The staff at Investopedia.com offers a detailed explanation of the delta of an option as being part of the Black-Scholes option pricing formula, which provides the implied volatility, however, they also stress why the Black-Scholes formula is limited.
The delta of an option is a component of the Black-Scholes option pricing formula, which provides the implied volatility for an option. The implied volatility is backed out of the formula, meaning all inputs for the option formula are known except for the implied volatility. The delta of an option measures the extent an option will move in price relative to price movements in the underlying asset. Implied volatility estimates the underlying asset's future volatility. Generally, implied volatility goes up when the asset's price goes down and it goes down when the asset's price goes up. This is because bearish markets are considered to be more risky than bullish ones.
Implied volatility is a value output of the Black-Scholes formula. The formula's inputs are the option's time to expiration, option’s strike price, underlying stock's price, and current interest rates. However, the Black-Scholes formula is limited since it can only be used to calculate the value of European options, which can only be exercised on the expiration day. This is different from American options, which may be exercised at any point up until expiration. Equity options are generally of the American variety.
With greater implied volatility comes a higher price on the option. Those who sell options want the actual volatility, or historical volatility, to be less than the implied volatility, while those who buy options want the implied volatility to be lower than the actual volatility. Even where investors are trading directional option strategies, volatility plays an integral role in the profitability of trades. Thus, it is important for investors to understand how implied volatility works with option pricing formulas.
By the staff at Investopedia.com
