What Is the Bjerksund-Stensland Model?

The Bjerksund-Stensland model is a closed-form option pricing model used to calculate the price of an American option. The Bjerksund-Stensland model competes with the Black-Scholes model, though the Black-Scholes model is specifically designed to price European options.

Key Takeaways

  • The Bjerksund-Stensland model is a closed-form option pricing model used to calculate the price of an American option.
  • It is designed specifically to determine the American call value at early exercise when the price of the underlying asset reaches a flat boundary.
  • The Bjerksund-Stensland model works for American options that have a continuous dividend, constant dividend yield, and discrete dividends.
  • It competes with the Black-Scholes model, though the Black-Scholes model is specifically designed to price European options.
  • Investors can use binomial and trinomial trees, which are considered “numerical” methods, as an alternative to the Bjerksund-Stensland model.

Understanding the Bjerksund-Stensland Model

The Bjerksund-Stensland model was developed in 1993 by Norwegians Petter Bjerksund and Gunnar Stensland and is used by investors to generate an estimate for the best time to execute an American option—financial derivatives that give buyers the right, but not the obligation, to buy (calls) or sell (puts) an underlying asset at an agreed-upon price and date.

The model is used specifically to determine the American call value at early exercise when the price of the underlying asset reaches a flat boundary and works for American options that have a continuous dividend, constant dividend yield, and discrete dividends. Bjerksund-Stensland divides the time to maturity into two periods with flat exercise boundaries — one flat boundary for each of the two periods.

American options differ from European options in that they can be exercised at any point during the contract period, rather than only on the expiration date. This feature should make the premium on an American option greater than the premium on a European option since the party selling the option is exposed to the risk of the option being exercised over the entire duration of the contract.

The Bjerksund-Stensland model takes into account that options may be exercised before the expiration date, while the popular Black Scholes Method does not. This means the latter isn't really suitable for calculating the price of American options and works best when pricing more straightforward European options.

Unlike the Black Scholes model, the Bjerksund-Stensland model factors in that U.S. options may be exercised before the expiration date. 

Advantages and Disadvantages of the Bjerksund-Stensland Model

The Bjerksund-Stensland model is able to complete complex calculations more quickly and efficiently compared to many other pricing methods. This was especially important because computers at the time of its inception were less powerful, and inefficient formulas could slow down calculations.

The model isn't perfect though. One flaw is that it is unable to provide the most optimal exercise strategy due to the estimates that it uses in calculations.

Special Considerations

Investors can use binomial and trinomial trees as an alternative to the Bjerksund-Stensland model. Trees are considered “numerical” methods, whereas Bjerksund-Stensland is considered an approximation method. Computers are typically able to complete approximation calculations faster than they can complete numerical methods.