American options (fast approximations)

QD+ (Andersen-Lake-Offengelden), Barone-Adesi-Whaley and Bjerksund-Stensland side by side, with the European value, early exercise premium, Greeks and a binomial check.

Inputs

ApproximationCurrency

Spot

Strike

Time to expiryy

Volatility%

Dividend yield%

Units

Discount curve

Discount curve: flat rate% cc

Results

Every input and result then gets a + calc button.

Explain this result

Get a plain-English reading of the numbers above and what drives them.

Preview: rule-based reading. AI-assisted explanations run on the analytics core.

Methodology

Conventions

An American option on a stock, index, commodity or currency, priced by a fast analytic approximation.
QD+ (Andersen-Lake-Offengelden) is the default; Barone-Adesi-Whaley and Bjerksund-Stensland are shown beside it.
A binomial tree is run as a check.

References

Barone-Adesi and Whaley (1987)
Bjerksund and Stensland (2002)
Andersen, Lake and Offengelden (2016), High-performance American option pricing

Formulas

American: V = European + early exercise premium
BAW: P = p + A (S / S*)^q for S > S*