When is it optimal to exercise an American put early?

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AcadiFi · Accepted Answer

An American put on a non-dividend stock CAN be optimal to exercise early, unlike a call. The key trade-off is: exercising early captures the strike K immediately, which earns interest, versus waiting preserves optionality but forgoes interest on K. Consider Borealis Materials trading at $12 with an American put strike $50, 2 years to expiry, 5% rate. Exercising now yields $38 immediately, which grows to $38*e^(0.05*2) = $41.99. Waiting gives max(50 - S_T, 0), capped at $50. Since $41.99 is close to $50 and the stock is very deep ITM with limited downside remaining, early exercise can dominate. The general condition: exercise early when the present value of the strike's interest benefit exceeds the remaining time value of the put. Formally, when P_american > max(K - S, PV of expected payoff from waiting). ```mermaid flowchart TD A[Deep ITM Put] --> B{Interest on K
beats time value?} B -->|Yes| C[Exercise Early] B -->|No| D[Hold] ``` For shallow ITM puts, time value usually dominates. For deep ITM puts near expiry, early exercise becomes attractive. Dividends complicate things — a pending dividend reduces the incentive to hold the stock short, making early put exercise LESS attractive (since exercising requires shorting the stock and paying the dividend).

When is it optimal to exercise an American put early?

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