American Put (Barone-Adesi-Whaley)
Computes the price of an American put option with the Barone-Adesi-Whaley quadratic approximation. Unlike the European put, the American one can be exercised at any time, and that right has value — the so-called early-exercise premium. The method iteratively finds the critical price below which exercising already pays off, and adds that premium to the European put value. It's fast and accurate, with no need for a binomial tree. Enter the spot price, the strike, the rate, the cost of carry, the volatility and the term.
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American Put (Barone-Adesi-Whaley)
Computes the price of an American put option with the Barone-Adesi-Whaley quadratic approximation. Unlike the European put, the American one can be exercised at any time, and that right has value — the so-called early-exercise premium. The method iteratively finds the critical price below which exercising already pays off, and adds that premium to the European put value. It's fast and accurate, with no need for a binomial tree. Enter the spot price, the strike, the rate, the cost of carry, the volatility and the term.
The American put without needing a tree
The American put is a tough nut to crack. Unlike the European one, it can be exercised at any time, and there are scenarios where exercising early really pays off — when the price falls so far that holding the option costs more than it's worth. That extra right has a price, the early-exercise premium, and there's no exact closed form for it.
Barone-Adesi and Whaley, in 1987, gave the approximation that became standard. Instead of a binomial tree with thousands of steps, they iteratively compute the critical price below which exercising is already optimal, and add a correction term to the European put value. The result is nearly as accurate as the tree and runs in a fraction of the time.
Enter the spot price, the strike, the interest rate, the cost of carry, the volatility and the term. The tool finds the critical price by Newton's method and returns the American put value. With cost of carry equal to the rate (no dividends), only the put has an early-exercise premium; the American call, in that case, is worth the same as the European.
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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.