Technical papers/Equity Derivatives
The beta stochastic volatility model
Local stochastic volatility models combine perfect calibration at time zero with realistic price dynamics. But traditional methods tend to underestimate the forward skew, and mis-price exotics such as...
Calibrating a local volatility model to options prices is a complicated process requiring both interpolation of liquid prices and extrapolation beyond them. Recently focus has turned to efficient numerical...
Lorenzo Bergomi addresses the issue of pricing multi-asset options in the context of asynchronous markets. Using the criterion that the carry profit and loss (P&L) vanishes, he derives the expression of...
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More Technical papers/Equity Derivatives articles
Breaking correlation breaks
Large deviations in dependencies – correlation breaks – are a hazard when risk managing multi-asset derivatives such as worst-of options. Adil Reghai presents a calibration scheme for local correlation that ensures a basket’s skew is compatible...
The value of a variance swap – a question of interest
Pricing equity variance swaps is well understood in the case of deterministic interest rates, but particularly for longer-dated swaps the stochastic nature of the rate cannot be ignored. Here, Per Hörfelt and Olaf Torné derive the fair strike when both...
Expanded Smiles
Implementing models with stochastic 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 associated with their implementation....
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 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...
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...
Calibration of local stochastic volatility models to market smiles
Pierre Henry-Labordère introduces a new technique for calibrating local volatility extensions of arbitrary multi-factor stochastic volatility models to market smiles. Although approximate, this technique is both fast and accurate. The procedure is illustrated...
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