Risk magazine/Technical paper
A dynamic model for correlation
Equity markets have experienced a significant increase in correlation during the crisis, resulting in exotic derivatives portfolios realising large losses. As larger correlations in downward scenarios are already implied in the index option market in the…
Bilateral counterparty risk with application to CDSs
Previous research on credit valuation adjustments (CVAs) with correlation between underlying and counterparty default, including volatilities of both, assumed unilateral default risk. However, the crisis prompted counterparties to ask institutions to…
Individual names in top-down CDO pricing models
The Gaussian copula collapsed as a means of pricing collateralised debt obligations in the crisis of 2008, as to match prices and deltas nonsensical correlation parameters were required. By adapting the traditional framework to cater for more general…
Pricing and hedging basket credit derivatives in the Gaussian copula
The static assumptions of the Gaussian copula model have long presented an obstacle to dynamic hedging of credit portfolio tranches. Here, Jean-David Fermanian and Olivier Vigneron combine the copula with a spread diffusion to derive hedging error as…
Funding beyond discounting: collateral agreements and derivatives pricing
Standard theory assumes traders can lend and borrow at a risk-free rate, ignoring the intricacies of the repo and collateralisation markets. Here, Vladimir Piterbarg shows that these force adjustments to discounting, forward prices and implied…
Putting the smile back on the face of derivatives
Cross-asset quadratic Gaussian models have been limited in the scale of their implementation by the difficulty in ensuring the correct drift conditions to omit arbitrage. Here, Paul McCloud shows how to exploit the symmetries of the functional form to…
Modest means
Credit loss models typically calibrate default separate from loss given default. Here, Jon Frye calibrates simultaneously, using credit loss data. This produces a surprising test result: the credit loss models do not significantly outperform a…
Pricing the bail-out
In an introduction to this month’s Cutting Edge, Risk’s technical editor, Mauro Cesa, and assistant technical editor, Laurie Carver, look at a new model proposed by a former Risk magazine quant of the year, which attempts to quantify the effect of state…
Smile dynamics IV
Lorenzo Bergomi addresses the relationship between the smile that stochastic volatility models produce and the dynamics they generate for implied volatilities. He introduces a new quantity, the skew stickiness ratio (SSR), and shows how, at order one in…
Information of interest
The flow of information in financial markets on future liquidity risk generates the rise and fall of demand for default-free bonds. Here, Dorje Brody and Robyn Friedman present an approach to pricing these bonds and the associated derivatives, based on…
A market model on the iTraxx
A market model for the dynamics of credit-risky baskets and indexes such as the iTraxx has long been sought, but because of difficulties with the natural numéraire has remained elusive. Here, Philippe Carpentier proposes using hedging arguments to…
Variance-covariance-based risk allocation in credit portfolios
Mikhail Voropaev proposes high-precision analytical approximation for variance-covariance-based risk allocation in a portfolio of risky assets. A general case of a single-period multi-factor Merton-type model with stochastic recovery is considered. The…
A rotationally invariant technique for rare event simulation
Because of their low probability, including extreme events in Monte Carlo calculations of the value-at-risk of a credit-risky portfolio requires many simulations. Here, Susanne Klöppel, Ranja Reda and Walter Schachermayer demonstrate a geometrically…
Shortfall: who contributes and how much?
Understanding risk contributions is a key part of successful risk management and portfolio optimisation. Richard Martin extends the discussion from value-at-risk to expected shortfall and shows that saddlepoint approximation preserves the convexity…
Last option before the armageddon
Damiano Brigo and Massimo Morini show how the pricing of credit index options depends on the probability of a financial portfolio 'armageddon'. They introduce a new equivalent pricing measure that lays the foundation for a market model framework in multi…
Calibration of local stochastic volatility models to market smiles
Pierre Henry-Labordère introduces a new technique for calibrating local volatility extensions of arbitrary multi-factor stochastic volatility models to market smiles. Although approximate, this technique is both fast and accurate. The procedure is…
Rehabilitating innovation
The financial crisis has put greater focus on the accuracy of models, with some regulators criticising banks for placing too much reliance on model outputs. In an introduction to this month's Cutting Edge section, Mauro Cesa, Risk's technical editor, and…
The hybrid saddlepoint method for credit portfolios
Anthony Owen, Alistair McLeod and Kevin Thompson derive a practical analytic approach, which they call the hybrid saddlepoint method, to calculate the credit loss distribution for a heterogeneous portfolio of correlated obligors
Credit spread shocks: how big and how often?
The second half of 2007 saw violent moves in credit spreads. In the fallout, there has been much discussion about how to estimate the probabilities of these severe events, but few conclusions have been obtained beyond the fact that historical data is…
Simulations with exact means and covariances
Attilio Meucci presents a simple method to generate scenarios from multivariate elliptical distributions with given sample means and covariances, and shows an application to the risk management of a book of options
Stepping through Fourier space
Diverse finite-difference schemes for solving pricing problems with Levy underlyings appear in financial literature. Invariably, the integral and diffusive terms are treated asymmetrically, large jumps are truncated, and the methods are difficult to…
Fast Monte Carlo Bermudan Greeks
In recent years, much effort has been devoted to improving the efficiency of the Libor market model. Matthias Leclerc, Qian Liang and Ingo Schneider extend the pioneering work of Giles & Glasserman (2006) and show how fast calculations of Monte Carlo…
Inflation modelling with SABR dynamics
Fabio Mercurio and Nicola Moreni introduce a new forward Consumer Price Index model that is based on a multi-factor volatility structure and leads to SABR-like dynamics for forward inflation rates. Their approach reconciles zero-coupon and year-on-year…