Expanded forward volatility

Using a one time-step finite difference implementation, Jesper Andreasen and Brian Huge eliminate the arbitrages in the wings of the volatility smile that result from most expansion techniques for local stochastic volatility models, including the widely used SABR model

market volatility

Modelling the implied volatility smile using local and stochastic volatility has been the subject of much research over the past 20 years (see, for example, Dupire, 1996, Hagan et al, 2002, Heston, 1993, Jex, Henderson & Wang, 1999, Lewis, 2000, and Lipton, 2002). Interest rate option desks typically need to maintain very large amounts of interlinked volatility data. For each currency, there might be 20 expiries and 20 tenors, that is, 400 volatility smiles. Furthermore, the smiles might be

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