Explaining the Volatility Smile and Plotting Implied Volatility
Summary
The article explains why implied volatility can vary across option strike prices instead of remaining flat as in the Black-Scholes-Merton model. It attributes the smile partly to real asset returns having more extreme moves than a lognormal model predicts, which can make deep out-of-the-money options more valuable. It notes that the model’s assumptions do not fully capture observed return distributions or volatility patterns.
A Python workflow uses historical option data for the Nifty 50, a Black-Scholes function to calculate implied volatility, and a plot of implied volatility against strike price for a chosen date. The article reports that the plotted curve has a smile shape and points to the Derman-Kani and Heston models as alternatives developed to address limitations of Black-Scholes. The example is descriptive: it gives no systematic fit comparison, trading evaluation, or discussion of data quality and model sensitivities.
Key ideas
- Black-Scholes-Merton assumes lognormal underlying returns and constant volatility.
- Real asset returns can have more extreme outcomes than a lognormal model implies.
- Implied volatility can rise for options away from the at-the-money strike, forming a smile.
- Option prices can be converted to implied volatility and plotted by strike for a selected date.
- The example illustrates a curve but does not test whether a volatility trading strategy is profitable.
Tags
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.