Define the Term ‘Implied Probability’ as It Relates to an Option’s Delta.
The Delta of an option can be used as a close approximation for the market's implied probability that the option will expire In-the-Money (ITM). For a European call option, the Delta is mathematically related to the cumulative normal distribution function, which represents the probability of the asset price being above the strike price at expiration.
Therefore, a Delta of 0.65 for a call option suggests the market believes there is approximately a 65% chance the call will expire ITM. This is a heuristic, not a precise probability.
Glossar
Probability
Modeling ⎊ Probability is fundamental to quantitative finance, providing the mathematical framework for modeling asset price movements and calculating risk.
Cumulative Normal Distribution
Probability ⎊ The cumulative normal distribution, within cryptocurrency options and financial derivatives, represents the probability that a random variable, typically representing an asset’s return or price change, will fall below a specified value.
Implied Probability
Derivation ⎊ This quantitative metric is derived from the market price of an option contract, representing the probability of the underlying cryptocurrency reaching a specific strike price by expiration, as perceived by the market.