Risk magazine/Technical paper
Questions of error
Consider the following two, difficult, questions. How should a financial institution allocate capital to different businesses? How should a financial institution be valued? The first question is a subject for the senior management of an institution. But…
Market-implied ratings
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…
Overcoming the hurdle
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…
Correlation evidence
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…
I will survive
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…
Bidding principles
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…
Credit barrier models
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
Black smirks
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…
Real option valuation and equity markets
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…
Pitfalls and alternatives
Correlation
The road to partition
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…
Enhancing CreditRisk+
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…
Credit ensembles
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…
Contributions to credit risk
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…
Random tranches
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…
Capturing the smile
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…
What causes crashes?
Are large market events caused by easily identifiable exogenous shocks such as major newsevents, or can they occur endogenously, without apparent external cause, as an inherent propertyof the market itself? Here, Didier Sornette, Yannick Malevergne and…
From horses to hedging
Financial derivatives rely on liquid underlying markets to work properly, but what happenswhen such underlying markets do not exist, as is the case for indexes such as GDP orunemployment? Here, Ken Baron and Jeffrey Lange suggest a parimutuel auction…
Extreme forex moves
What is the appropriate statistical description of tail risk in a market portfolio? In the context offoreign exchange, Peter Blum and Michel Dacorogna address this problem using extreme valuetheory. Using 20 years of data, they estimate parameters for an…
Why be backward?
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…
Coarse-grained CDOs
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…
Dealing with discrete dividends
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…
Volatile volatilities
When pricing exotic interest rate derivatives, calibration of model parameters to vanilla cap or swaption prices can be especially time-consuming, especially if stochastic volatility is incorporated into the standard Libor market models or low…
Loan portfolio value
Using a conditional independence framework, Oldrich Vasicek derives a useful limiting form for the portfolio loss distribution with a single systematic factor. He then derives a risk-neutral distribution suitable for traded portfolios, and shows how…