Black-Scholes Formula

In 1973, mathematicians Fischer Black, Myron Scholes, and Robert Merton published their formula for calculating the premium of an option. Known as the Black-Scholes model, this formula accounted for a variety of factors that affect premium:

  • Underlying stock price
  • Options strike price
  • Time until expiration
  • Implied volatility
  • Dividend status
  • Interest rates

Although the Black-Scholes formula is well known, it isn’t the only method for computing an option’s theoretical value. American-style equity options are typically priced using a bi-nomial model due to the early exercise feature.

Investors can tweak or manually adjust inputs to any pricing model to illustrate the impact of stock movement, volatility changes or other factors that influence an option’s actual value. For example, you could adjust the days until expirations or underlying price to see the effect on the Delta, Gamma and other Greeks.

The limitation of all pricing models is that market forces determine actual premiums, not formulas, no matter how sophisticated a formula might be. Market influences can result in highly unexpected price behavior during the life of a given options contract.

While no model can reliably predict what options premiums will be available in the future, some investors use pricing models to anticipate an option’s premium under certain future circumstances. For instance, you can calculate how an option might react to an interest rate increase or a dividend distribution to help better predict the outcomes of your options strategies.

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