Cutting Edge

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…

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…

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…

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…

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…

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,…

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

Joining the SABR and Libor models together

Fabio Mercurio and Massimo Morini propose a Libor market model consistent with SABR dynamics and develop approximations that allow for the use of the SABR formula with modified inputs. They verify that the approximations are acceptably precise, imply…

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…

Being two-faced over counterparty credit risk

A recent trend in quantifying counterparty credit risk for over-the-counter derivatives has involved taking into account the bilateral nature of the risk so that an institution would consider their counterparty risk to be reduced in line with their own…

Rates squared

Vladimir Piterbarg introduces a conveniently parameterised class of multi-factor quadratic Gaussian models, develops calibration formulas, and explains the advantages of this class of models over alternatives currently available for pricing and risk…

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