How come plotting IV vs Delta incorporate option term (while plotting volatility smile), as compared to IV vs K/S ?
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The volatility smile/smirk is a graphical representation of the implied volatility (IV) of options at different strikes or deltas. The smile/smirk refers to the shape of the implied volatility curve, which tends to be higher for out-of-the-money (OTM) options compared to at-the-money (ATM) or in-the-money (ITM) options.
When plotting IV against delta, the option term (time to expiration) is implicitly incorporated in the delta calculation. Delta is a measure of an option’s sensitivity to changes in the underlying asset’s price, and it is calculated as the rate of change of the option price with respect to changes in the underlying asset’s price.
Since delta changes with time to expiration, plotting IV against delta implicitly incorporates the option term. As time to expiration decreases, the delta of an option will change more rapidly for changes in the underlying asset’s price, and this will be reflected in the shape of the implied volatility curve.
In contrast, plotting IV against strike price (K) or the option’s price relative to the underlying’s spot price (K/S) does not directly incorporate the option term. However, the implied volatility curve derived from these plots can be adjusted to account for the option term using an appropriate volatility interpolation method, such as the VIX-style interpolation.