There appears to be a relationship between option delta and daily volatility. When you take the spot price and add daily volatility, the resulting price often aligns with a call option strike that has a delta near 0.3.
Note that I first developed this intuition using daily volatility from 30-Day Historical Volatility (\(HV30\)), but I now use implied volatility from Implied Volatility (\(IV\)) for Black-Scholes-Merton (BSM).
Here is an example:
- TSLA spot price = $309.78
- HV30 = 55.47%
- IV = 46.34%
Call option data for options expiring this week, data captured on Monday:
- Strike 315: Delta 0.3854
- Strike 317.5: Delta 0.3299
- Strike 320: Delta 0.2772
Daily volatility based on HV30:
\[ \sigma_{daily}^{HV} = \frac{0.5547}{\sqrt{252}} \approx 0.035 \]
Expected daily price change is +-$10.84. Therefore, desired strike is near $320. The delta is 0.2772.
Daily volatility based on IV:
\[ \sigma_{daily}^{IV} = \frac{0.4634}{\sqrt{252}} \approx 0.029 \]
Expected daily price change is +-$8.98. Therefore, desired strike is near $138. The delta is 0.3299.
This example illustrates that the delta ≈ 0.3 zone is commonly found near strike prices that are one daily volatility above the spot price, especially when using implied volatility in the Black-Scholes-Merton model.