Put Option

At expiration the put's value is determined by a single comparison: strike price minus underlying price, floored at zero. If the underlying settles below the strike, exercise value equals the strike minus the market price; if it settles at or above the strike, the contract expires worthless. The buyer's profit is that exercise value less the premium paid, so the breakeven underlying price is the strike minus the premium. Maximum gain is bounded because the underlying cannot fall below zero, giving a ceiling of the strike less the premium, while maximum loss is limited to the premium.

The seller's position is the exact mirror. Premium received is the best case, realised when the option expires out of the money. Worst case is the strike less the premium, incurred if the underlying collapses. Because the writer's obligation is to buy at the strike, a short put carries long exposure to the underlying, not short exposure.

Premium splits into intrinsic value, the exercise value if settled immediately, and time value, the remainder. A put gains value as the underlying falls, as the strike rises, and as volatility increases, because greater dispersion raises the probability and magnitude of finishing in the money. Delta is negative, bounded between minus one and zero, steepening toward minus one as the option moves deep in the money.

Two drivers behave counterintuitively. A higher risk-free rate reduces a European put's value, since the strike is effectively received later and discounts more heavily; carry costs and expected dividends on the underlying increase put value. Longer time to expiration usually helps, but for a deep in-the-money European put more time can hurt, because the holder must wait longer to receive the strike. Put-call parity ties it together: a put plus the underlying replicates a call plus a risk-free bond maturing at the strike.

The most common institutional use is the protective put, pairing a long asset position with a put to cap downside while retaining upside less the premium cost. Because that cost recurs each time protection is rolled, managers frequently finance it by selling calls, producing a collar. Writing cash-secured puts is the opposite motive: a way to earn premium and acquire an asset at an effective price below the current market, at the cost of accepting all downside beyond the premium.

Put features are also embedded in securities. A putable bond gives the holder the right to sell the bond back to the issuer at a preset price, which supports the bond's price when yields rise and therefore trades above an otherwise identical straight bond. Shareholder redemption rights, contractual price floors and certain guarantees all behave economically as written puts for the party providing them.

Candidates should be able to construct the payoff and profit diagram for a long and short put from the strike and premium, then identify breakeven, maximum profit and maximum loss without hesitation. The same fluency is needed for combinations: protective put, collar, and the equivalence stated by put-call parity, which is frequently tested by asking for a synthetic position or an arbitrage when quoted prices violate the relationship.

A second point of emphasis is early exercise. An American put on a non-dividend-paying stock can rationally be exercised before expiration when it is deep in the money, because the holder receives the strike immediately and earns interest on it, and further downside is limited. This is why an American put can be worth strictly more than its European counterpart, whereas for calls on non-dividend-paying stock early exercise is not optimal.