The Impact of Computational Error on the Volatility Smile

It is well-known that the market prices of options produce implied volatilities that inexplicably vary by exercise price in a pattern often referred to as the volatility smile. This paper shows that not only do market prices produce volatility smiles, but so do model prices. This result occurs because of root finding algorithms, tolerance assumptions, numerical precisions, and quotation finiteness. Moreover, some assumptions result in patterns that resemble the smirks, and skews sometimes observed in market data. Consistent with empirical observations, the effects are greater the shorter the expiration. Elimination of these patterns is virtually impossible on a practical level, and even second-best results can be obtained only if options are traded with quadruple precision pricing and machine precision tolerance is assumed. We conclude that while alternative explanations for the smile can be true, prices generated under perfect conditions cannot even eliminate these smile, smirk, and skew patterns