SciComp - Futures Volatility Surface Calibrator
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Modeling Volatility and Valuing Derivatives Under Anchoring
Paul Wilmott, Daniel Duffy & Alan Lewis

We develop a complete-markets model with volatility smiles, tractability, and intuitive appeal as an anchoring or habit-formation model. Like traditional stochastic volatility models, it is invariant to a multiplicative scaling the stock price levels. The anchoring effect is that the volatility depends on the relative value of the current stock price compared to its past history, with an exponential weighting.

Click here for free access to this and more exclusive content from the September Issue of Wilmott Magazine.

Low Strike Extrapolation for SABR - d-fine
Sebastian Schlenkrich, André Miemiec, Tilman Wolff-Siemssen, d-fine GmbH, Frankfurt, Germany

In this paper we analyse the modelling of rate options in a low interest rate market environment. In particular, the pricing of low, zero and negative strike vanilla options is considered. We review the modelling approaches available in the literature. For the important special case of the widely used SABR formula we illustrate the shortcomings connected with the low strike wing of the smile.

Moreover, a simple approach of low strike extrapolation will be presented. It is based on gluing the density function implied by the standard SABR formula to a suitable density function at low strikes in an arbitrage free manner. This approach yields a robust and transparent method to price low, zero and negative strike vanilla options.

Least Squares Importance Sampling for Libor Market Models: Wilmott Magazine Article
Luca Capriotti 662 Views

A recently introduced Importance Sampling strategy based on a least squares optimization is applied to the Monte Carlo simulation of Libor Market Models. Such Least Squares Importance Sampling (LSIS) allows the automatic optimization of the sampling distribution within a trial class by means of a quick presimulation algorithm of straightforward implementation.

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