American Call with Dividend (Roll-Geske-Whaley)
Computes the price of an American call option on a stock paying a discrete dividend, with the Roll-Geske-Whaley model. Unlike the European call, the American one can be exercised early, and that's only optimal precisely an instant before the dividend, when the price will drop. The model finds the critical exercise price and combines probabilities via the bivariate normal. Enter the spot price, the strike, the rate, the volatility, the term, the dividend and the date it's paid.
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American Call with Dividend (Roll-Geske-Whaley)
Computes the price of an American call option on a stock paying a discrete dividend, with the Roll-Geske-Whaley model. Unlike the European call, the American one can be exercised early, and that's only optimal precisely an instant before the dividend, when the price will drop. The model finds the critical exercise price and combines probabilities via the bivariate normal. Enter the spot price, the strike, the rate, the volatility, the term, the dividend and the date it's paid.
When it pays to exercise the call early
There's a classic rule: never exercise an American call on a non-dividend-paying stock before expiry, because you throw away the time value. But when there's a dividend along the way, the story changes. Exercising an instant before the dividend can be worthwhile, because the stock price will drop when it's paid. Roll, Geske and Whaley gave the exact formula for this case.
The model is clever. It treats the dividend as an amount to be discounted off the price (the escrowed-dividend method) and computes a critical price: above it, early exercise pays off. Combining the probabilities of exercising or not, across two dates, requires the bivariate normal distribution. When the dividend is too small to justify early exercise, the formula falls back to the plain European call.
Enter the spot price, the strike, the interest rate, the volatility, the term, the dividend amount and the date it's paid. The tool returns the American call premium and embeds the optimal exercise decision. It's one of the few cases where the American option has a closed analytical solution, with no need for a binomial tree.
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American Call (Bjerksund-Stensland)
Computes the price of an American call option with the Bjerksund-Stensland (1993) approximation, valid when the asset pays dividends (cost of carry below the interest rate). It defines an exercise trigger price and, below it, combines exponential terms to approximate the value with early exercise. It's faster than a binomial tree and widely used in practice for American calls on dividend-paying stocks. Enter the spot price, the strike, the rate, the cost of carry, the volatility and the term.
The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.