Cutting Edge

Enhancing CreditRisk+

Of the various analytical approaches to credit portfolio modelling, CreditRisk+ has become the most popular due to its tractability. However, the model suffers from the restrictive assumption of sector independence. Moreover, the recursion relation for…

Credit ensembles

Kevin Thompson and Roland Ordovas address the question of how individual counterparties contribute to the total credit risk of a portfolio. They provide an analytic method, new to credit modelling, to estimate all joint default statistics conditional…

Project risk: improving Monte Carlo value-at-risk

Cashflows from projects and other structured deals can be as complicated as we are willing to allow, but the complexities of Monte Carlo project modelling need not complicate value-at-risk calculation. Here, Andrew Klinger imports least-squares valuation…

Contributions to credit risk

Optimisation of credit portfolios requires that risk contributions be quantified. However, there has been disagreement over which of three popular tail risk measures should be used. Here, Alexandre Kurth and Dirk Tasche offer a way forward, showing how…

Random tranches

How should economic or regulatory capital be allocated to tranches of securitisations? The standard Basel conditional dependence calculations are complicated in this case by non-linearity effects and complex deal dependence. Here, Michael Gordy and David…

Capturing the smile

Since the discovery that traditional calibration methods fail to capture the dynamics of the smile, new approaches based on mixtures or ensembles of models have been developed. Simon Johnson and Han Lee present a variant of this approach that can be used…

Asian basket spreads and other exotic averaging options

Giuseppe Castellacci and Michael Siclari of OpenLink introduce a class of exotic options that simultaneously generalises both Asian and basket options. They develop approximate analytic models for real-time pricing of complex instruments that average…

What causes crashes?

Are large market events caused by easily identifiable exogenous shocks such as major newsevents, or can they occur endogenously, without apparent external cause, as an inherent propertyof the market itself? Here, Didier Sornette, Yannick Malevergne and…

From horses to hedging

Financial derivatives rely on liquid underlying markets to work properly, but what happenswhen such underlying markets do not exist, as is the case for indexes such as GDP orunemployment? Here, Ken Baron and Jeffrey Lange suggest a parimutuel auction…

Extreme forex moves

What is the appropriate statistical description of tail risk in a market portfolio? In the context offoreign exchange, Peter Blum and Michel Dacorogna address this problem using extreme valuetheory. Using 20 years of data, they estimate parameters for an…

A decision model for selling park and loan services

The park and loan model is useful for gas storages and pipelines. The concept can be applied to many ‘when to sell’-type decisions. Here, Huagang ‘Hugh’ Li considers selling park and loan services as a financial and statistical decision on revenue and…

Why be backward?

Originally developed as a tool for calibrating smile models, so-called forward methods can also be used to price options and derive Greeks. Here, Peter Carr and Ali Hirsa apply the technique to the pricing of continuously exercisable American-style put…

Coarse-grained CDOs

While analytical models of credit portfolio risk using conditional independence have been one of the most promising areas of recent research, they often involve granularity assumptions that are violated in CDO reference portfolios. Here, Michael Pykhtin…

by Dealing with discrete dividends

Over the past year, we have published several papers on the issue of options on stocks with discrete dividends. At least three distinct models are used by practitioners, involving trade-offs between accuracy and tractability. Here, Remco Bos, Alexander…

The front-month proxy hedge

The front-month proxy hedge is a correlation-based hedge that seeks to neutralise the aggregate sensitivity of a portfolio to a futures curve by converting the individual futures hedges into a single hedge with respect to only the front-month contract…

Volatile volatilities

When pricing exotic interest rate derivatives, calibration of model parameters to vanilla cap or swaption prices can be especially time-consuming, especially if stochastic volatility is incorporated into the standard Libor market models or low…

Loan portfolio value

Using a conditional independence framework, Oldrich Vasicek derives a useful limiting form for the portfolio loss distribution with a single systematic factor. He then derives a risk-neutral distribution suitable for traded portfolios, and shows how…

Weather option pricing with transaction costs

The weather derivatives market is becoming more liquid, and dynamic hedging of weather options with weather swaps is now possible, though limited by transaction costs. Here Stephen Jewson investigates the effect of such hedging on option pricing

Unsystematic credit risk

Although Basel has shifted its treatment of unsystematic credit risk from the first, capital rules pillar (where it was called the ‘granularity adjustment’) to the second, supervisory pillar of the forthcoming Accord, this issue is of great practical…

Minimising extremes

Portfolio diversification often breaks down in stressed market environments, but the co-movement of asset prices in a tail risk regime may be modelled using a coefficient of tail dependence. Here, Yannick Malevergne and Didier Sornette show how such…

A joint state-space model for spot and futures power

Portfolio-wide risk management requires a model that accounts correctly for correlations between the spot asset and various futures products. Kjetil Kåresen and Egil Husby discuss a joint multi-factor model for power spot and futures prices and show how…

Reconstructing volatility

Options on stock baskets have become a mainstay of the equity derivatives business, but pricing and hedging of such products is highly sensitive to implied volatility and correlation assumptions. Here, Marco Avellaneda, Dash Boyer-Olson, Jérôme Busca and…

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