Put options

Kurze Antwort

A put option gives its holder the right to sell 100 shares of the underlying stock at a fixed strike price any time before expiration. The buyer pays a premium for that right.

Because the contract locks in a selling price, a put generally gains value when the stock falls and loses value when it rises, all else equal. In that sense it works like an insurance policy on the share price, with the premium as the cost of cover.

The seller collects the premium and takes on the obligation to buy the shares at the strike price if the contract is exercised.

Genauere Betrachtung

A worked example. A stock trades at $100. A put with a $95 strike and 30 days to expiration is quoted at $1.80 per share, so one contract costs $180.

Outcomes at expiration:

• Stock at $85. The right to sell at $95 is worth $10 per share, so the contract is worth $1,000 against the $180 paid.
• Stock at $93. The right to sell at $95 is worth $2 per share, or $200, slightly more than the premium paid.
• Stock at $95 or above. The right to sell at $95 has no value, and the contract expires worthless. The $180 premium is lost in full.

The arithmetic break-even at expiration is $93.20, the $95 strike minus the $1.80 premium. As with calls, that is a property of expiry arithmetic; before then the put trades at market prices shaped by time and volatility as well as the stock.

One structural detail is worth spelling out: a put's value is capped. Even if the stock went to zero, this $95 put could never be worth more than $95 per share, or $9,500 per contract. A put buyer's maximum loss remains the premium paid; a put writer's maximum loss is the strike minus the premium collected, reached only if the shares become worthless.

Optional: die formalen Details für die Aufgaben nicht erforderlich

Puts and calls on the same strike and expiration are linked by put-call parity, which for European-style options states:

Call − Put = Stock price − Present value of the strike

When the relationship drifts, arbitrage pulls it back, which is why put prices and call prices move together rather than independently. Dividends and interest rates enter through the present-value term, and American-style early exercise loosens the equality into bounds.

A frequent misconception is that buying a put is the same as shorting the stock. It is not. A short stock position has linear, open-ended exposure and no expiry; a long put has a fixed maximum loss (the premium), a capped maximum value at the strike, and a price that erodes with time via theta. In-the-money puts also carry early assignment considerations for their sellers, described under exercise and assignment.