Call options

Kurze Antwort

A call option gives its holder the right to buy 100 shares of the underlying stock at a fixed strike price any time before the contract's expiration date. The buyer pays a premium for that right.

Because the contract locks in a purchase price, a call generally becomes more valuable when the stock rises and less valuable when it falls, all else equal. Time and volatility also feed into the price, so the relationship is not one-for-one.

The seller, called the writer, collects the premium and takes on the obligation to deliver the shares at the strike price if the contract is exercised.

Genauere Betrachtung

A worked example with round numbers. A stock trades at $100. A call with a $105 strike and 30 days to expiration is quoted at $2.40 per share, so one contract costs $240.

Consider three closing prices on expiration day:

• Stock at $112. The right to buy at $105 is worth $7 per share. The contract's value is $700, against the $240 paid.
• Stock at $106. The right to buy at $105 is worth $1 per share, or $100. The contract has value, but less than the premium paid.
• Stock at $105 or below. The right to buy at $105 is worth nothing, and the contract expires worthless. The full $240 premium is lost.

At expiration, the arithmetic break-even point for this position sits at $107.40, the $105 strike plus the $2.40 premium. That is a property of the numbers at expiry, not a prediction; before expiration the contract trades at market prices that also reflect time and volatility.

The seller's outcomes mirror the buyer's line for line. The writer keeps the full $240 only in the third scenario; in the first two, closing the obligation costs whatever the contract is then worth. A writer who does not own the underlying shares faces open-ended exposure as the stock rises, which is why brokers hold margin against short calls.

Optional: die formalen Details für die Aufgaben nicht erforderlich

A call's sensitivity to the stock is summarized by delta, which for calls runs between 0 and 1. Deep in-the-money calls approach a delta of 1 and behave much like stock; far out-of-the-money calls have deltas near 0 and respond mostly to volatility and time.

Writers come in two forms with very different exposure profiles. A covered writer holds the underlying shares, so an exercised call is settled by delivering stock already owned. A naked writer holds no shares and must buy them at the prevailing market price to deliver, whatever that price is.

Two misconceptions are common. First, that a call must be held to expiration: listed calls can be sold in the market at any time during trading hours. Second, that a rising stock always means a rising call price: a drop in implied volatility or the passage of time can offset a favorable move in the underlying, particularly for short-dated out-of-the-money strikes.