How does dividend yield adjust the BSM formula?

Replace S with S*exp(-q*T) in the standard BSM formula, so d1 = (ln(S/K) + (r - q + sigma^2/2)*T) / (sigma*sqrt(T)).

When is continuous dividend yield appropriate?

For indices and heavily traded stocks where dividends are approximately continuous. For discrete dividends use the binomial or explicit dividend adjustment.

Black-Scholes Merton Dividend-Adjusted Option Price

Price European options under Black-Scholes-Merton with continuous dividend yield. Adjusts d1 and d2 for yield q, giving accurate equity option prices on dividend-paying stocks.

Principal ($)

Annual Rate (%)

Years

Compounding / Year

$ Finance Disclaimer: These calculators are for educational and illustrative purposes only. Results do not constitute financial advice. Consult a licensed financial advisor before making investment or borrowing decisions.

How to Use

Enter the values for the scenario you are assessing. Price European options under Black-Scholes-Merton with continuous dividend yield. Adjusts d1 and d2 for yield q, giving accurate equity option prices on dividend-paying stocks. Use the bsm dividend adjusted result to inform your calculation.

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Frequently Asked Questions

How does dividend yield adjust the BSM formula?

When is continuous dividend yield appropriate?