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The Bjerksund-Stensland model provides a closed-form approximation for pricing American options by treating early exercise as a flat barrier problem. It is faster than binomial trees while maintaining reasonable accuracy for American calls and puts on dividend-paying stocks.
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Key takeawayWhen selling American-style equity options, Black-Scholes underprices the early exercise premium. Bjerksund-Stensland gives a more realistic valuation, helping premium sellers avoid leaving money on the table when setting limit prices for short options.
💡 Why It Matters
Bjerksund-Stensland gives premium sellers a fast, practical way to price the early exercise premium on American options. This is important because the premium you collect on a short American-style put includes compensation for assignment risk that Black-Scholes does not capture.
⚙ How It Works
The model treats early exercise as a flat barrier problem: if the underlying crosses a critical price boundary, immediate exercise is optimal. It approximates this boundary and derives a closed-form solution for the American option price. The model decomposes the American price into European value plus early exercise premium.
📋 Example
An AAPL 150 put with 60 DTE, stock at $160, IV at 28%, dividend in 25 days. Black-Scholes prices the European put at $3.20. Bjerksund-Stensland prices the American put at $3.45. The $0.25 early exercise premium represents the probability that early assignment becomes optimal around the ex-dividend date.
⚠ Common Mistakes
Traders ignore the early exercise premium when selling American puts. If you sell the put at $3.45 (American) but price it using Black-Scholes at $3.20, you think you are getting $0.25 extra edge. In reality, you are being fairly compensated for the assignment risk, not earning excess premium.
❓ FAQ
What is Bjerksund-Stensland Model?
The Bjerksund-Stensland model provides a closed-form approximation for pricing American options by treating early exercise as a flat barrier problem. It is faster than binomial trees while maintaining reasonable accuracy for American calls and puts on dividend-paying stocks.
Why does Bjerksund-Stensland Model matter for premium sellers?
When selling American-style equity options, Black-Scholes underprices the early exercise premium. Bjerksund-Stensland gives a more realistic valuation, helping premium sellers avoid leaving money on the table when setting limit prices for short options.
How does Bjerksund-Stensland Model work?
The model treats early exercise as a flat barrier problem: if the underlying crosses a critical price boundary, immediate exercise is optimal. It approximates this boundary and derives a closed-form solution for the American option price. The model decomposes the American price into European value plus early exercise premium.
What are common mistakes with Bjerksund-Stensland Model?
Traders ignore the early exercise premium when selling American puts. If you sell the put at $3.45 (American) but price it using Black-Scholes at $3.20, you think you are getting $0.25 extra edge. In reality, you are being fairly compensated for the assignment risk, not earning excess premium.
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Binomial Option Pricing
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