Quantitative analysis
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…
Cutting edge: Visualising value-at-risk
Risk transparency is an important yet elusive goal of any risk management process. One challenge is to understand the diversification effects of the portfolio elements. Wentao Zhao and Kevin Kindall introduce a graphical technique based on value-at-risk…
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…
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…
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…
Model students
Mauro Cesa, Energy Risk's technical editor, talks to quants about how quantitative analysis for energy markets has developed and what they see as the most influential technical publications of the past 15 years
A framework for extrapolation of long-term interest rates
Technical papers
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…
A dynamic model for hard-to-borrow stocks
Traders with short positions in stocks that are subject to short-selling restrictions risk being 'bought in', in the sense that their positions may be closed out by the clearing firm at market prices. Marco Avellaneda and Mike Lipkin present a model for…
Estimating intrinsic currency values
Forex market practitioners constantly talk about the strengthening or weakening of individual currencies. In this article, Jian Chen and Paul Doust present a new methodology to quantify these statements in a manner that is consistent with forex market…
Robust asset allocation under model risk
Financial investors often develop a multitude of models to explain financial securities' dynamics, none of which they can fully trust. Model risk (also referred to as ambiguity) prevents investors from using the classical framework of expected utility…
Pricing options on film revenue
This article illustrates two models for cumulative revenues from films, a time-changed gamma process and a compound Poisson process, and how these models can be used to price options. Don Chance, Eric Hillebrand and Jimmy Hilliard find that while both…
Managing diversification
Attilio Meucci introduces a diversification index that represents the effective number of bets in a portfolio. With this index, based on entropy and constrained principal component analysis, he performs mean-diversification management adjusted for…
A stochastic model for pricing longevity-linked guarantees
Technical papers
Scaling conditional tail probability and quantile estimators
John Cotter presents a novel procedure for scaling relatively high-frequency tail probability and quantile estimates for the conditional distribution of returns
Factor models for credit correlation
Stewart Inglis, Alex Lipton and Artur Sepp present an extension of the static factor model for pricing credit correlation products introduced by Lipton (2006) and detailed in Inglis & Lipton (2007)
Accelerated ensemble Monte Carlo simulation
Traditional vanilla methods of Monte Carlo simulation can be extremely time-consuming if accurate estimation of the loss distribution is required. Kevin Thompson and Alistair McLeod show that the ensemble Monte Carlo method, introduced here,…
Vanilla option replication for ALM shortfall risk
Technical papers
Smile dynamics III
In two articles published in 2004 and 2005 in Risk, Lorenzo Bergomi assessed the structural limitations of existing models for equity derivatives and introduced a new model based on the direct modelling of the joint dynamics of the spot and the implied…
Error of VAR by overlapping intervals
When overlapping intervals in time series are used, volatility and price changes' percentiles are underestimated. Consequently, value-at-risk is also underestimated. Heng Sun, Izzy Nelken, Guowen Han and Jiping Guo measure the size of this underestimation