Arbitrage-free SVI volatility surfaces

Abstract

In this article, we show how to calibrate the widely-used SVI parameterization of the implied volatility surface in such a way as to guarantee the absence of static arbitrage. In particular, we exhibit a large class of arbitrage-free SVI volatility surfaces with a simple closed-form representation. We demonstrate the high quality of typical SVI fits with a numerical example using recent SPX options data.

25 pages, 6 figures Corrected some typos. Extended bibliography. Paper restructured, Main theorem (Theorem 4.1) improved. Proof of Theorem 4.3 amended