Volatility interpolation
Developing an arbitrage-free, consistent volatility surface in both expiry and strike from a discrete set of option quotes is a difficult and computationally intense problem. In this article, Jesper Andreasen and Brian Huge use a non-standard variant of the fully implicit finite difference method to reduce the computational cost by orders of magnitude. An example shows how the model can fit the Eurostoxx 50 option market in approximately 0.05 seconds of CPU time
Local volatility models such as those of Dupire (1994), Andersen & Andreasen (1999), JP Morgan (1999) and Andreasen & Huge (2010) ideally require a full continuum in expiry and strike of arbitrage-consistent European-style option prices as input. In practice, of course, we only observe a discrete set of option prices.
Volatility interpolation
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