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Option pricing theory estimates a value of an options contract by assigning a price, known as a premium, based on the calculated probability that the contract will finish in the money (ITM) at expiration. Essentially, option pricing theory provides an evaluation of an option's fair value, which traders incorporate into their strategies.
The evolution of the modern-day options market is attributed to the 1973 pricing model published by Fischer Black and Myron Scholes. The Black-Scholes formula is used to derive a theoretical price for financial instruments with a known expiration date. However, this is not the only model. The Cox, Ross, and Rubinstein binomial option pricing model and Monte-Carlo simulation are also widely used.
The primary goal of option pricing theory is to calculate the probability that an option will be exercised, or be ITM, at expiration and assign a dollar value to it. The underlying asset price (e.g., a stock price), exercise price, volatility, interest rate, and time to expiration, which is the number of days between the calculation date and the option's exercise date, are commonly-employed variables that are input into mathematical models to derive an option's theoretical fair value.
Options pricing theory also derives various risk factors or sensitivities based on those inputs, which are known as an option's Greeks. Since market conditions are constantly changing, the Greeks provide traders with a means of determining how sensitive a specific trade is to price fluctuations, volatility fluctuations, and the passage of time.
The longer that an investor has to exercise the option, the greater the likelihood that it will be ITM and profitable at expiration. This means, all else equal, longer-dated options are more valuable. Similarly, the more volatile the underlying asset, the greater the odds that it will expire ITM. Higher interest rates, too, should translate into higher option prices.