A bias in the volatility smile.

*(English)*Zbl 1417.91494Summary: We show that even if options traded with Black-Scholes-Merton pricing under a known and constant volatility, meaning essentially in perfect markets, one would still obtain smiles, skews, and smirks. We detect this problem by pricing options with a known volatility and reverse engineering to back into the implied volatility from the model price that was derived from the assumed volatility. The returned volatilities follow distinctive patterns resulting from algorithmic choices of the user and the quotation unit of the option. In particular, the common practice of penny pricing on option exchanges results in a significant loss of accuracy in implied volatility. For the most common scenarios faced in practice, the problem primarily exists in short-term options, but it manifests for virtually all cases of moneyness of at least 10% and often 5%. While it is theoretically possible to almost eliminate the problem, practical limitations in trading prevent any realistic chance of avoiding this error. It is even more difficult to identify and control the problem when smiles also arise from market imperfections, as is widely accepted. We empirically estimate a very conservative lower bound of the effect at about 16% of the observed smile for 30-day options. Thus, we document a previously unknown phenomenon that a portion of the volatility smile is not of an economic nature. We provide some best-practice recommendations, including the explicit specification of the algorithmic choices and a warning against using off-the-shelf routines.

##### MSC:

91G20 | Derivative securities (option pricing, hedging, etc.) |

##### Keywords:

Black-Scholes-Merton model; option pricing; implied volatility; volatility; volatility smile; computational finance; algorithmic finance; options
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\textit{D. M. Chance} et al., Rev. Deriv. Res. 20, No. 1, 47--90 (2017; Zbl 1417.91494)

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