Volatility Smile
A volatility smile was a pattern in the implied volatility surface where both deep OTM calls and deep OTM puts carried higher implied volatility than at-the-money options, producing a U-shaped or smile-shaped curve when IV was plotted against strike price, and was most commonly observed in currency and commodity options rather than equity index options.
The volatility smile stood in contrast to the volatility skew or smirk observed in equity index options. While equity indices typically showed a one-sided asymmetry — high IV for OTM puts, relatively lower IV for OTM calls — currencies and certain commodities exhibited symmetric elevations at both tails. The USD/INR options market on NSE's currency derivatives segment historically demonstrated elements of the smile, with both OTM dollar calls (rupee weakening scenarios) and OTM dollar puts (rupee strengthening scenarios) trading at premiums to ATM volatility, though the degree of symmetry varied with the prevailing macro environment.
The economic logic underlying the smile was the market's acknowledgment of fat tails in both directions. Currency pairs were driven by factors that could produce large moves in either direction — capital flow reversals, RBI intervention, geopolitical shocks, or global risk events. Unlike equity indices, where crashes were historically more abrupt than rallies (producing the asymmetric skew), currencies could gap violently in either direction. Participants buying protection against extreme moves in both directions created demand pressure at both tails of the strike distribution, lifting IV symmetrically.
In practice, a pure symmetric smile was rarely perfect. Most observed patterns were somewhere between a fully symmetric smile and a pure one-sided skew. Options traders described this spectrum using risk reversal (which measured the difference between OTM put IV and OTM call IV) and the butterfly spread metric (which measured the average of OTM put and call IV versus ATM IV). A large positive butterfly metric with a near-zero risk reversal indicated a smile; a large risk reversal indicated a skew.
For Nifty and Bank Nifty equity options on NSE, the smile pattern was not the dominant feature. The pronounced put skew meant that the smile characterisation was misleading when applied to Indian index options — calling it a smile understated the asymmetry. However, at very long tenors or in specific regimes following sharp upside moves, the IV differential between OTM calls and ATM options occasionally became more pronounced, producing a partial smile effect on the call wing.
Options model calibration in quantitative finance involved fitting mathematical models — the SABR model, the SVI parameterisation, or the local volatility model — to reproduce the observed smile or skew across strikes. These calibrated models were then used for consistent pricing of exotic options and structured products, a workflow relevant to institutional options desks operating in Indian markets through foreign portfolio investment channels.