Arbitrages in the Volatility Surface Interpolation and Extrapolation
8 Pages Posted: 14 Nov 2012 Last revised: 27 Jan 2013
Date Written: September 21, 2012
The implied volatility surface is built from a discrete set of vanilla option quotes. To move from a discrete set to a continuous surface, interpolation and extrapolation are therefore needed in the expiry dimension as well as in the strike dimension. This paper will study the interpolation and extrapolation in the time-to-expiry dimension. In particular, we show here that a linear interpolation in variance, a very common way of interpolation, of two arbitrage-free slices of increasing variance can lead to an arbitrage in an interpolated slice. We also show that flat volatility extrapolation, another common usage, will also lead to arbitrages. To conclude, we present an alternative simple extrapolation.
Keywords: volatility surface
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