Call Option

At expiration a call is worth the greater of zero and the underlying price minus the strike. That single relationship drives everything else. If the underlying settles below the strike, the contract expires worthless and the holder's loss equals the premium paid; above the strike, exercise value grows one-for-one with the underlying. The writer's payoff is the mirror image: premium retained in the best case, unlimited theoretical loss in the worst.

Breakeven for the buyer sits at the strike plus the premium, not at the strike itself. Between those two points the option finishes in the money yet the position still loses money on a net basis, because the premium is a sunk cash outflow. Moneyness describes only exercise value: a call is in the money when the underlying exceeds the strike, at the money when they coincide, out of the money below. Moneyness and profitability are separate questions, and exam items routinely test the gap between them.

Prior to expiration a call premium splits into intrinsic value, the immediate exercise value floored at zero, and time value, the amount buyers pay for the possibility of further favourable movement. Time value is greatest near the money and decays toward zero as expiration approaches, accelerating in the final weeks.

Higher underlying prices, higher volatility, longer time to expiry and higher risk-free rates all raise a call's value; a higher strike and larger expected dividends lower it. Volatility matters because the payoff is asymmetric: greater dispersion increases the upside tail without deepening the downside, which is capped at the premium. Put-call parity ties the pieces together for European options on the same underlying, strike and expiry: a call plus the present value of the strike held in a risk-free asset equals a put plus the underlying. Rearranged, it prices any one instrument from the other three and defines the synthetic equivalents used in arbitrage arguments.

Embedded calls are far more common than standalone contracts. A callable bond contains a call written by the investor to the issuer on the bond itself, which is why its value equals the straight bond less the call value. A convertible bond hands the holder a call on the issuer's equity. Warrants, employee stock options and rights issues are all long call positions with non-standard terms, and equity itself can be modelled as a call on the firm's assets struck at the face value of debt, the intuition behind structural credit models.

On the trading side, dealers who sell calls hedge by holding a fraction of the underlying equal to delta, then adjust as delta changes. That mechanical rebalancing links option positioning to cash-market flows and explains why heavy short-dated call activity can amplify moves in the underlying rather than merely reflecting them.

Be able to compute expiration payoff and profit for both the long and short side, identify breakeven, and sketch the kinked payoff diagram from memory. Know the boundary conditions: a European call cannot be worth less than the underlying minus the present value of the strike, nor more than the underlying itself, and it can never be negative. Understand why an American call on a non-dividend-paying stock is not exercised early, since selling the option captures remaining time value that exercising destroys, while a large upcoming dividend can make early exercise rational.

Candidates should also handle standard combinations. A covered call pairs long stock with a written call, trading upside beyond the strike for premium income; a protective put buys downside insurance. Applying put-call parity to construct synthetic positions and to spot mispricing between calls, puts, the underlying and a risk-free bond is examined regularly, usually in a single arithmetic step.