Risk magazine/Technical paper

Operational VAR: meaningful means

Making the assumption that the distribution of operational loss severity has finite mean, Klaus Böcker and Jacob Sprittulla suggest a refined version of the analytical operational value-at-risk theorem derived in Böcker & Klüppelberg (2005), which…

A telling scope

The number of technical articles submitted each year to Risk has stabilised at around 90, and a high proportion of them are still about credit derivatives and credit portfolio risk analysis. In fact, in our Cutting Edge pages and behind the scenes we…

The saddlepoint method and portfolio optionalities

Richard Martin describes the application of saddlepoint methods to the calculation of tranche payouts and expected shortfall in loss distributions. Aside from computational use in their own right, the resulting formulas motivate a forthcoming discussion…

Maximum draw-down and directional trading

Maximum draw-down measures the worst drop in a market in a given time period. Jan Vecer shows how to price and replicate this event. Replication can be naturally linked to existing popular trading strategies, such as momentum or contrarian trading

Cutting edges using domain integration

Zhengyun Hu, Jeroen Kerkhof, Paul McCloud and Jorg Wackertapp present the semi-analytic lattice integrator tree, a domain integrator method for pricing derivatives. This method can eliminate almost all numerical noises in derivatives pricing, and…

Optimising omega

Optimising a portfolio's omega generally requires non-linear optimisation methods. Helmut Mausser, David Saunders and Luis Seco show that, under suitable conditions, a simple change of variables transforms the problem into a linear program that is much…

An indirect view from the saddle

The saddlepoint method has become established as a tool for portfolio analysis. In this article, Richard Martin and Roland Ordovas review the main concepts and show that there are two essentially distinct ways of applying it to conditional independence…

Dynamic frailties and credit portfolio modelling

Martin Delloye, Jean-David Fermanian and Mohammed Sbai estimate and discuss a reduced-form credit portfolio model in a proportional hazard framework. They propose an innovative method of generating flexible amounts of dependence between underlying…

Dealing with seller's risk

The risk of trade receivables securitisations comes from both the pool of assets and the seller of the assets. Vivien Brunel develops a model for securitisation exposures that deals with both risks, and analyses in detail the interplay between debtors'…

Beyond Black-Litterman in practice

In principle, the copula-opinion pooling (COP) approach extends the Black-Litterman methodology to non-normally distributed markets and views. However, the implementations of the COP framework presented so far rely on restrictive quasi-normal assumptions…

Modelling and estimating dependent loss given default

Martin Hillebrand proposes a portfolio credit risk model with dependent loss given default (LGD), offering a reasonable economic interpretation that is easily applicable to real data. He builds a precise mathematical framework, and stresses some…

Smiling at convexity

The price of a constant maturity swap (CMS)-based derivative is largely determined by the value of swaption volatilities at extreme strikes. Fabio Mercurio and Andrea Pallavicini propose a simple procedure for stripping consistently implied volatilities…

Cracking VAR with kernels

Value-at-risk analysis has become a key measure of portfolio risk in recent years, but how can we calculate the contribution of some portfolio component? Eduardo Epperlein and Alan Smillie show how kernel estimators can be used to provide a fast,…

Low-default portfolios without simulation

Low-default portfolios are a key Basel II implementation challenge, and various statistical techniques have been proposed for use in PD estimation for such portfolios. To produce estimates using these techniques, typically Monte Carlo simulation is…

A saddle for complex credit portfolio models

Guido Giese applies the saddle-point approximation to analyse tail losses for very general credit portfolios, including correlated defaults, stochastic recovery rates, and dependency between default probabilities and recovery rates. The numerical…

Intensity gamma

Mark Joshi and Alan Stacey develop a new model for correlation of credit defaults based on a financially intuitive concept of business time similar to that in the variance gamma model for stock price evolution

A model of op risk with imperfect controls

Jorge Sobehart considers a model for the loss severity of operational risk events whose distribution is determined by risk control and risk mitigation. In particular, he shows that ineffective risk controls can lead to heavy-tailed distributions of…

The real value of stock

Collars involve the payment of a variable amount of stock, depending on an average stock price. In this article, Anthony Pavlovich uses the Black-Scholes framework to value these exotic derivatives and explore issues with hedging, as well as providing an…

Absolute return volatility

The use of absolute return volatility has manymodelling benefits, says John Cotter. An illustration isgiven for the market risk measure, minimum capitalrequirements

CMCDS valuation with market models

There is little, if any, literature available on constant maturity credit default swap valuation. Here, Damiano Brigo builds on his no-arbitrage dynamic credit default swap (CDS) market model to derive a formula involving a 'convexity adjustment' feature…