Anmerkungen:
Nach Informationen von SSRN wurde die ursprüngliche Fassung des Dokuments May 15, 2023 erstellt
Beschreibung:
New arbitrability bounds derived for the quotations of the vanilla option’s market are exposed here for the implied volatility, its skew and its convexity. First, exploiting preceding theoretical results from (Fukasawa [11]), the implied volatility for any strike is shown to be comprised between finite lower and upper bounds that are derived from the existing implied volatilities derived from market quotes. These bounds are then proved to be narrower than other existing ones in the litterature. Moreover any model not perfectly calibrated to each market quote is shown to expose its user to arbitrages not only on the quoted strike but in a compact interval around any such quoted range, this interval being as wide as the error of calibration is big. Second, the skew of implied volatility at quoted strike is also shown to be comprised between two levels shaping an interval narrower than other ones exposed in preceding theoretical papers as these two bounds are derived from market quotes too. These results enforce the Durrleman condition existing on the convexity of the implied volatility and bring strong constraints for a model to be arbitrage free as they provide bounds for any finite level of strike. A practical example with the SVI parametric shape calibrated to SX5E market data is given for illustration of the method at the end of the paper