple but yet efficient solution that is widely used by both academics and practitioners. However, the shift approach may not be appropriate when positivity is required, a common constraint when dealing with credit spreads or default intensities. In this paper, we tackle this problem by adopting a time change approach, leading to the TC-JCIR model. On the top of providing an elegant solution to the calibration problem under positivity constraint, our model features additional interesting properties in terms of variance. It is compared to the shift extension on various credit risk applications such as credit default swap, credit default swaption and credit valuation adjustment under wrong-way risk. The TC-JCIR model is able to generate much larger implied volatilities and covariance effects than JCIR++ under positivity constraint, and therefore offers an appealing alternative to the shift extension in such cases.Model calibration is a standard problem in many areas of finance Brigo and Mercurio (2006);Joshi (2003); Veronesi (2010). It consists of tuning a model such that it "best fits" market quotes at a given time. As an example, financial markets provide a set of prices associated with liquid instruments, that openly trade on the market. Alongside with risk management (hedging), the main purpose of a model here is to act as an "interpolation/extrapolation" tool, i.e., to obtain the value of products at a given time t for which the market does not disclose prices in a transparent way. This could happen because either the product to be priced is "exotic" (i.e., is too "special", it does not quote openly on a platform, only on a bilateral basis) or because its cashflow schedule is not in line with the products that currently trade openly at t (a situation that commonly happens since products that were "standard" at inception, may have time-to-expiry or moneyness levels that are no longer "standard" afterwards).Mathematically, model calibration is nothing but an optimization problem. Starting from a set of prices quoted on the market (called "market prices") for a set of specific financial products (called "calibration instruments"), model calibration consists of computing the model parameters such that the prices generated by the model (called "model prices") best fit to the market prices, according to some error function. Model calibration is crucial in finance;it is strongly related to arbitrage opportunities. In practice, only models that are able to reproduce the market prices of "simple instruments" ...

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Section: Discounting In a Defaultable Marketmentioning

confidence: 99%

“…However, the independent case ρ = 0 is unrealistic, and may lead to severe over or underestimations of CVA Kim and Leung (2016); Brigo and Vrins (2018); Breton and Marzouk (2018).…”

Section: Wrong-way Risk Impact In Credit Valuation Adjustmentsmentioning

confidence: 99%

Affine Term-Structure Models: A Time-Changed Approach with Perfect Fit to Market Curves

Mbaye

Vrins²

2019

SSRN Journal

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“…In other words, CVA only depends separately on the expected discounted exposure E V + u Bu and the prevailing mrisk-neutral survival probability curve G 0 (.). We refer to [6] for more details.…”

Section: Cva Formula In the Diffusion Modelmentioning

confidence: 99%

A Subordinated CIR Intensity Model with Application to Wrong-Way Risk CVA

Mbaye

Vrins²

2018

SSRN Journal

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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 model (CIR) combined with independent positive jumps and deterministic shift (JCIR++) 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++ need to be compensated by a downward shift. To limit this problem, we consider the two-side jump model recently introduced by Mendoza-Arriaga & Linetsky, built by time-changing CIR intensities. In a multivariate setup like CVA, time-changing the * Voie du Roman Pays 34, 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++ model. The computation cost of the resulting Monte Carlo framework is reduced by using an adaptive control variate procedure.

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“…where x + := max(x, 0). It has been shown in [1] that when the default time is modeled as the first jump's time of a Cox process, the "τ = s" condition in the expectation in Eq. (1) -associated to market-credit dependency that is, to wrong-way risk -can be absorbed in the drift of the portfolio price process:…”

Section: Introductionmentioning

confidence: 99%

“…Here, C t is a rolling numéraire corresponding to the default leg of a CDS offering protection in a small interval around t, and is not to be confused with the call option price at t, noted C t . We refer the reader to [1] for more details about this technique. We define the expected positive exposure (EPE) without taking wrongway risk into account as the expectation in Eq.…”

Section: Introductionmentioning

confidence: 99%

Wrong-Way Risk Adjusted Exposure: Analytical Approximations for Options in Default Intensity Models

Brigo

Hvolby

Vrins

2018

Innovations in Insurance, Risk- And Asset Management

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We examine credit value adjustment (CVA) estimation under wrong-way risk (WWR) by computing the expected positive exposure (EPE) under an equivalent measure as suggested in [1], adjusting the drift of the underlying for default risk. We apply this technique to European put and call options and derive the analytic formulas for EPE under WWR obtained with various approximations of the drift adjustment. We give the results of numerical experiments based on 4 parameter sets, and supply figures of the CVA based on both of the suggested proxys, comparing with CVA based on a 2D-Monte Carlo scheme and Gaussian Copula resampling. We also show the CVA obtained by the formulas from Basel III. We observe that the Basel III formula does not account for the credit-market correlation, while the Gaussian Copula resampling method estimates a too large impact of this correlation. The two proxies account for the credit-market correlation, and give results that are mostly similar to the 2D-Monte Carlo results.

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Disentangling Wrong-Way Risk: Pricing CVA via Change of Measures and Drift Adjustment

Cited by 8 publications

References 25 publications

Affine Term-Structure Models: A Time-Changed Approach with Perfect Fit to Market Curves

Affine Term-Structure Models: A Time-Changed Approach with Perfect Fit to Market Curves

A Subordinated CIR Intensity Model with Application to Wrong-Way Risk CVA

Wrong-Way Risk Adjusted Exposure: Analytical Approximations for Options in Default Intensity Models

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