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What Is the Primary Difference in Assumptions between the Black-Scholes and the Bjerksund-Stensland Models?

The primary difference is that the Bjerksund-Stensland model is an analytical approximation specifically designed to price American options, thus incorporating the possibility of early exercise. The Black-Scholes model is an exact solution for European options, assuming exercise only at maturity.

What Modifications to the Black-Scholes Model Are Used to Price American Options?
How Does the Binomial Tree Model Approximate the Continuous Time of the Black-Scholes Model?
What Is the Primary Difference between a ‘European’ and an ‘American’ Style Option?
What Is the Primary Difference between American and European Style Options?