CVA Challenges in Methodology and Implementation

CVA – Challenges in Methodology

and Implementation

Prof. Dr. Marcus R.W. Martin Hochschule Darmstadt

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Credit Valuation Adjustment (CVA) - Definition

Implementation and Methodology

Regulatory Framework

Outlook

Prof. Dr. Marcus R.W. Martin

Professor für Finanzmathematik und Stochastik Fachbereich Mathematik und Naturwissenschaften Hochschule Darmstadt

Email: [email protected] / URL: http://fbmn.h-da.de/~martin fb mn

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Pre-Crisis Pricing of Derivatives did not take any credit risks into

account (default-free pricing).

To adjust for the price of credit risk, the credit risk-free price has to be adjusted by the so-called Credit Valuation Adjustments (CVA) :

(unilateral) price of credit risk (as the price of the protection leg of a

„virtual“ Credit Default Swap) is given as the risk-neutral expectation of future cash-flows

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risk-neutral

expectation recovery rate (stochastic) of the risk-neutral discounting short rate (stochastic) exposure at time u distribution of the (risk-neutral) default

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1. Credit Valuation Adjustment (CVA)

Under simplifying assumptions we obtain the Basel III CVA position (for advanced institutions applying the Internal Model Method (IMM) and the Internal Model Approach (IMA) including specific risk modeling) as a numerical approximation:

where

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Definition of CVA

inspired by regulatory point of view (Basel III); still not consistent among market participients!

Unilateral vs. Bilateral CVA (a.k.a. DVA)? Market data and calibration

risk-neutral / market-implied (fall-back: historic) liquid vs. illiquid (segmentation of counterparties?) Intended/Preferred way to deal with CVA:

set up CVA trading desk to actively manage CVA vs.

accounting- or reserve-based approach fb mn

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2. Implementation & Methodology

Post-crisis pricing models (discounting rates vs. tenor-specific rates

and implied volatilities, funding constraints, …) in future exposure calculation:

increasing complexity of pricing models post-crisis (even for

plain vanilla products due to multiple-curve interest rate framework in CVA calculations; cf. Crépey (2011))

capture all products (scenario-consistent approach; avoiding

nested MC simulations for complex products; applicability of Delta-Gamma-approximations, cf. Bree & Linder (LMW, 2011))

real-time pricing (trading / CVA desks?)

calculation of sensitivities, marginal CVA/DVA, hedging … (cf.

Capriotti, Lee & Peacock (RISK, June 2011), and Bree, Linder & Schlener (LMW, 2011))

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Future Exposure calculations / models

segmentated (classical) vs. integrated (UBS) approach (cf. Gregory

(2009) and Cesari et al. (2009); a promising new approach to handle calibration and pricing of exotic instruments is provided by Andreasen & Huge (RISK, July 2011))

backtesting (risk factor, trade level, portfolio level, netting set –

best-practices still evolving; cf. Ackermann, Putschögl & Wickenhauser (LMW, 2011))

stresstesting (choice of scenarios, reverse stress testing; best

practices still evolving; cf. Blochwitz & Martin (LMW, 2011))

Collateral / margining (margin period of risk were conservatively

adjusted in Basel III; improved collateral management processes are requested; cf. Böcker & Schröder (LMW, 2011))

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2. Implementation & Methodology

Efficient Data Model & IT architecture necessary! (cf. Schlener

(PRMIA, 2011), Ackermann, Putschögl & Wickenhauser (LMW, 2011), and Engelbrecht & Ludwig (LMW, 2011))

Wrong Way Risk (effect of positive correlation between exposure and

default probability)

specific WWR positions have to be carved out from netting sets and are charged with extra regulatory capital according to Basel III, general WWR is still captured in the alpha-factor for IMM; for an overview we refer to Cesari et al. (2009) and Gregory (2009).

Explicit modeling of WWR is done by Hull & White (Working Paper, June 2011) and Rosen (RiskLab, June 2011); for some heuristic considerations as well as semi analytic models see Stürmer (M.Sc. Thesis, to appear August 2011).

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Cross-Gamma Effects (in particular if the exposure driving market

variables are highly correlated to the credit spreads, are an important source for WWR; cf. Plank (LWM, 2011))

Model Risks (exposure and CVA calculations are based on rather

complex models to assess credit quality, recovery rates, evolution of market risk factors as well as potential future market prices; for different flavours of this topic we refer cf. Gregory (2009), Martin (2010), Beck (M.Sc. Thesis, 2010) and Noé (M.Sc. Thesis, 2011))

The new Regulatory Framework is sketched in the following section. For further details and background we refer to the excellent paper by Hj. Schmidt (LMW, 2011); see also Martin (2011).

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Basel III regulatory framework:

3. Regulatory Framework

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Standardised CVA Charge

(S-CVA) Advanced CVA Charge(A-CVA)

yes yes yes no no no OTC Derivatives SFT* 01/01/2013 *) if material Scope of application

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Standardized CVA Charge (S-CVA)

is based on a single factor credit portfolio model for all counterparties (applying a factor correlation ρ=50%) which

adopts the simplifying equivalent bond approach (!) for calculating CVA: This yields a closed-form expression for the 1 year CVA-VaR on a confidence level of 99% which measures the potential market risk gains and losses of CVA w.r.t. declining or improving credit quality of the counterparties in terms of credit spread (CDS spread, if available).

Exposures are calculated according to the regulatory applicable method for the institution (CEM, SM or, if approved, IMM) and

only a rather restricted set of hedging instruments is allowed (e.q. single name CDS, Index-CDS) to off-set CVA market risk.

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3. Regulatory Framework

Advanced CVA Charge (A-CVA)

is based on the credit spread VaR of the CVA-position calculated in the specific risk component/module of the internal market risk model on a 99% confidence level over a 1 year horizon

including the stressed VaR on the total counterparty position

(according to Basel 2.5 requirements) but excluding the incremental risk charge (IRC)!

Therefore, the regulatory capital is given by

K_CCR := max{K_defIMM, K

def,stressedIMM} + 3.x .

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where 3.x is the market risk addon given by the national regulator when approving the internal market risk model and

the first part of the above formula refers to the IMM regulatory

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Consistent framework and market practices for efficient calculation of counterparty exposures?

Regulatory Developments?

Recalibration of „standardized methods“? Internal CVA models?

Further requirements on backtesting and stresstesting due to evolving market practices and standards?

Integrated market-credit risk models

Alpha and IRC calculation as a first steps towards (fully) integrated market-credit risk models; will become regulatory focus.

Wrong way risk is one particular aspect of this.

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Bibliography

Andreasen, J. & Huge, B.: Random grids. RISK, July 2011.

Capriotti, L., Lee, J. & Peacock, M.: Real time counterparty credit risk management in Monte Carlo, RISK, June 2011.

Cesari, G., J. Aquilina, N. Charpillon, Z. Filipovic, G. Lee, and I. Manda: Modelling, Pricing, and Hedging Counterparty Credit Exposure. Springer Finance, 2009.

Crépey, S.: A BSDE approach to Counterparty Risk under Funding Constraints. Working Paper, Université d’Évry Val d’Essonne, June 2011.

Gregory, J.: Counterparty Credit Risk: The New Challenge for Global Financial Markets. Wiley, 2009.

Hull, J.C. & A. White: CVA and Wrong Way Risk, Working Paper, University of Toronto, June 2011.

Martin, M.R.W.: Model risk in Counterparty Exposure Modeling. In: Model Risk

Evaluation Handbook, ed. Hoppe, Ch., Gregoriou, G.N., Wehn, C.S., McGraw-Hill, 2010. Martin, M.R.W.: Messung von Kontrahentenrisiken – IMM, Zentrale Kontrahenten und CVA. Kundensymposium 1 plus i GmbH, Frankfurt am Main, May 2011.

Rosen, D.: CVA, Basel III and Wrong-Way Risk, IX RiskLab Madrid Meeting on Financial Risks, May 2011

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Valuation Adjustments und Kontrahenten-exposures nach Basel III, Praxiswissen für ökonomische und regulatorische Aspekte, Herausgegeben von S. Ludwig, C.S. Wehn & MRWM, erscheint im Schäffer-Poeschel Verlag, 2011 (i.F. (LMW, 2011)).

Ackermann, F., Putschögl, W. & Wickenhauser, M.: Methodische Umsetzung der Berechnung des Kontrahentenrisikos und des Credit Valuation Adjustments in der Praxis.

Blochwitz, S. & Martin, M.R.W.: Stresstests für Kontrahentenexposures und Credit Valuation Adjustments.

Böcker, K. & Schröder, B.: Collateral Management.

Bree, Ch. & Linder, A.: Semi analytische Approximation des Credit Valuation Adjustments.

Bree. Ch., Linder, A. & Schlener, M.: Einsatz von Derivaten zum Hedging. Engelbrecht, S. & Ludwig, S.: Technische Implementierung.

Plank, M.: Credit Valuation Adjustments – Eine kurze mathematische Einführung und ein praktischer Überblick.

Schmidt, Hj.: Basel III und CVA aus regulatorischer Sicht.

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Bibliography

Master Theses on Counterparty Risk (advised by MRWM, finalized or close-to-finalized ones only - further counterparty risk Master Theses on the way; available at URL http//www.fbmn.h-da.de/~martin/):

T. Beck:A Market Model Approach for Measuring Counterparty Credit Risk of Interest Rate Derivatives. Hochschule Darmstadt, April 2010.

M. Noé: Valuation of Counterparty Risk for Commodity Derivatives. Hochschule Darmstadt, July 2011.

S. Stürmer: Das Kontrahentenrisiko und die besondere Rolle der Besicherung und des Wrong Way Risk. Bearbeitungsende voraussichtlich Ende August 2011.

Prof. Dr. Marcus R.W. Martin

Professor für Finanzmathematik und Stochastik Fachbereich Mathematik und Naturwissenschaften Hochschule Darmstadt

Email: [email protected]