How Does the Risk-Neutral Probability Concept Relate to Delta?

In the Black-Scholes framework, the Delta of a call option is mathematically equal to the cumulative probability distribution function N(d1), which is the risk-neutral probability that the option will expire in-the-money. This probability is derived under the assumption that the expected return on the underlying asset is the risk-free rate.

How Is Delta Used as a Probability Estimate for an Option Expiring ITM?
What Is the Relationship between the Option’s Delta and Its Probability of Expiring In-the-Money?
What Does a Delta of -0.80 on a Bitcoin Put Option Indicate?
Does an ITM Option Lose Time Value Faster or Slower than an OTM Option, All Else Equal?
What Is the ‘Delta’ of an Option?
What Is the Relationship between Delta and the Probability of an Option Expiring In-the-Money?
How Does the Black-Scholes Model Mathematically Represent This Acceleration?
Define In-The-Money (ITM) for Both a Call and a Put Option

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