Constructing a volatility smile involves plotting the implied volatility of options against their strike prices for a specific underlying asset and expiration date. The process begins by collecting data on option prices for various strikes. Next, we utilize an options pricing model, such as the Black-Scholes model, to back out the implied volatility for each option. Implied volatility is the volatility input needed in the model to match the observed market price of the option. When plotted, the resulting curve usually displays a characteristic "smile" shape, where implied volatility is higher for both very low and very high strike prices compared to at-the-money (ATM) options.
This "smile" shape arises due to various factors:
Skewness and Kurtosis: The distribution of the underlying asset's returns may exhibit skewness and kurtosis, implying a higher likelihood of extreme events than a normal distribution. This translates to a higher implied volati....
Log in to view the answer
