Local Volatility: Smooth Calibration and Fast Usage
14 Pages Posted: 20 Feb 2012 Last revised: 31 Dec 2015
Date Written: February 20, 2012
This paper explores a powerful calibration technique of local volatility models based on the fixed point algorithm. It proves to be more robust and generic than the standard Dupire Approach. We also show how to dramatically increase the performance of Monte Carlo simulations by means of techniques borrowed from quantum physics. In particular, we use operator theory combined with fast discrete random generation to construct fast, efficient and robust algorithms for production purposes. This contribution is an engineering piece of work.
Keywords: Local volatility, calibration, fixed point algorithm, Operator Methods, Fast Discrete Random Number simulation, Magnus
JEL Classification: G13
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