Cutting Edge

Expanded smiles

Implementing models with stochastic as well as deterministic local volatility can be challenging. Here, Jesper Andreasen and Brian Huge describe an expansion approach for such models that avoids the high-dimensional partial differential equations usually…

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…

Cutting Edge: Pure jump models for energy prices

Université de Lausanne’s Roberto Marfè investigates pure jump processes as modelling blocks for the distributions of energy returns under the pricing measure. An easy-to-implement option-implied approach is outlined, which circumvents most of the…

A dynamic model for correlation

Equity markets have experienced a significant increase in correlation during the crisis, resulting in exotic derivatives portfolios realising large losses. As larger correlations in downward scenarios are already implied in the index option market in the…

Individual names in top-down CDO pricing models

The Gaussian copula collapsed as a means of pricing collateralised debt obligations in the crisis of 2008, as to match prices and deltas nonsensical correlation parameters were required. By adapting the traditional framework to cater for more general…

Putting the smile back on the face of derivatives

Cross-asset quadratic Gaussian models have been limited in the scale of their implementation by the difficulty in ensuring the correct drift conditions to omit arbitrage. Here, Paul McCloud shows how to exploit the symmetries of the functional form to…

Modest means

Credit loss models typically calibrate default separate from loss given default. Here, Jon Frye calibrates simultaneously, using credit loss data. This produces a surprising test result: the credit loss models do not significantly outperform a…

Pricing the bail-out

In an introduction to this month’s Cutting Edge, Risk’s technical editor, Mauro Cesa, and assistant technical editor, Laurie Carver, look at a new model proposed by a former Risk magazine quant of the year, which attempts to quantify the effect of state…

Smile dynamics IV

Lorenzo Bergomi addresses the relationship between the smile that stochastic volatility models produce and the dynamics they generate for implied volatilities. He introduces a new quantity, the skew stickiness ratio (SSR), and shows how, at order one in…

Information of interest

The flow of information in financial markets on future liquidity risk generates the rise and fall of demand for default-free bonds. Here, Dorje Brody and Robyn Friedman present an approach to pricing these bonds and the associated derivatives, based on…

A market model on the iTraxx

A market model for the dynamics of credit-risky baskets and indexes such as the iTraxx has long been sought, but because of difficulties with the natural numéraire has remained elusive. Here, Philippe Carpentier proposes using hedging arguments to…

Risk Management After Lehman

Can the constants used by quants and risk managers be trusted in the post-Lehman environment? Chris Schlegel of Southern Company looks at some of the pitfalls risk managers need to look out for when using constants and assesses why they are both vitally…

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…

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