Maximum Implied Variance Slope -- Practical Aspects

Abstract

In the Black-Scholes model, the absence of arbitrages imposes necessary constraints on the slope of the implied variance in terms of log-moneyness, asymptotically for large log-moneyness. The constraints are used for example in the SVI implied volatility parameterization to ensure the resulting smile has no arbitrages. This note shows that those no-arbitrage contraints are very mild, and that arbitrage is almost always guaranteed in a large range of slopes where the contraints are enforced.