Quantitative analysis
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…
Pricing and hedging of variable annuities
Technical papers
Delta and vega hedging in the SABR and LMM-SABR models
Riccardo Rebonato, Andrey Pogudin and Richard White examine the hedging performance of the SABR and LMM-SABR models using real market data. As a by-product, they gain indirect evidence about how well specified the two models are. The results are…
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…
Model selection for loss reserves: The Growing Triangle technique
Technical papers
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…
Seasonally adjusted prices for inflation-linked bonds
Inflation-linked bond markets are used ever more frequently by policy-makers, economists and commentators to assess the market's opinion about the future path of inflation and real yields. But important effects such as seasonality and carry are often…
Solvency II Reinsurance - Counterparty default risk
Technical papers
Component VAR for a non-normal world
It has become standard to account for non-normality when estimating portfolio value-at-risk, but there are few methods available to calculate the risk contributions of each component in a non-normal portfolio. Brian Peterson and Kris Boudt present a…
Juggling snowballs
Previous work on the valuation of cancellable snowball swaps in the Libor market model suggested the use of nested Monte Carlo simulations was needed to obtain accurate prices. Here, Christopher Beveridge and Mark Joshi introduce new techniques that…
Delta and vega hedging in the SABR and LMM-SABR models
Riccardo Rebonato, Andrey Pogudin and Richard White examine the hedging performance of the SABR and LMM-SABR models using real market data. As a by-product, they gain indirect evidence about how well specified the two models are. The results are…
Credit remains the focus
Degree of Influence
Putting a dampener on Solvency II
Technical papers
Component VAR for a non-normal world
Market Risk
Struck off
Credit default swaps (CDSs) offer protection against issuer default, and in general the protection is paid via a running spread rather than upfront. When the par spread changes, the contract cannot be unwound without leaving a default-contingent annuity…
Parameter estimation with k-means clustering
Ever since the pioneering work of Cox, Ross & Rubinstein (1979), tree models have been popular as an asset pricing method. However, statistical estimation of the parameters of tree models has been less studied. In this article, Kiseop Lee and Mingxin Xu…
Mortality fluctuations modelling with a shared frailty approach
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…
Fully flexible views: theory and practice
Attilio Meucci proposes a unified methodology to input non-linear views from any number of users in fully general non-normal markets and perform, among others, stress testing, scenario analysis and ranking allocation. He walks the reader through the…
Improving annuity pricing with address data
Technical papers
A multi-state Vasicek model for correlated default rate and loss severity
Correlation between default and recovery has an important bearing on credit risk capital. Here, Rahul Sen shows that the effect can be modelled efficiently by allowing multiple loss states in the Vasicek framework. Heavy-tailed distributions result for…
Convexity adjustments in inflation-linked derivatives
Dorje Brody, John Crosby and Hongyun Li value several types of inflation-linked derivatives using a multi-factor version of the Hughston (1998) and Jarrow & Yildirim (2003) model. Expressions for the prices of zero-coupon inflation swaps with delayed…
Gamma loss and prepayment
Peter Jackel presents a model for the dynamics of fractional notional losses and prepayments on asset-backed securities for the valuation and risk management of derivatives, including waterfall structures and other structured debt obligations on bespoke…