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Bringing together all 36 of the technical papers published in Risk magazine during 2003, this substantial collection presents the very latest research and thinking on quantitative finance and risk management.

Risk magazine is the foremost publisher of technical articles on quantitative finance, and this is the complete collection of articles published in the Cutting Edge section of Risk in 2003. In total there are 36 highly original articles covering the wide range of topics for which Risk has become known around the world. Each one has been rigorously reviewed by Risk's panel of expert referees.

From valuing CDOs and discrete dividends, to the latest ideas about real options and parimutuel auction systems. From VAR calculations to the impact of the new Basel II accord on bank regulatory capital. It's all there, authorised by the leading lights of academia and finance with a fully descriptive list of contents and an introduction by Nicolas Dunbar, the technical editor of Risk.

• First time in book format, the entire 2003 collection of Risks cutting edge section in one self-contained and convenient volume
• Let internationally renowned practitioners and academics in their field bring you up-to-date on the very latest technical ideas and research across various subject areas including - credit derivatives, credit portfolio modelling, Basel II, option pricing, stock options, programme trading, private equity, credit basket models, interest rates, real options, recovery rates, credit portfolio risk, counterparty credit risk, market risk, tail risk, parimutuel markets, business risk, ratings, default correlation and equity derivatives

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Table of contents

PART 1: PRODUCTS AND TRADING

1 Diversity Scoring for Market Value CDOs
C. Rouvinez
Capital Dynamics

A useful concept, the collateralised debt obligation (CDO) diversity score measures the size of a fictional pool of identical, uncorrelated assets that has similar distributional properties to the real collateral pool underlying a cash flow CDO. Here, Christophe Rouvinez shows how to generalise the concept to market value CDOs, where the collateral is actively traded.

2 I Will Survive
Jon Gregory; Jean-Paul Laurent
BNP Paribas

Jon Gregory and Jean-Paul Laurent apply an analytical conditional dependence framework to the valuation of default baskets and synthetic CDO tranches, matching Monte Carlo results for pricing and showing significant improvement in the calculation of deltas.

3 All Your Hedges in One Basket
Leif Andersen; Jakob Sidenius; Susanta Basu
Banc of America Securities

Leif Andersen, Jakob Sidenius and Susanta Basu present new techniques for single-tranche CDO sensitivity and hedge ratio calculations. Using factorisation of the copula correlation matrix, discretisation of the conditional loss distribution followed by a recursion-based probability calculation, and derivation of analytical formulas for deltas, they demonstrate a significant improvement in computational speeds.

4 Credit Barrier Models
Claudio Albanese; Oliver Chen; Andrei Zavidonov; Giuseppe Campolieti
University of Toronto; NumeriX; Wilfred Laurier University

Claudio Albanese, Giuseppe Campolieti, Oliver Chen and Andrei Zavidonov construct an analytic credit barrier model driven by credit ratings, constrained to fit the term structure of credit spreads.

5 On the Dependence of Equity and Asset Returns
Roy Mashal; Marco Naldi; Assaf Zeevi
Lehman Brothers; Columbia University

Asset returns play an important role in credit risk modelling. Here, Roy Mashal, Marco Naldi and Assaf Zeevi investigate the co-dependence behaviour of asset returns semi-parametrically. They find that the Student-t copula outperforms the normal copula as a description of the co-dependence structure. They also find that the joint tail dependence of equity and asset returns is similar, suggesting that equity returns are a good proxy for asset returns, both for investmentgrade and high-yield names.

6 Index Volatility Surface via Moment-Matching Techniques
Peter Lee; Limin Wang; Abdelkerim Karim
Lehman Brothers

Peter Lee, Limin Wang and Abdelkerim Karim present a basket construction technique using Gram-Charlier-Edgeworth expansions. They show how to express basket option skews and smiles in terms of its underlying components, and demonstrate how market-dependent correlation is necessary to fit observed properties of index options.

7 Capturing the Smile
Simon Johnson; Han Lee
NumeriX Ltd.

Since the discovery that traditional calibration methods fail to capture the dynamics of the smile, new approaches based on mixtures or ensembles of models have been developed. Simon Johnson and Han Lee present a variant of this approach that can be used to simultaneously calibrate European-style and barrier options, as well as cliquets.

8 Dealing with Discrete Dividends
Remco Bos; Anna Shepeleva; Alexander Gairat
ING; Fortis Bank

Over the past year, we have published several papers on the issue of options on stocks with discrete dividends. At least three distinct models are used by practitioners, involving trade-offs between accuracy and tractability. Here, Remco Bos, Alexander Gairat and Anna Shepeleva discuss how to use mixtures of discrete dividend models in a consistent way.

9 Why Be Backward?
Peter Carr; Ali Hirsa
New York University; Morgan Stanley

Originally developed as a tool for calibrating smile models, so-called forward methods can also be used to price options and derive Greeks. Here, Peter Carr and Ali Hirsa apply the technique to the pricing of continuously exercisable American-style put options, developing a forward partial integro-differential equation within a jump diffusion framework.

10 From Horses to Hedging
Ken Baron; Jeffrey Lange
Longitude

Financial derivatives rely on liquid underlying markets to work properly, but what happens when such underlying markets do not exist, as is the case for indexes such as GDP or unemployment? Here, Ken Baron and Jeffrey Lange suggest a parimutuel auction system adapted from the betting industry as a solution to this problem.

11 Assessing Views
Gianluca Fusai; Attilio Meucci
University of Piemonte Orientale; Relative Value International

A key breakthrough in portfolio management theory was the Black-Litterman framework for finding which subjective view of market performance was best supported by empirical data. However, the question remains of how to measure the divergence of a single manager view conditioned using this framework with a firm-wide view of the market embodying the equilibrium returns found from data. Here, Gianluca Fusai and Attilio Meucci provide a technique for doing this.

12 Real Option Valuation and Equity Markets
Thomas Dawson; Jennifer Considine
D2 Capital; Energy politics

Many non-financial assets can be viewed as 'real options' linked to some underlying variable such as a commodity price. Here, Thomas Dawson and Jennifer Considine show that the stock price of a well-known electricity generating company is significantly correlated with the volatility of electricity-gas spark spreads, providing empirical support for real options valuation.

13 A Liquidity Haircut for Hedge Funds
Hari Krishnan; Izzy Nelken
Morgan Stanley; Super Computer Consulting

Investors in hedge funds have learned to be cautious when making decisions due to problems of survivorship bias, autocorrelation and hidden optionality. Here, Hari Krishnan and Izzy Nelken show how to quantify such caution. By analysing the incentive structure of hedge fund managers using an option pricing approach, they derive a liquidity haircut to compensate for lockup periods, and an illiquidity premium that effectively increases volatility.

14 Bidding Principles
Robert Almgren; Neil Chriss
University of Toronto; SAC Capital

Robert Almgren and Neil Chriss show how principal bid programme trades can be priced and evaluated as part of a trading business. By annualising the price impacts and variances of such trades, they construct an information ratio measure that can be used to set hurdles below which bids at a given discount should not be accepted.

15 Black Smirks
Fei Zhou
Lehman Brothers

Fei Zhou presents a simple stochastic volatility extension of the Black interest rate option pricing model widely used by traders. Using a perturbative expansion in volatility of volatility, he derives modified Black formulas that correctly fit the observed volatility smirk, and can be used in turn to calibrate more sophisticated models.

16 Shadow Interest
Viatcheslav Gorovoi; Vadim Linetsky
Northwestern University

Using a Vasicek process for the shadow rate, Viatcheslav Gorovoi and Vadim Linetsky develop an analytical solution for pricing zerocoupon bonds using eigenfunction expansions, and show how to calibrate their model to the Japanese bond market. This article is not the last word on the subject  in particular, the relationship between shadow interest rates, real rates and inflation should be explored  but we hope it will encourage further research.

PART 2 : RISK AND CAPITAL

17 Extreme Forex Moves
Peter Blum; Michel M. Dacorogna
ETH; Converium Ltd

What is the appropriate statistical description of tail risk in a market portfolio? In the context of foreign exchange, Peter Blum and Michel Dacorogna address this problem using extreme value theory. Using 20 years of data, they estimate parameters for an appropriate tail event probability distribution and use it to calculate risk limits for open overnight foreign exchange positions.

18 What Causes Crashes?
Didier Sornette; Yannick Malevergne; Jean-François Muzy
University of Nice-Sophia Antipolis and University of California; University of Lyon; University of Coralca

Are large market events caused by easily identifiable exogenous shocks such as major news events, or can they occur endogenously, without apparent external cause, as an inherent property of the market itself? Here, Didier Sornette, Yannick Malevergne and Jean-Francois Muzy ask this question of a number of large stock market events and conclude that endogenous crashes do exist.

19 VAR: History or Simulation?
George Skiadopoulos; Greg Lambadiaris; Louiza Papadopoulou; Yiannis Zoulis
University of Piraeus; University of Warwick

Greg Lambadiaris, Louiza Papadopoulou, George Skiadopoulos and Yiannis Zoulis assess the performance of historical and Monte Carlo simulation in calculating VAR, using data from the Greek stock and bond market. They find that while historical simulation results in over-commitment of capital for linear stock portfolios, the results for non-linear bond portfolios are less clear.

20 Random Tranches
Michael Gordy; David Jones
US Federal Reserve Board

How should economic or regulatory capital be allocated to tranches of securitisations? The standard Basel conditional dependence calculations are complicated in this case by non-linearity effects and complex deal dependence. Here, Michael Gordy and David Jones present an uncertainty in loss provision approach that simplifies these problems, and leads to a single economic capital formula suitable for regulatory purposes.

21 Analysing Counterparty Risk
Eduardo Canabarro; Evan Picoult; Tom Wilde
Goldman Sachs; Citigroup; Credit Suisse First Boston

In an attempt to improve on existing regulatory approaches to derivatives counterparty credit risk, Eduardo Canabarro, Evan Picoult and Tom Wilde present a new method based on expected positive exposure (EPE). Using a one-factor conditional independence framework, they derive a formula for the ratio of EPE to fixed loan-equivalent exposures, showing its dependence on various portfolio parameters and comparing analytical with Monte Carlo calculations.

22 Testing Rating Accuracy
Bernd Engelmann; Evelyn Hayden; Dirk Tasche
Deutsche Bundesbank; University of Vienna; Deutsche Bundesbank

As Basel II approaches the implementation stage, regulators have identified internal ratings validation as a key challenge for banks using this approach. Here, Bernd Engelmann, Evelyn Hayden and Dirk Tasche build upon previous research showing how to use the so-called receiver operator characteristic method in ratings validation, testing their results on a real database of small and medium-sized enterprise loans.

23 Market-Implied Ratings
Ludovic Breger; Lisa Goldberg; Oren Cheyette
Barra

There has been much debate over the respective merits of credit ratings and market-based indicators. Ludovic Breger, Lisa Goldberg and Oren Cheyette present a new approach that tries to incorporate the benefits of both approaches. Starting with agency ratings, they ask how the information obtained from market credit spreads can be used to improve them.

24 Benchmarking Asset Correlations
Alfred Hamerle; Daniel Rosch; Thilo Liebig
University of Regensburg; Deutsche Bundesbank

Basel II stipulates that the asset correlation to be used in calibration of obligor risk weights is 20%. Here, Alfred Hamerle, Thilo Liebig and Daniel Rosch use a parametric model to empirically obtain asset correlations from a large database of historical defaults. They find the observed correlation to be an order of magnitude less than the Basel assumption, and suggest that the parameter could be made adjustable as a result.

25 Correlation Evidence
Arnaud de Servigny; Olivier Renault
Standard & Poors Risk Solutions

Like ratings, default correlation is an area of fierce industry debate. But any fundamental, long-term investor searching for fair value in credit correlation will want to understand what the historical data actually says. Here, Arnaud de Servigny and Olivier Renault address this need. By exploring a large rating agency database, they suggest that the link between equity and default correlations is obscured by statistical noise, while risk-free interest rates appear to have little measurable effect.

26 A False Sense of Security
Jon Frye
Federal Reserve Bank of Chicago

Credit portfolio models often assume that recovery rates are independent of default probabilities. Here, Jon Frye presents empirical evidence showing that such assumptions are wrong. Using US historical default data, he shows that not only are recovery rates sensitive to the economic cycle, but also that they vary more for senior debt than for junior debt categories.

27 Ultimate Recoveries
Craig Friedman; Sven Sandow
Standard & Poors

Measuring recovery using the ultimate rate observed at emergence from bankruptcy may be conceptually desirable, but modelling it is difficult. Craig Friedman and Sven Sandow tackle the problem by maximising the creditor's utility function, constructed from a recovery rate probability distribution, conditional on information that ought to influence it, such as collateral quality and debt seniority.

28 Unexpected Recovery Risk
Michael Pykhtin
KeyCorp

For credit portfolio managers, the priority is to properly incorporate recovery rates into existing models. Here, Michael Pykhtin improves upon earlier approaches, allowing recovery rates to depend on the idiosyncratic part of a borrower's asset return, in addition to the systematic factor. Using a lognormal distribution of collateral value, ensuring that it always remains positive, he derives closed-form expressions for expected loss and economic capital.

29 Credit Ensembles
Kevin Thompson; Roland Ordovas
BNP Paribas; BSCH

Kevin Thompson and Roland Ordovas address the question of how individual counterparties contribute to the total credit risk of a portfolio. They provide an analytic method, new to credit modelling, to estimate all joint default statistics conditional upon a given portfolio loss. The results clarify how the structure of the portfolio changes with loss amount and how clusters of default arise in credit portfolios.

30 The Road to Partition
Kevin Thompson; Roland Ordovas
BNP Paribas; Caixa Catalunya

Applying the ensemble approach developed in these pages last month, Kevin Thompson and Roland Ordovas calculate risk contributions and show how to measure higher-order default dependence using the method of partitions. The results provide tools allowing credit portfolio managers to assess the risks within their portfolios conditional upon different levels of loss.

31 Coarse-Grained CDOs
Michael Pykhtin; Ashish Dev
Keycorp

While analytical models of credit portfolio risk using conditional independence have been one of the most promising areas of recent research, they often involve granularity assumptions that are violated in CDO reference portfolios. Here, Michael Pykhtin and Ashish Dev lift the usual fine-grained portfolio restriction to calculate CDO loss distributions for coarse-grained reference portfolios. Interestingly, they show that senior tranches are particularly sensitive to the level of granularity.

32 Residual Risk in Auto Leases
Michael Pykhtin; Ashish Dev
Keycorp

Michael Pykhtin and Ashish Dev use a conditional independence framework to calculate the economic loss distribution for a portfolio of auto leases. Using the fact that portfolios of this type are usually fine-grained, the authors derive an analytic formula for the economic capital dependent on systematic risk factors.

33 Contributions to Credit Risk
Alexandre Kurth; Dirk Tasche
UBS Wealth Management; Deutsche Bundesbank

Optimisation of credit portfolios requires that risk contributions be quantified. However, there has been disagreement over which of three popular tail risk measures should be used. Here, Alexandre Kurth and Dirk Tasche offer a way forward, showing how to calculate all three measures in the context of CreditRisk+, and then applying the calculation to a set of sample portfolios, with interesting results.

34 Enhancing CreditRisk+
Götz Giese
Commerzbank

Of the various analytical approaches to credit portfolio modelling, CreditRisk+ has become the most popular due to its tractability. However, the model suffers from the restrictive assumption of sector independence. Moreover, the recursion relation for calculating the loss distribution is unstable for very large portfolios. Here, Götz Giese presents an improved version of the model with a stable recursion scheme and sector correlations, which compares favourably with other approximation techniques when used to calculate loss distributions.

35 Using the Grouped t-Copula
Stéphane Daul; Enrico De Giorgi; Filip Lindskog; Alexander McNeil
Swiss Re; University of Zurich; Risk Lab; ETH Zurich

Student-t copula models are popular, but can be over-simplistic when used to describe credit portfolios where the risk factors are numerous or dissimilar. Here, Stéphane Daul, Enrico De Giorgi, Filip Lindskog and Alexander McNeil construct a new, generalised model - the 'grouped t-copula' - that clusters individual risk factors within various geographical sectors. The authors show how to estimate parameters for the grouped t-copula, and compare estimates for VAR and expected shortfall with those given by other models.

36 Overcoming the Hurdle
Thomas C. Wilson
Oliver, Wyman & Company

How should capital be allocated to different business lines in a financial institution? Thomas Wilson explores this question from an investor's perspective by constructing a statistical model that measures the risk of individual business types. The results suggest that capital allocation decisions that ignore variations in the cost of capital are erroneous.
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