Asia Risk/Technical paper
Event risk modelling for equities
Event risk modelling for equities
Choice of collateral currency
Collateral agreements are becoming popular in the over-the-counter derivatives market. Masaaki Fujii and Akihiko Takahashi demonstrate its significant impact on derivatives pricing with a direct link to the cross-currency market. The importance of…
Name concentration correction
Credit Risk
Smiling jumps
Smiling jumps
Two curves, one price
Interest Rate Derivatives
A dynamic model for leveraged funds
Guido Giese derives a model for the performance and Sharpe ratio of leveraged and inverse index funds that follow a dynamic leveraged trading strategy, that is, they are rebalanced on a daily basis to ensure a constant degree of leverage with respect to…
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 proper
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…
Fast Monte Carlo Bermudan Greeks
Cutting Edge - Interest Rates
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…
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…
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
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 the pricing and risk…
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…
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…
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…
Estimating credit contagion in a standard-factor model
Cutting Edge - Credit Portfolio Risk
Inflation is normal
Chris Kenyon introduces normal-based smile models for year-on-year inflation motivated by the observation that market lognormal caplet volatilities of less than 1% imply normality for maturities of up to 30 years. He is also motivated by the range of…
Combining the SABR and LMM models
Pierre Henry-Labordere analyses a stochastic volatility Libor market model that combines the SABR and Brace-Gatarek-Musiela (BGM) models in a natural way. Using an innovative geometrical method, he explains how to obtain analytical formulas for swaption…
A multi-state Vasicek model for correlated default rate and loss severity
Correlation between default and recovery has a major bearing on credit risk capital. Rahul Sen shows the effect can be modelled efficiently by allowing multiple loss states in the Vasicek framework. Heavy-tailed distributions result for arbitrary loss…