Bielecki credit risk frontiers; subprime crisis, pricing and hedging, CVA, MBS, ratings, and liquidity (2011)

CREDIT RISK FRONTIERSSubprime Crisis, Pricing and Hedging, CVA, MBS, Ratings, and Liquidity Tomasz R.. CHAPTER 8 Options on Credit Default Swaps and CreditMarek Rutkowski PART III: CREDI

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CREDIT RISK FRONTIERS

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CREDIT RISK FRONTIERS

Subprime Crisis, Pricing and Hedging, CVA, MBS, Ratings, and Liquidity

Tomasz R Bielecki, Damiano Brigo, and Fr´ed´eric Patras

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Copyright
C 2011 by Tomasz R Bielecki, Damiano Brigo, and Fr´ed´eric Patras All rights reserved.

Published by John Wiley & Sons, Inc., Hoboken, New Jersey.

Published simultaneously in Canada.

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Library of Congress Cataloging-in-Publication Data:

1 Credit derivatives—United States 2 Global financial crisis, 2008–2009 I Brigo, Damiano, 1966–

II Patras, Fr´ed´eric III Title.

HG6024.U6B54 2011 332.64'57—dc22

2010045236 Printed in the United States of America

iv

Greg M Gupton

Tomasz R Bielecki, Damiano Brigo, and Fr´ed´eric Patras

PART I: EXPERT VIEWS CHAPTER 1

Jean-Pierre Lardy

CHAPTER 2

Benjamin Herzog and Julien Turc

PART II: CREDIT DERIVATIVES: METHODS CHAPTER 3

Igor Halperin

CHAPTER 6 Dynamic Hedging of Synthetic CDO Tranches: Bridging the

Areski Cousin and Jean-Paul Laurent

CHAPTER 7

R¨udiger Frey and Thorsten Schmidt

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CHAPTER 8 Options on Credit Default Swaps and Credit

Marek Rutkowski

PART III: CREDIT DERIVATIVES: PRODUCTS CHAPTER 9

Valuation of Structured Finance Products with

Jovan Nedeljkovic, Dan Rosen, and David Saunders

CHAPTER 10 Toward Market-Implied Valuations of Cash-Flow

Philippos Papadopoulos

CHAPTER 11 Analysis of Mortgage-Backed Securities: Before and

Harvey J Stein, Alexander L Belikoff, Kirill Levin, and Xusheng Tian

PART IV: COUNTERPARTY RISK PRICING AND CREDIT VALUATION ADJUSTMENT

CHAPTER 12 CVA Computation for Counterparty Risk Assessment in

Samson Assefa, Tomasz R Bielecki, St´ephane Cr´epey, and Monique Jeanblanc

CHAPTER 13 Structural Counterparty Risk Valuation for

Christophette Blanchet-Scalliet and Fr´ed´eric Patras

CHAPTER 14 Credit Calibration with Structural Models and Equity Return

Damiano Brigo, Massimo Morini, and Marco Tarenghi

CHAPTER 15

Harvey J Stein and Kin Pong Lee

CHAPTER 16

Michael Pykhtin

PART V: EQUITY TO CREDIT CHAPTER 17

Benjamin Herzog and Julien Turc

CHAPTER 18

Vadim Linetsky and Rafael Mendoza-Arriaga

PART VI: MISCELLANEA: LIQUIDITY, RATINGS, RISK CONTRIBUTIONS, AND SIMULATION

CHAPTER 19

Damiano Brigo, Mirela Predescu, and Agostino Capponi

CHAPTER 20 Stressing Rating Criteria Allowing for Default Clustering:

Roberto Torresetti and Andrea Pallavicini

CHAPTER 21

Pierre Del Moral and Fr´ed´eric Patras

CHAPTER 22

Dan Rosen and David Saunders

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The current economic environment, with its unprecedented global financial crisis andslow resolution, has stimulated a wealth of innovative and constructive solutions incredit risk modeling and credit derivatives in particular While it is true that thisvolume includes some of the more important research of the past year, significantly,

I credit the editors for having facilitated a heightened quality within the individualcontributions

Importantly, chapters are split with a good balance of the theoretical versus thepractical Especially since 2007, credit markets have extraordinarily stressed boththeoretical frameworks and empirical calibrations

Similarly, and refreshingly, contributing authors are evenly split between academicversus practitioners from industry For example, different contributions on collateral-ized debt obligations (CDOs) illustrate the diversity

Parenthetically, I have been continually amazed these past two years to see thatnew CDO research has been the fastest growing category of research posted onDefaultRisk.com This is quite ironic because the new issuance of CDOs has collapsed

to a small fraction of 2007 levels

I feel this volume of research is explained by not only the existing/troublinginventory of CDOs that must be managed, but also because CDOs—as a structure—offer a defined microcosm of the larger/general credit portfolio

There are gratifyingly few redundancies across the contributing authors Of course,

it is beneficial to have a good diversity of views brought from different perspectives Forexample, the different collateralized loan obligation (CLO) and residential mortgage-backed security (RMBS) chapters offer complementary discussions

By contrast, it is not at all surprising that several contributions address the evermore liquid credit default swap (CDS) market, their options, and their liquidity.Other important and very timely contributions concern counterparty risk and creditvaluation adjustment (CVA), which are here addressed in five chapters, and hybridmodeling of credit and equity, which is addressed in a novel way

These are just a few examples of the innovation and originality in a single volumethat has, among other merits, the courage to deal in a single source with several urgenttopics such as the subprime crisis, pricing and hedging of credit risk, CVA, CDO,CLO, MBS, ratings, and liquidity

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Finally, this volume would not have been possible without the diligent work thispast year from many people too numerous to list Beyond the editors and contributingauthors, we are grateful to all the conference attendees and panel members in September

2009 at the Universit´e de Nice Sophia Antipolis The interaction was spirited and thecomments were invaluable Enjoy

GREGM GUPTON

May 2010DefaultRisk.comAuthor of the CreditMetrics Technical Document

CREDIT RISK FRONTIERS

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The recent decade has witnessed a rapid development of more and more advancedquantitative methodologies for modeling, valuation, and risk management of creditrisk, with focus on credit derivatives that constitute the vast majority of credit markets

In part, this rapid development was a response of academics and practitioners to thedemands of trading and risk managing in the rapidly growing market of more andmore complex credit derivative products Even basic credit derivatives such as creditdefault swaps (CDSs) have witnessed considerable growth, reaching a notional value

of US$45 trillion by the end of 2007, although notional amounts fell during 2008 to

$38.6 trillion.1More complex credit derivatives, such as collateralized debt obligations(CDOs), featured a global issuance of $157.8 billion in 2004, reaching $481 billion

in 2007, although in 2009 this has gone down to $4.3 billion.2

The size and complexity of credit markets in general, and credit derivatives markets

in particular, undoubtedly posed a challenge for (quantitative) modelers and for marketpractitioners The recent turmoil in the credit markets can be attributed to manyfactors, but one of the factors is probably the fact that in many respects the challengehas not been properly addressed

This volume studies aspects of modeling and analysis of credit risk that, in ouropinion, have not been adequately understood in the past This is immediately evidentalso from the book subtitle, in that counterparty risk, mortgage-backed securities(MBSs), liquidity modeling, ratings, and in general pricing and hedging of complexcredit derivatives are all among the areas that have not been fully or adequatelyaddressed

An important and original feature of this book is that it gathers contributionsfrom practitioners and academics in an equilibrated way Whereas the practitioners’contributions are deeply grounded in concrete experience of markets and products,the contributing academics are often involved in consulting and similar activities andhave therefore a real empirical knowledge of financial products as well

We indeed found it essential, when conceiving the volume, to keep in mindtwo guiding principles that, according to us, have to structure the research and prac-tice in credit risk and, more generally, in modern finance First, research has to berooted in experience and rely on the knowledge of the empirical behavior of mar-kets Losing sight of experience or disconnecting the sophisticated mathematics ofmodern financial theories from the day-to-day practice may be dangerous for obviousreasons, besides compromising the necessary dialogue between decision makers and

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quantitative analysts Second, a high level of technicality is required to deal with currentcredit markets A naive approach that would not rely on cutting-edge research wouldsimply be condemned to fail, at least as far as derivatives or tail distributions involved inrisk management are concerned We hope the present volume will contribute to mak-ing the difficult synthesis of these two requirements (rooting in experience, technicalcomplexity) effective.

The volume contains expert opinion articles, survey articles, as well as articlesfeaturing the cutting-edge research regarding these aspects This is important, as webelieve that once the dust settles after the recent credit crisis, the credit markets will

be facing challenges that this research addresses, so the volume may contribute toimprovement of the health of the postcrisis credit universe

The volume is directed to senior management and quants in financial institutions,such as banks and hedge funds, but also to traders and academics In particular,academics and students in need of strengthening their understanding of how complexmathematics can be effectively used in realistic financial settings can benefit from itsreading

The volume provides a coherent presentation of the recent advancements in ory and practice of credit risk analysis and management with emphasis on somespecific topics that are relevant to the current state and to the future of creditmarkets The presented research is high-level on all the involved sides: financial,mathematical, and computational This is the only way, we believe, that modelingshould be presented and discussed so as to be meaningful, constructive, and useful

the-In addition, readers will also benefit from quality survey articles regarding selectedtopics

The present collection of articles is one of several analytical texts that have appeared

in recent months as a reaction by the quantitative community to the financial crisisthat exploded in 2008 We refer, for example, to Lipton and Rennie (2007), whichappeared before the crisis, and Brigo, Pallavicini, and Torresetti (2010), reporting bothpre- and postcrisis research These two books are just two examples of the necessityfor the quantitative community to assess its status quo vis-`a-vis financial markets ingeneral, and credit markets in particular

The volume opens with two expert opinion articles reflecting on the role ofquantitative modeling in the past and in the future, on how it did or how it did notcontribute to the current credit crisis, on what lessons modeling should incorporatefrom the credit crunch crisis, and on whether modeling should still be relevant.These opening chapters form the first part of the book and are followed by articlesfocusing on some specific issues and areas reaching toward the frontiers of credit riskmodeling, valuation, and hedging

The second and third parts are closely related, although we found it convenient todivide their contents into two separate groups They both deal with credit derivatives.Part II focuses on general methods in multiname credit derivatives, namely derivativeproducts that depend on more than one credit entity at the same time This part

is meant to deal with the usual key issues of multiname credit derivatives but usingrevisited approaches and analysis The topics covered include a survey of multiname

credit derivatives methods and approaches, methods to deal with heterogeneity anddynamic features, analysis of hedging behavior of models, filtering and information,and the modeling of options on credit derivatives.

The focus of the third part is more oriented toward products and more specificallytoward asset-backed securities (ABSs) in which the analysis of cash flows presentsspecific difficulties that are not present in the familiar synthetic CDO framework—although we should point out that these contributions involve general ideas andtechniques that are relevant for all asset classes in the field of credit The first chapter

of this part introduces the factor models, with a particular emphasis on the ABXindexes Topics included in the other chapters are a modeling and analysis frameworkfor collateralized loan obligations (CLOs), a valuation and risk analysis framework forresidential mortgage-backed securities (RMBSs), together with a survey of postcrisissolutions to various issues such as interest rate modeling and the handling of numericalcomplexity

The fourth part is devoted to the valuation of credit valuation adjustment (CVA)and counterparty risk in the current environment It is well-known that counterpartyrisk was underestimated before the subprime crisis This contributed heavily to thecrisis when many financial institutions discovered billions of dollars’ worth of counter-party exposures were at risk, either directly in case the counterparty would default, orindirectly through downgrades (the downgrades of monoline insurers come to mind).Since then, counterparty risk measurement has become a key issue and has attracted

a lot of attention, both from the financial industry and from academia The firstchapter of this part settles the general framework of CVA valuation, including subtlemathematical features Topics in this part include: models and mathematical tools forCVA on credit derivatives, from both the intensity and the structural points of view;CVA for bonds and swaps; accounting issues; and advanced features related to nettedpositions and margin agreements

The fifth part is devoted to equity-to-credit modeling The idea of unifying theuniverses of credit and equity into a single mathematical framework is an old dream

of mathematical finance The so-called Merton model, predicting defaults by viewingthe stock market value of a listed firm as a call option on its assets with a thresholdcomputed from its debt, offers a general strategy, but the corresponding numericalresults are known to be unsatisfactory: hence the need for new models incorporatingadvanced features such as jumps or random volatility The two chapters introducesuch models and discuss the application domain of equity-to-credit modeling thatruns from joint pricing of credit and equity to relative value analysis One of thepapers in the CVA part also deals with equity-to-credit modeling but with a focus oncounterparty risk for equity payoffs

The last “Miscellanea” part gathers various contributions on important topics.They include: liquidity risk (offering a detailed survey of the existing methodologiesfor liquidity modeling in credit default swaps), ratings (with the case study of constantproportion debt obligations [CPDOs]), modern Monte Carlo methods (with an em-phasis on interacting particle systems), and a survey of the theory of risk contributions

in credit risk management

1 International Swap and Derivatives Association, “Market Survey Year-End 2008.”

2 Securities Industry and Financial Markets Association, 2010 “Global CDO data” press release 2010-07-02.

PART I

Expert Views

5

6

CHAPTER 1

Origins of the Crisis and Suggestions for Further Research

Jean-Pierre Lardy

JPLC

We review several of the factual failures that the 2008 subprime crisis has revealed and analyze the root causes for these Credit rating, regulation, models, accounting, leverage, risk management, and other aspects are reviewed In each case, we survey solutions proposed as well as suggest directions for further research.

1.1 Introduction

The many roots of the 2008 financial crisis have been well covered in several cations The aim of this review is to provide a short list of the ones most frequentlyraised and in each case try to distill one important aspect of the problem, the currentproposals, and, possibly, what could be a direction of research to better understand theissue A lesson from past decades is certainly that crises are not easy to forecast in terms

publi-of timing and magnitude, and when they occur (we can only forecast that they will

occur), it is not always easy to separate, to paraphrase a famous quote from financierJ.P Morgan,1what was wrong as a matter of judgment from what was wrong as a mat-ter of principle These same questions apply in today’s modern finance of sophisticatedmarkets, products, and models, with the additional complexity of separating, whensomething went wrong, a technical failure of the “machine” (or of the principles onwhich it is built) from a failure of the “user” (or its judgment) To use an analogy (I find

it useful)—investing is like riding a bicycle, and there is always a trade-off betweenperformance and risk and improvements from better machines or better driving

7

After working 20 years in the financial markets, including roles at two ment banks in equity and credit derivatives,2I have witnessed several stages of theirdevelopment I was lucky enough to reach levels of responsibility giving me a view

invest-on how decisiinvest-ons are made, good and bad, individually or collectively Being mostly

in the “engines room” kept me in the front lines of crises and allowed me to see howthings work in practice on investment banks’ trading floors Last, having been present

at early stages of the developments of these markets helped me to keep a healthy sense

of pragmatism about them: The following paragraphs are personal reflections on thedrivers of the crisis.3

In the remainder of this article, the various topics are organized into three sections:actors and markets, methods and products, and finally a last section on global riskmanagement To use an analogy with transportation, the first section would be aboutgeography and population preferences; the second section about engineering of roads,airplanes, railways, and so on; and the third section about the rules of the road, safetyprocedures, and so forth The choice of these three sections helps to distinguish thedifferent natures of the topics, but the topics are greatly interrelated and overlap thesections in several ways

1.2 The Real Economy: Actors and Markets

In this section, I review the issues in the 2008 financial crisis that are more closelyrelated to the natural needs and organization of the real economy This may be wherethe most important roots of the crisis lie, but also where alternatives are not easy topropose or to achieve quickly, or even possible to do so, especially when it comes tohuman behavior

1.2.1 Loan Origination

With regard to the subprime crisis, it’s legitimate to start with loan origination.Although no one yet knows what the full extent of the damage will be, the gradualdeterioration of U.S retail loan quality standards over the years is a fact The negativeincentives of securitization markets (originate to distribute), the flaws (and fraud) ondocumentation and appraisal values, the political environment supportive to increasehome ownership, the lack of intervention by federal regulatory authorities despiteseveral local whistle-blower cases all played a role (Berner and Grow 2008) The irony

is that the United States was by far the most advanced country in terms of retail creditscoring (FICO scores, etc.)

The new regulatory proposals will force loan originators to keep more “skin inthe game,” with a vertical slice of any securitization (not cherry-picking a part of theorigination).4 Further research could also explore what is the right balance betweenstatistical credit scoring and proximity and human judgment, with all its diversity, andfor which there is no substitute, in credit decisions

1.2.2 Macroeconomic Imbalance

The increased Asian savings following the 1997 crisis, compounded with the surplus ofChina and oil-exporting countries, created a large supply of liquidity and a formidabledemand for (apparently) high-quality fixed-income assets Despite the large supply ofnotes and bonds from Western government deficits, the low-interest-rate environmentfueled a demand for higher-yielding fixed-income assets Wall Street engineered theproducts that met such demand, which was broadly characterized by a risk aversionfor idiosyncratic risk (first-loss or nonrated products), but generally complacent forsystemic risk, favoring highly rated products (especially AAA), albeit from complexstructures and rating techniques

Low interest rates also favored the emergence of the financial bubble in realestate prices, construction, and infrastructure, boosting growth and job creation—allwelcomed by politicians and their communities

The new regulatory proposals favor the creation of a systemic regulator5to monitorthese imbalances, and to raise concerns with persuasive (yet nonbinding) powers.Further research could now explore what anticyclical macro policies can be global,targeting all countries at once, to avoid diplomatic crises.6

1.2.3 Rating Agencies

Rating agencies regularly and successfully improved their methodologies to take vantage of the increase in computing power and the increased availability of financialand market data The wider availability of external ratings became a key component

ad-of regulation with Basel II, increasing furthermore the need for ratings The irony isthat the rating agencies’ worst failures relate to credit products that were, by design,built on credit ratings, such as collateralized debt obligations (CDOs) of mezzanineasset-backed securities (ABSs)

In fact, the rating agencies have been hurt by the consequences of the weakparts of their business models: Who pays obviously makes a difference, sophisticatedquantitative methodologies should not be pushed beyond their limits, and criticalhuman judgment must always remain (McCreevy 2009)

As concerns further research, one wonders whether perhaps ratings should corporate some external or open-source elements (academics’ and practitioners’ con-tributions, etc.) to their methodologies or reports to keep pace with innovation andinformation (in particular for complex or new structures)

in-1.2.4 Hedge Funds

After the precedent of Long-Term Capital Management (LTCM) in 1998, there hadbeen growing fears in the years before 2007 about the growth of the hedge fundindustry, but hedge funds were not at the origin of the 2008 crisis (High-Level Group

on Financial Supervision in the EU 2009) A few hedge funds failed (Amaranth, etc.),and many had to trigger gates, causing damage to their investors, but all of these

were idiosyncratic events Obviously, withdrawing excess liquidity from Bear Stearns

or Lehman Brothers added to the runs on these banks, but hedge funds were nodifferent in this respect than corporations or mutual funds, and they also withdrewexcess liquidity from Goldman Sachs, Morgan Stanley, and others The irony is thatprime brokerage contracts are all about haircuts, independent amounts, stress tests,daily margining, and so on, designed to protect the banks from the hedge fund risk,and suddenly these contracts backfired against the banks’ liquidity, as hedge fundswere scared about the risk of their prime brokers and were left little choice (theirdeposits are not guaranteed like retail depositors’ are) The other irony from theLehman bankruptcy is that hedge funds active in derivatives ended up better thanfunds invested in cash securities (in particular in jurisdictions with no segregations ofsecurities)

Regulators should enforce that hedge funds’ play by the technical rules of themarkets Beyond that, encouraging through regulatory best practices for collateralhandling seems the best direction in order to limit the systemic impact of hedge fundfailure.7

1.2.5 Remunerations

For many thinkers, the remuneration of human capital is the main engine of progress.8

It is also a source of excess and injustice However, the irony is that Wall Street, inthe language of economists, is one of a very few examples of Marxist industries,where the greatest share of added value is kept by workers, instead of the capitalists’

“surplus-value.” In this field, a delicate balance must be found: a better alignment

of remuneration horizons in order not to give up-front rewards for long-term risks,while the virtue of division-level cash compensation budgets necessarily moderatespayoffs and therefore the moral hazard that can be associated with corporate-widestock options plans

Further research should explore whether the remuneration problem is an extension

of the shareholder versus bondholder governance issue (Billet, Mauer, and Zheng2006) For example, should bondholders of highly levered entities have a vote in thetop remunerations schemes?

1.2.6 Leverage

The social benefit of the financial system is to transform information into liquidity forthe rest of the world: Assets that are illiquid but good risks are transformed by banksand markets into liquid liabilities (that are liquid assets for the rest of the world) Yetthe 2008 crisis is also a consequence of an excessive leverage from banks and fromthe shadow banking system of banks’ vehicles, money market funds, and hedge fundfinancing: Basel I created an incentive for banks to use off-balance-sheet vehicles forcertain (apparently) low-risk assets; money market funds were also competing for thesame assets with lower regulatory and capital constraints; and providing leverage tohedge funds is a highly collateralized lending and fee-generating business

As banks’ regulatory capital ratios are risk weighted and do not directly trol leverage, the current discussions revolve around the accounting of a universallyaccepted leverage ratio (as is currently the case in the United States and Switzerland).Further research could be conducted as to whether, for that purpose, full debtconsolidation would be desirable, with the necessary accounting precaution to differ-entiate the part of consolidated debt that is associated with the minority interests inthe equity (or minority debt).

con-1.3 The Financial Techniques: Products and Methods

In this section, I review the issues in the subprime crisis that are more related to thetechnical choices that have been made historically or more recently by the financialworld to provide or facilitate its business This may be the part where correctingmistakes is more a matter of time and experience In financial markets, like everywhereelse, progress is not linear, and knowledge is built on both successes and mistakes ofprior periods

1.3.1 Mathematics

Whether the representation of the real world by mathematics is adequate must partlyinvolve the mathematicians’ responsibility, especially as they indirectly expect to get ahigher demand for their services Initially, there is a virtuous circle where practitioners’rules of thumb can be rebuilt by more formal approaches that confirm one other andallow further innovations After a while, innovations can go too far; naive assumptionstaken for granted are no longer valid but no longer questioned; teachers and studentsplace theory before practice; and so on The irony is the parallel with rating agencies:

a possible excess of sophistication that is not counterbalanced by experience

There is ground for further research on what assumptions in financial mathematicsshould not be made by convenience Shouldn’t there be more academic refutations,counter-examples according to their consequences if they aren’t verified?

1.3.2 Models

Models generally do not take well enough into account the potential for markets todeviate far from equilibrium, especially illiquid assets In this case, third-party modelsbased on reasonable assumptions (such as rating agency models) usually underesti-mated tail risks, which were envisioned only by internal stress tests, and the laterones were often judged as lacking plausibility Proprietary models used for their ownaccounts generally performed better as long as they were nimble enough to allow theuser’s critical eye and the ability to continually correct deficiencies It can be preferable

to have several (albeit simpler) competing models that can bring different inputs tothe same risk, instead of an ultrasophisticated monolithic approach that might missthe point The irony is again a possible excess of sophistication, crowding out caution

Further research: From the past experiences of macroeconomic and financialmodels, what is the right level of complexity not to be fooled by equations?9

1.3.3 Derivative Products

The social benefit of a derivative product should be the same as that of any otherfinancial market instrument: allowing the transfer of risk and reward from a willingseller to a willing buyer, and providing information to the rest of the world aboutsuch transfer to help further decisions to invest, produce, consume, and so on Evenwith turbulence, market risks are preferable to Knightian uncertainty (Knight 1921).The successful product innovation of derivatives growth is twofold: more customizedproducts to fit transfer preferences, more vanilla products to build liquidity and marketinformation The industry must balance both aspects for success

Derivative structures are also part of the tool kit used by services offered bythe financial industry It is in such services that possible conflicts of interest aremore likely.10 Last, although the management of counterparty and legal risks inderivative transactions has made tremendous progress, it is still an area of concern due

to the size of these markets

Further research: Exchanges and central clearing can improve liquid derivatives.What about public initiatives in favor of third-party collateral schemes11 to addressthe broader needs of bilateral contracts?

1.3.4 Funding

Historically, funding was somewhat an exception to the risk management trend topush the responsibilities of all risks as closely as possible to their originators Tradingdesks have usually few options in their funding policy The bank or institution treasurytakes care of long-term cash provided by certain activities on the bid, while fundingthe debits of other desks at the offer: Term funding is typically not the problem oftrading desks

Moreover, financial models are doing the same by discounting risk-free future cashflows at short-term interbank “XIBOR” rates and using swap rates for medium andlong-term maturities

The global crisis of 2008 demonstrated how funding risk can derail the normalarbitrage relationship between cash and related unfunded products: The short-termLondon Interbank Offered Rate (LIBOR) is a real loan (and can incorporate a fundingrisk premium), while swap rates, which are unfunded, can significantly miss the point

of prices driven by fire sales or unwinds of riskless but cash-funded products

Further research should quantify how a global systemic short-term funding squeezetranslates not only into temporary negative interest margins, but also fire-sale trans-actions on the basis of cash capital as term funding of last resort, prompting negativelong-term swap spreads, large negative basis on cash bonds versus credit default swaps(CDSs), and so on

1.3.5 Short Sales

In the 1990s crises (both Latin America 1994 and Asia 1997), short sales were blamedfor declining markets, and authorities hastily changed the rules of equity lendingand borrowing and short sales (Malaysia, Taiwan, etc.) Even though G-7 countries’markets have constant surveillance against price manipulation (as they should), similarmoves happened in G-7 countries in the autumn of 2008: This is more surprising butobviously understandable At the same time, the worst daily market moves (such aslimit down days) occur when the panic of long investors finds no bid from a lack ofshort interest Only the shorts are buying during crashes Also, markets with no ability

to sell short are more prone to the creation of bubbles and subsequent disasters (realestate being a prime example) In summary, the irony is that past short sales are themost natural financial market contracyclical mechanism

In the future, we could see an interesting duality from regulators toward shortsales: While market regulators continue to actively regulate the appropriate executionand reporting of short sales, shouldn’t newly established systemic regulators want toencourage more efficient frameworks for term borrowing? And why not encourage asufficient amount of long-term short interest?

1.3.6 Accounting

Accrual accounting was at the root of many disasters where banks had negative nomic net worth while remaining liquid in the 1980s: Accrual accounting can allowpoor management for too long Fair value accounting was brought in to provide in-vestors (and management) financial results where the flexibility of accrual accounting

eco-is replaced by binding market levels (directly or indirectly through predefined uation models) Bank managers should have known that markets can be brutal; therules applying to individual traders were suddenly applied at an entirely different scale,leading to severe systemic consequences In particular, illiquid markets with granularpositions are inefficient, and the unwinding of one losing position creates further lossesand further forced sales

val-Proposals seem to go in the direction of a middle ground: a simplification ofdoubtful refinements around available for sale (AFS), held to maturity (HTM), and

so on, with the possibility of some management judgment to overrule aberrant marketprices (either too high or too low), whenever necessary to reflect a reality based onprudent accounting, and not misleading automatic rules (IASB Exposure Draft 2009).Further research could explore whether taxes can also play a role to promoteprudent accounting, and also potentially reduce the volatility of tax revenues

1.3.7 Legal

The proper handling of legal risks is critical for the financial industry where so much

of the business relates to promises of future performance To limit the temptation towalk away from wrong past decisions requires a strong legal framework The capital

markets are also very technical, and precise rules of compliance must be followed inorder to prevent manipulations, trading on inside information, false rumors, and so

on The markets’ legal environment has made great progress on all of this The crisispointed out a few important problems: strictly national bankruptcy laws where assetscan be frozen in one country against the legitimate rights of alien owners (collateraltransfers and rehypothecation) (King 2009) Also, certain derivatives terminations orinterpretations by the nondefaulting counterparts of Lehman Brothers are controversialand being disputed (Ng and Spector 2009)

Immediate proposals call for broader use of transaction documents where thelegalities are closer to the economic intent, and based on electronic format (FpML)instead of paper

However, further research should review whether an international bankruptcystandard could be enforceable for asset conveyance—for example, by transferring thedisputed asset in a third-party jurisdiction

1.4 The Global Risk Management Challenge

In this last section are grouped issues that relate to the organization and control ofthe interactions or the communication of information between all the moving parts.Although they do not belong—strictly speaking—to the previous two sections, theyparticipate directly or have great influence indirectly on the real world itself and thecorresponding financial techniques

1.4.1 Regulation

Basel I allowed a better capitalization of the banking systems following the crisis ofthe 1980s Basel II was designed to correct Basel I undifferentiated risk weights, whichcreated incentives for banks to take assets off balance sheets Basel II greatly reducedthese regulatory arbitrages but potentially increased systemic risks with the reliance onexternal ratings and models The irony is that the subprime crisis—and the collapse

of many off-balance-sheet structures12inspired by Basel I—struck at the time Basel IIwas coming into effect

It is critical that regulations anticipate and be aware of unintended consequences:Many of the toxic off-balance-sheet vehicles were a consequence of Basel I, and much

of the demand for toxic highly rated fixed-income products was a consequence ofBasel II

Further research could explore how to address quickly regulatory weaknesses,which otherwise are systemic and procyclical by nature A practical solution could bethrough fast-track specific additional disclosures required under Basel II’s Pillar 3

and derivative markets were indirectly responsible for the globalization of certain risks.The last-named, combined with the increase of correlations, probably outweighed thediversification benefits Yet many studies had previously shown how quickly adverseselection could cancel out diversification (Acharya, Hasan, and Saunders 2002) Moresimply, whatever the subordination, the most senior positions of a securitization willremain affected by the troubles of the vehicle, or of the entire asset class, and command

a discount

Further research should look into what share of any asset class corresponds tosystemic, truly undiversifiable risk, which one way or another will remain in the globaleconomy, and more systematically how this aggregate exposure compares with the networth and leverage of the global economy

1.4.3 Counterpart Risk

Certain institutions were weak in the management of counterpart risk, and in ular lacked judgment on the realization of wrong-way risks from monoline insurers.Counterpart risk management, from the internal governance of credit authorities, riskassessments, limits, collateral, and so on down to the stop-payment instructions, isoperationally hugely complex From there, counterpart credit valuation adjustment(CVA) is naturally a challenge

partic-It is also entangled with disputable accounting rules for the credit risk on yourown liabilities—or debit valuation adjustment (DVA): Your liabilities are assets forothers; if their losses are your gain, should poor investments be globally a zero-sumgame? More importantly, isn’t what matters to one’s balance sheet the fair value of theliabilities (and assets) independently of the host (e.g., if they were the liabilities of anyacceptable replacement party)?

The debate is not closed on the DVA (Dimon 2008), and current proposals go inthe direction of central clearing for standardized products as a way to reduce circularcounterparty risk from multiple entities with large portfolios among them (Duffie2009)

Further research should be dedicated to the level and nature of interbank andregulatory communication channels that are needed to avoid the potential failure of acentral counterpart (Tett 2009)

1.4.4 Risk Policy

Being overly restrictive in the risk tolerance of visible factors of risk can translateinto more invisible risks being built into the system Many institutions involuntarilyreplaced market risks with even more toxic credit, counterpart, or legal risks In effect,the risk management policy has shifted some quarterly volatility to potentially moredisastrous consequences The lessons are very clear: Risk management must consider allrisks, not only vanilla or easily measurable ones; and owners and managers must havetolerance for a level of acceptable profit and loss (P&L) volatility, fully understandingthat under a certain level, it is simply unrealistic to be in the business

Further research: Banks are not all the same, and have subtle differences of riskattitude, aversion, and tolerance, which depend on their internal culture, their his-tory, the background of their managers, and so on Shouldn’t bank regulators’ focus

be directed to finding such weaknesses in relation to the previous items, which bydefinition are difficult to know from the inside?

1.4.5 Disclosure

The disclosure of financial data has generally kept pace with the possibility offered byinformation technology The quantitative amount of text and data does not necessarilyincrease the information and its usefulness if standards are different, and with thedifficulty to process it due to formats, access costs, lack of standards, extensive list offields with missing or incorrect data, and so on Pillar 3 of Basel II officially mandatesthe standards of quantity and quality of risk information that must be provided bybanks In practice, it is, however, still quite difficult to reconcile many of the data Ismore data always better?

Alternatively, more efforts should take place to determine the simplest and imum data that could be reported by all firms (and possibly governments and publicentities), with universal interpretation (and minimal possibility of manipulation), andyet capture the biggest density of information about risks and rewards

min-1.5 Conclusion

Credit risk is at the core of the 2008 crisis: first, because of its retail U.S subprimeorigins, and also more importantly in all the dimensions that allowed the contagion:lack of depth of secondary markets, interbank market freeze, credit crunch, and so

on Banks have clearly suffered from liquidity risk, overleverage, and possibly alsolack of capital; regulations will be revised accordingly The lessons are that modelsinsufficiently took into account the potential for market prices to deviate far fromequilibrium due to a simultaneous increase of risk premium and lack of cash-fundedrisk capital At the same time, management and control of the visible main riskfactors—which are quantified—must not indirectly favor more toxic risks that are lessvisible Ultimately, the crisis demonstrated that sophistication can give a false illusion

of risk management ability; extremely smart techniques can fail where commonsensecaution may not

Research must take up the challenge: The equations are not an end in themselvesbut merely tools for improving the merits of investing Experience and judgmentmatter; otherwise, too much talent (young and old) is being wasted

2 Managing Director, JPMorgan and Soci´et´e G´en´erale.

3 These are not reflective of views of former colleagues, clients of JPLC, or partners of the CRIS consortium.

4 The 5 percent rule of Article 122 of the EU Capital Requirement Directive (2009).

5 European Systemic Risk Board (ERSB) of the European Union.

6 It is legitimate to assume that systemic regulation is subordinated to diplomacy.

7 Such rules could also apply to limit the systemic risk of central clearing in periods of crisis.

8 Jean Bodin: Il n’est de richesses que d’hommes.

9 Improving bikes takes as much from driving experience as from pure engineering.

10 Derivative structures—with a dedicated derivative contractual setup—are opposed here

to derivative products whose contractual setup is standardized.

11 Collateral of counterparts is held by an appropriate third party.

12 Structured investment vehicles (SIVs), conduits, and so on.

References

Acharya V., I Hasan, and A Saunders 2002 Should banks be diversified? Evidence from individual bank loan portfolios BIS Working Papers, September.

Berner, R., and B Grow 2008 They warned us about the mortgage crisis BusinessWeek, October.

Billet, M., D Mauer, and Y Zhang 2006 Stockholder and bondholder wealth effect of CEO incentives grants University of Iowa, August.

Dimon, J 2008 III—Fundamental causes and contributions to the financial crisis JPMorgan Chase Annual Report, 14.

Duffie, D., and H Zhu 2009 Does a central clearing counterparty reduce counterparty risk? Stanford University, March.

The High-Level Group on Financial Supervision in the EU 2009 Chaired by Jacques de Larosi`ere Report (February): 24.

International Accounting Standards Board (IASB) Exposure Draft 2009 Financial instruments: fication and measurement (July).

Classi-King, M 2009 Global banks are global in life, but national in death, [by] Mervyn Classi-King, Governor of

the Bank of England Financial Stability Report (June).

Knight, F H 1921 Risk, uncertainty and profit Boston: Houghton Mifflin.

McCreevy, C 2009 The credit crisis—Looking ahead Institute of European Affairs, February.

Ng, S., and M Spector 2009 The specter of Lehman shadows trade partners Wall Street Journal,

September 17.

Tett, G 2009 Insight: The clearing house rules Financial Times, November 5.

18

of modern pricing models and lessons learned from the crisis.

Models do not accurately render the real behavior of financial markets However,they do provide a common language that enables market players to interact Thesimplicity of this language has allowed derivative markets to grow quickly across assetclasses When the assumptions underlying a model break down, the consequencesare proportional to the model’s success It is therefore crucial to analyze the risks ofusing quantitative models both for pricing and hedging financial securities and for riskmanagement

sensitivity of that price to market parameters, using both observable and able inputs The nonobservable inputs are typically used to calibrate the model tomarket prices, while the observable ones can be used to find an optimal replication

nonobserv-19

of a security’s payoff using tradable assets We discuss these models in the secondpart of this article.

scenarios on the mark-to-market and risk profiles of single securities or portfolios

of securities The market scenarios are weighted by their probabilities in order toprovide a synthetic view of a trading book’s risks Risk management models providemark-to-market valuations and risk profiles, as well as frameworks to estimate theprobability of the market scenarios The first part of this article is dedicated to suchvalue at risk (VaR) models and illustrated with the use of extreme value theory toanalyze the first two years of the crisis (2007–2008) in and out of sample

2.1 What Future for VaR Models?

Value at risk (VaR) models are popularly used to estimate regulatory capital for financialinstitutions In a nutshell, they estimate the amount at risk on a given portfolio inworst-case scenarios This is achieved in two steps:

1 Marginal and joint distributions are estimated for a series of observable and hiddenparameters that determine the portfolio’s dynamics

2 A worst-case scenario is then simulated based on the previous joint distribution

In the following we focus on the estimation of probability distributions for servable parameters, which has been at the center of recent criticism of VaR models.This chapter does not examine VaR from a portfolio standpoint, so we do not discussnetting effects and correlation models

ob-2.1.1 Introducing Extreme Value Distributions

Quantitative finance is sometimes criticized for an alleged excessive use of Gaussiandistributions Gaussian distributions are useful to describe business-as-usual situations,but perform poorly in cases of deviations—large or even moderate ones—from usualmarket equilibriums Fortunately, one major field of quantitative finance is dedicated

to modeling extreme risks Extreme value theory provides tools to model financialrisks for all types of deviations

In particular, the extremal types theorem (see Fisher and Tippett 1928 and vonMises 1936) states that the maximum of a large pool of independent and identicallydistributed (i.i.d.) variables follows a specific well-known probability law, the general-ized extreme value (GEV) law This makes GEV the tool of choice to model extrememovements in financial markets

The extreme value distribution provides one parameter to locate the peak of thedistribution and another to measure the size of possible deviations from this peak.GEV differs from Gaussian distribution thanks to its third parameter, which generates

FIGURE 2.1 Generalized Extreme Value Distribution Allows Modeling of Extreme Scenarios

Source: SG Cross Asset Research.

asymmetry or skewness in the distribution and kurtosis, which measures the fatness

of the tails (see Figure 2.1)

GEV parameters are:

2.1.2 Extreme Value Theory in Practice

We begin this section with a few examples of GEV distributions We show that it canadapt efficiently to various empirical observations thanks to simple adjustments to itsthree parameters

We start our analysis with one of the most liquid credit indexes, the iTraxx Main(see Figure 2.2) As credit indexes began to trade only in 2004, we have reconstructedthe time series back to 2001 using principal component analysis (PCA) on a basket of

300 single-name credit default swaps (CDSs)

The 30-day density is clearly skewed toward widening scenarios This is consistentwith the observed behavior of credit spreads, which tend to jump wider more oftenand more abruptly than they jump tighter Using a weekly sampling frequency, thedensity becomes more symmetrical, although still skewed toward negative scenarios.Moving on to equity indexes, we find fairly similar results (see Figure 2.3) The30-day distribution is skewed toward the negative scenarios, but in a slightly different

FIGURE 2.2 iTraxx Main Density Sampling period: 30 days Sampling period: 7 days

% –13% –8% –2% 4% 11%18% 26% 34% 43% 52%

Empirical density GEV density

Source: SG Cross Asset Research.

way In credit, the amplitude of the biggest observed widening move is almost threetimes that of the biggest tightening move The difference is much less for the EuroStoxx

50 index, although the downward scenarios still clearly exhibit a much fatter tail Thishighlights the jumpy nature of credit spreads compared to stock prices

Finally, we calibrate our GEV model to 10-year EUR swap rates (see Figure 2.4) Atfirst sight, the 30-day density of 10-year EUR swap rates seems relatively symmetrical.However, the empirical density of the maximum increase in 30 days is centered at

2 percent in relative terms, while the density of the maximum decrease is centered at–4 percent This shows that on average, 10-year rates tend to decrease more rapidlythan they increase Moreover, the GEV density provides an excellent fit to seven-dayempirical density

So far, we have provided theoretical justification for using the GEV distributionfor VaR calculations and we have illustrated the explanatory power of GEV through aseries of examples

FIGURE 2.3 EuroStoxx 50 Density Sampling period: 30 days Sampling period: 7 days

Empirical density GEV density

%

Source: SG Cross Asset Research.

FIGURE 2.4 EUR 10-Year Density Sampling period: 30 days Sampling period: 7 days

Source: SG Cross Asset Research.

2.1.3 Calculating Value at Risk

GEV distributions can be used by risk managers to compute value at risk by extractingextreme quantiles conditional on some chosen GEV parameters For example, the

1 percent quantile is a tail event that has a 1 percent probability of occurring according

to a given probability law For example, using the GEV law, the 1 percent quantile

x1% is such that PGEV[X < x1%]= 1%

Geometrically speaking, the quantile measures the size of the tails of our tion as shown in Figure 2.5

distribu-Risk managers express quantiles in terms of frequency: A 1 percent quantile whenlooking at monthly variations corresponds to an event that should occur every eightyears on average

FIGURE 2.5 Quantiles Measure the Size of Distributions’ Tails

FIGURE 2.6 Comparing GEV Quantiles to the Worst Moves of the Crisis

Nikkei iTraxx Main

Source: SG Cross Asset Research.

2.1.4 Impact of a Crisis on VaR Calculations

Critics of quantitative risk management argue that extreme events by their very natureescape attempts to model them They consider that by blindly using risk models, mar-ket players would wrongly assume that risks are under control, and suffer unexpectedlosses in case of a real crisis We now challenge that assumption

The previous section has shown that not all distributions used in quantitativefinance ignore extreme risks We now turn to concrete applications in term of riskmanagement We assume that at the end of 2006, a portfolio manager measures theVaR using GEV distributions We will compare GEV estimates to the losses sufferedduring the years 2007–2008 on directional trades in various markets

Concretely, we calibrate the GEV parameters (µ,σ, and ξ) to data series ending

in 2006 and calculate the VaR of directional trades for various securities We comparethese VaR estimates to actual losses occurring through the 2007–2008 period

We consider the most extreme upward and downward moves observed on 30assets during 2007 and 2008 and compare them to the 1 percent quantiles obtainedusing GEV on weekly data based on the 2001–2006 period (see Figure 2.6)

Most of the moves are in line with the GEV quantiles The biggest discrepanciesare on credit indexes, which were at the center of the subprime crisis of 2007.Table 2.1 provides more detailed results We show the worst losses seen duringthe years 2007–2008, as well as GEV quantiles corresponding to both decennial andcentennial VaR

We show results for both downward moves (rates, oil, equities, credit spreads)and upward moves Remember that model results are estimated on data that stoppedbefore the crisis actually started

TABLE 2.1 Comparing VaR Estimates to Worst Moves of Current Crisis

Worst Decennial Centennial Worst Decennial Centennial

EUR interest rates −13.08% −13.35% −16.88% 12.83% 15.52% 19.70% USD interest rates −20.31% −18.09% −23.31% 21.54% 30.92% 49.96%

Credit indexes (spread) −35.52% −27.12% −32.82% 96.57% 53.90% 112.65%

Source: SG Cross Asset Research.

January 2007 through October 2008

The capital estimated as necessary for a decennial crisis covers more than 85percent of actual losses on long positions in interest rates or oil It covers 76 percent

of losses on long credit spread (i.e., short risk) positions and 70 percent of losses onlong equity positions It is quite interesting to note that only 30 percent of losseswould have been incurred on equity positions, despite the unprecedented volatility

we saw during that period On short positions, losses would have been overhedged inmost asset classes—except on credit spreads (i.e., long risk), where barely 55 percent

of losses would have been covered

However, losses from the current crisis remain well below those from the centennialcrisis simulated by our model (even on credit) This shows that quant models are wellable to consider extreme scenarios In the credit market, losses were roughly in linewith the estimated centennial crisis This result highlights the severity of the creditcrisis, but it is also due to the lack of long-term historical data for credit spreads at thefrequency required for our analysis That said, even with arguably little representativehistorical data, this simple model proves to be a good guide for the crisis

2.1.5 Proper Use of a Risk Model

The previous results show that some asset classes were not sufficiently hedged by theGEV-based VaR model (short credit protection positions, for example) while otherswere overhedged and therefore too expensive to put on This brings us to the question

of how we want to use the model following its initial calibration to historical prices.Playing onξ to increase the size of the tails would make some positions safer and more

costly to implement On the contrary, reducing tail size would allow more aggressivepositions and more leverage

TABLE 2.2 Percentage Change in GEV Parameters and 1 Percent Quantiles Following 2007–2008 Crisis

EUR interest −0.98% −0.46% −3.59% −1.50% 19.11% −1.38% 12.86% −2.31% rates

USD interest −0.66% 5.43% −3.20% 1.85% −6.23% −1.75% −70.05% −3.82% rates

Oil prices 3.84% −3.04% −5.64% −2.76% 3.87% −7.78% −5.99% −0.56% Equity indexes 1.65% 0.16% −0.94% 0.06% −3.00% −2.26% −14.96% −2.91%

vs USD Credit indexes 9.74% 26.82% 23.89% 19.66% 68.83% 26.21% 11.79% 87.41%

Source: SG Cross Asset Research.

Clearly, the choice of the quantile and of the stress test we apply to the GEVdistribution will result in a trade-off between leverage and risk There are severalparameters available to the risk manager to design a policy:

frequency of once every eight years This means that the value at risk is calculated

as the loss due to an event occurring once every eight years

of adding some arbitrary extreme simulations to a VaR framework, we can play withthe GEV parameters to impact quantiles For example,ξ will directly impact tail

size and therefore modify the 1 percent quantile

Table 2.2 shows the impact of the crisis on the GEV parameters and the sponding 1 percent quantiles This gives an idea of the kind of stress test that wouldhave improved the efficiency of the GEV method over the current crisis

corre-Looking at the distributions of minima, the crisis mainly impacted long-term rates,some currencies against the U.S dollar, and credit indexes Interestingly, the parametersfor equity indexes were left mostly unchanged, meaning that capital requirements for

a long position on stocks would not have been affected by the crisis if the GEV-basedVaR model had been used

On the distributions of maxima, the fat tail parameterξ has suffered more ups

and downs The most significant changes in terms of the corresponding quantileare on some foreign exchange (FX) and on credit indexes in general The mostextreme changes are on the investment-grade (IG) indexes: They contain a significantproportion of financial names and have therefore been at the center of the recent crisis.The tail parameter of their GEV distributions moved by more than 250 percent, and