No-Arbitrage Conditions for Equity Implied Volatility Surfaces
Document ID: 2008-998
Published on: 30th June 2008
When we create an Equity Implied Volatility (IV) surface using either market data directly, or interpolated market data, it is extremely important that we check that our implied prices are free of arbitrage. There are a number of very basic arbitrage tests that we can perform on our IV surface; these include butterfly (convexity) spreads, strike spreads, calendar spreads, and the total variance tests. Option prices should be convex with respect to strike, that is, a butterfly spread should have positive value. A negative value implies negative transition probabilities, and can lead to significant pricing errors in models like the local volatility model, which by construction assumes an arbitrage free surface as an input.
