Counterparty credit risk across all asset classes and Basel III Serguei Issakov Senior Vice President / Quantitative Research & Development, NUMERIX Member of the Committee to Establish the National Institute of Finance (USA)
Committee to Establish the National Institute of Finance National Institute of Finance: US Government agency Goal: Research, understand, and monitor systemic risk Counterparty risk (two institutions) is an important part of systemic risk. Collect and analyze data. Work out standard rules for transaction reporting. www.ce-nif.org/about-us Result: Office of Financial Research at US Treasury April 2011 2
Outline About Numerix Hybrid model framework for pricing and risk computations Basel II and Basel III approaches to counterparty credit risk: credit exposures and credit valuation adjustment Counterparty credit risk with accounting for correlations between asset classes, collateral and netting conditions Unified approach to counterparty credit risk and market risk Relation to generating economic scenarios for insurance industry April 2011 3
Numerix Mission Numerix mission Pricing Models and Methods Taking Analytics Further Implement industry standard models Implement cutting edge models/methods Enhance the existing models by adding more advanced algorithms of calibration and pricing The same principles are applied to Risk, Economic Scenario Generation, Hedging. April 2011 4
Numerix Awards Risk Magazine Technology Ranking 2010 Pricing & Analytics (across all asset classes) 1 Thomson Reuters 2 Murex 3 Bloomberg 4 Numerix Structured products: #1 for several years 1 Numerix 2 Thomson Reuters 3 Murex 4 Bloomberg Structured Products Technology Vendor Ranking 2011 1 Murex 2 Numerix 3 SunGard 4 Pricing Partners 5= Algorithmics, Sophis 7 Misys 8= Calypso, Thomson Reuters 10= Bloomberg, Modelity April 2011 5
Numerix: Partners, Clients, projects examples Partners (>25): Bloomberg, Thomson Reuters, Algorithmics, SunGard, GFI > 400 clients in 25 countries Banks, Hedge Funds, Valuation Providers RBC (N. America), ING, DEPFA, EIB (Europe), NRI (Japan); Yuanta (Taiwan); HDFC (India), NAB, ANZ (Australia) Development Banks: World Bank, EBRD, ADB, AfDB Government: US Treasury Insurance, Pension Groups: MetLife, Aegon Valuation Projects: Lehman Brothers pricing all transactions (~1 million) April 2011 6
Numerix offices Americas New York, Chicago, San Francisco, Vancouver EMEA London, Paris, Dubai Asia Pacific Tokyo, Seoul, Hong Kong, Beijing, Singapore, Mumbai, Sydney Development Offices Santa Fe, Toronto, St. Petersburg April 2011 7
Numerix Quantitative Advisory Board Name Credentials Affiliation Position Alan Brace Co-author of Libor Market Model ( BGM model ) National Australia Bank Adjunct Professor, University of Technology Sydney Vladimir Piterbarg Quant of the Year 2006, 2011 Barclays Capital Head of Quantitative Analytics Peter Carr Quant of the Year 2003 Financial Engineer of the Year 2010 Bruno Dupire Lifetime (Quant) Achievement Award 2008 Morgan Stanley Bloomberg Global Head of Market Modeling Head of Quantitative Research Alex Lipton Quant of the Year 2000 Bank of America Meryl Lynch Leif Andersen Quant of the Year 2001 Bank of America Meryl Lynch Paul Glasserman Quant of the Year 2007 Columbia Business School Marco Avellaneda Quant of the Year 2010 New York University April 2011 8 Co-Head of Global Analytics Group Co-Head of Quantitative Analytics Group Jack R. Anderson Professor of Business Professor of Mathematics Courant Institute of Math Sci. Patrick Hagan Co-author of SABR model JPMorgan Head of Quantitative Analytics
Hybrid Framework Unifying All Asset Classes Universal Hybrid Model Framework April 2011 9
Inflation Market Models 2011 Phase 1: Inflation Market Models, modeling CPI forward rates N. Belgrade, E. Benhamou, E. Koehler (2004); F. Mercurio (2005) Can be calibrated to flat term structure of volatilities, both ZC (Zero coupon) and YY (Year-on-year) sectors. Q1 2011 Phase 2: Inflation Market Models (IMM) with stochastic volatility processes oimm with CIR/Heston stochastic volatility processes F. Mercurio, N. Moreni (2005, Risk 2006) Can be calibrated to the ZC option smiles. Q2 2011 oimm with SABR stochastic volatility processes F. Mercurio, N. Moreni (2009) Can be calibrated to the YY sector option smiles; reasonably recover the ZC sector vols. Q2 2011 April 2011 10
Universal Hybrid Framework Properties Hybrid model properties relevant to risk computations Correlation Structure Correlation matrix links the component models corresponding to different asset classes in a factor-wise manner Calibration Each model is calibrated before being added as a component of a hybrid model Joint calibration is applied when the hybrid model is built Foundation Numerix Generic Monte Carlo method April 2011 11
Generic Monte Carlo Generic Monte Carlo method in Hybrid Models Other names for this method Least Squares Monte Carlo method (Insurance, see e.g. Barrie & Hibbert ) American Monte Carlo method (Risk) G. Cesari, J. Aquilina, N. Charpillon, Z. Filipovic, G. Lee, I. Manda, Modelling, Pricing, and Hedging Counterparty Credit Exposure: A Technical Guide (Springer Finance, February 2010). UBS Capabilities o o Allows for forward and backward Monte Carlo pricing Can price deals of any complexity, including callable path dependent deals April 2011 12
Hybrid models for Economic Scenario Generation Economic Scenario Generation for Insurance Industry Multiple economies / currencies For each economy: IR (Nominal rate) Inflation rate / Real rate Several Credit processes corresponding to different credit rankings Major Equity indexes Several Commodity indexes Algorithm: Calibrate models to historical data or implied volatility data Generate Monte Carlo scenarios in risk neutral or real world measure. Fix the measure by setting expected average future values of rates and indexes. April 2011 13
Exposure Centric Analytics Generalization of Price Analytics to Exposure Analytics Price centric analytics Central object of computation is price, as of today Independent of the stochastic measure Exposure centric analytics Central object of simulation is Exposure: Distribution of prices on future dates Distribution of rates on future dates Depends on the choice of stochastic measure Measure can be fixed by choosing expected future values of rates and indexes, such as Inflation, Equity, FX, and Commodity indexes April 2011 14 l
Numerix White Paper Advanced Risk (2010) Table of Contents 1 Introduction 2 Generic Monte Carlo method 3 Instruments 3.1 Exercises and Payments 3.2 Instrument pricing by backward induction 4 Exposure 4.1 Definition 4.2 Decomposition and Calculation 4.3 Exposure distribution 5 Risk measures for Market Risk and Counterparty Credit Risk 5.1 Value at Risk and Expected Shortfall 5.2 Potential Future Exposure, Expected Positive Exposure 6 Probability measure change 6.1 Example of two currencies 6.2 Measure change and discounted expectations 6.3 Measure change and non-discounted expectations 6.4 Measure change and risk calculus 6.5 Measure change and Brownian motion 7 Real-world measure 8 Credit Valuation Adjustment 8.1 Unilateral CVA 8.2 Bilateral CVA 8.3 Debit Valuation Adjustment (DVA) 8.4 Averaging over jumps and finite sum approximation 9 Close-Out Risk April 2011 15
Exposure Centric Analytics Applications & Benefits Applications Market Risk (Monte Carlo Value at Risk, Expected Shortfall) Counterparty Credit Risk (Basel II and Basel III approaches) Economic Scenario Generation (Insurance) Benefits Unified language for Pricing (Front Office) an Risk (Middle Office) The same accuracy and computation consistency for Risk as for Pricing Unified language for Pricing, Risk, and Economic Scenario Generation Works uniformly across all types of financial instruments (covered by Hybrid Framework, i.e. except for large credits baskets at this time) April 2011 16
Exposure computation and aggregation Exposure kernels for individual deals/instruments: Compute exposures Exposur e Kernel Exposur e Kernel Exposur e Kernel Exposure computations are independent for individual deals Advanced Risk Report (i)aggregates exposures across portfolio (ii)computes risk measures Monte Carlo VaR CCE (Counterparty Credit Exposure) CVA (Credit Valuation Adjustment) 3 types of Exposure Kernels 3 types of Advanced Risk Reports April 2011 17
Counterparty Credit Risk Definition The risk taken on by an entity ( Investor, Self ) entering an OTC contract ( Underlying ) that a counterparty will default prior to the expiration of the contract and will be unable to make all contractual payments. Factors that impact counterparty risk OTC contract's underlying volatility Counterparty credit spreads volatility Correlation between the underlying and default of the counterparty Consequence: Credit hybrid model is required (credit process for the counterparty, correlated with the processes for the underlying) April 2011 18
Counterparty Risk Credit Exposures and CVA Counterparty Credit Exposure Basel II Loss amount if the counterparty defaults at a future time o Assumes no recovery o Does not depend on the probability of default Risk measures Potential Future Exposures (PFE), Maximum PFE Expected Positive Exposures (EPE), Effective EPE Credit Valuation Adjustment (CVA) Basel III Adjustment to a derivative price based on the counterparty default risk o Price of the counterparty credit risk o Accounts for the probability of default and recovery rate o Can be applied to any financial instrument April 2011 19
CVA risk Basel III timeline Credit Valuation Adjustment (CVA) risk part of Basel III Dec 2009 Draft of Basel III Dec 2010 Final set of standards Basel III: A global regulatory framework for more resilient banks and banking systems 14. To this end, the Committee is introducing the following reforms: (b) Banks will be subject to a capital charge for potential mark-to-market losses (ie credit valuation adjustment CVA risk) associated with a deterioration in the credit worthiness of a counterparty. While the Basel II standard covers the risk of a counterparty default, it does not address such CVA risk, which during the financial crisis was a greater source of losses than those arising from outright defaults. 1 Jan 2013 Implementation target 97. This section outlines the reforms to the counterparty credit risk framework, which become effective on 1 January 2013. April 2011 20
CVA risk Basel III Model Calibration Basel III: A global regulatory framework for more resilient banks and banking systems (Dec 2010) 61. When the Effective EPE model is calibrated using historic market data, the bank must employ current market data to compute current exposures and at least three years of historical data must be used to estimate parameters of the model. Alternatively, market implied data may be used to estimate parameters of the model. Our models use market implied data for calibration. 25(i). To determine the default risk capital charge for counterparty credit risk as defined in paragraph 105, banks must use the greater of the portfolio-level capital charge (not including the CVA charge in paragraphs 96-104) based on Effective EPE using current market data and the portfolio-level capital charge based on Effective EPE using a stress calibration. The stress calibration should be a single consistent stress calibration for the whole portfolio of counterparties. The greater of Effective EPE using current market data and the stress calibration should not be applied on a counterparty by counterparty basis, but on a total portfolio level. We have the analytics to compute the first part (Effective EPE) and need to add stress calibration. April 2011 21
Basel Committee 2 more press releases Sound practices for backtesting counterparty credit risk models (Dec 2010) Very specific backtesting rules Consultative Document Capitalisation of bank exposures to central counterparties (Dec 2010) April 2011 22
ISDA Roadmap for Collateral Management June 30, 2010 ISDA Best Practices for the OTC Derivatives Collateral Process OTC derivative trades collateralized on a bi-lateralbasis under the ISDA English and New York law Credit Support Annexes (CSAs) and English Law Credit Support Deed (CSD) agreed between two parties. June 30, 2010 (Fed Commitment) Start monthly unilateral portfolio reconciliation with OTC Counterparties comprising more than 1,000 trades 2011 Phase II Increasing the frequency of reconciling individual collateralized portfolios over 1,000 trades from a minimum of monthly to weekly Expanding commitments to reconcile any collateralized portfolio comprising more than 500 trades at least monthly Periodic reconciliation of portfolios with less than 500 trades April 2011 23
Collateral and Netting Agreements Used for o Counterparty Credit Exposure (PFE, Expected Positive Exposure) o Credit Valuation Adjustment (CVA) Collateral agreements Collateral type: Cash Equity, Commodity Government bonds Arbitrary asset Collateral agreements features Initial margin Schedule of margin calls Threshold Minimum transfer amount Margin period of risk Netting agreements: Netting agreements per netting set for a given counterparty April 2011 24
CVA, DVA, and BCVA Credit Valuation Adjustment (CVA) Account for default of Counterparty Debit Valuation Adjustment (DVA) Account only for default of Self Bilateral CVA (BCVA) Account for default of both Counterparty and Self Collaterals are used on both sides of transaction, by Self and Counterparty April 2011 25
Credit Valuation Adjustment General Definition CVA is the price of the counterparty credit risk Calculation: risk neutral expectation of the discounted loss over the life of the longest transaction CVA E Q [(1 RR) ( t < τ T ) D( t, τ ) E( τ )] = 1 C C C RR is counterparty-level recovery rate τ C is counterparty s default time D( t, τc) is discount factor E( τ ) = [ V ( τ ), 0] + is contract level exposure V (t) is contract value April 2011 26
Credit Valuation Adjustment Constant Recovery Value of the contract accounting for the Counterparty default (Investor is default free) E { D } V ( t, T ) E { V ( t, T ) } t = t { + } ( t < τ T ) D( t, τ ) [NPV ( τ ) LGD E ] t 1 C C C 1 st term: Value without counterparty risk. 2 nd term: Counterparty risk adjustment (CVA). [ NPV ( τ C)] = Eτ { V ( τ C, T ) } is the value of the contract on the C counterparty default date. LGD = (1 RR) for Counterparty. April 2011 27
Bilateral CVA Bilateral risk CVA (accounting for the default of Investor/Self) E { D } V ( t, T ) E { V ( t, T ) } t = t { + } ( τ ) D(, τ ) [NPV ( τ ) LGDC Et 1 τ C I t C C ] { + } ( τ ) D(, τ ) [ NPV ( τ ) + LGDI Et 1 τ I C t I I ] 1 st term: Value without counterparty risk 2 nd term: CVA Counterparty defaults before Investor 3 rd term: CVA Investor defaults before Counterparty If computed from the point of view of counterparty, the CVA adjustment in opposite. Brigo, D., and Capponi, A. (2009) For more general formulas with collaterals, see Numerix Advanced Risk white paper (2010) April 2011 28
Workflow of computing CVA Computing CVA in Numerix hybrid model framework Construct a hybrid model for pricing a portfolio with a given Counterparty Add a credit process for Counterparty Add a credit process for Self Add Collateral Conditions Add Netting Conditions Compute Exposures Compute CVA, DVA, BCVA April 2011 29
Conclusions Numerix Hybrid Model Framework provides a uniform way to compute Monte Carlo VaR / Expected Shortfall Counterparty Credit Exposure Credit Valuation Adjustment across all asset classes and financial instrument types. It accounts, by the hybrid model construction, for correlations between risk factors from all asset classes. April 2011 30
Thank You! serguei.issakov@numerix.com www.numerix.com/serguei-issakov www.linkedin.com/in/sergueiissakov