Black-Scholes Formula

In 1973, three mathematicians—Fischer Black, Myron Scholes, and Robert Merton—published their formula, known as the Black-Scholes model, for calculating the premium of an option, accounting for the variety of factors that affect premium. It is important to know the variables that go into the formula:

• Underlying Stock Price
• Options Strike Price
• Time Until Expiration
• Implied Volatility
• Dividend Status
• Interest Rates

The Black-Scholes formula, though perhaps the best known, 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. Inputs to any pricing model can be tweaked, or manually adjusted, to illustrate the impact of stock movement, volatility changes, or other factors that may influence an option’s actual value. For example, you could adjust the quantities of a potential spread to see how that change would affect the delta, gamma, and other Greeks.

The limitation of all pricing models is that actual premiums are determined by market forces, not by formula—no matter how sophisticated that formula might be. Market influences can actually result in highly unexpected price behavior during the life of a given options contract. But while no model can reliably predict what options premiums will be available to you or other investors at some point in the future, some investors do 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 you better predict the outcomes of your options strategies.

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