Optionsbeginner

Call Option

A call option gives the holder the right to buy the underlying asset at the strike price KK during the life of the contract. The payoff at expiry is max(STK,0)\max(S_T - K, 0). Buyers are bullish on the underlying. The writer (seller) accepts the obligation to deliver the asset at KK if the buyer exercises. A long call's downside is capped at the premium CC, while its upside is theoretically unlimited.

Why it matters

Buying a call is like paying a deposit to lock in tomorrow's purchase price of a stock you think will rise. If the stock rallies, you exercise at the cheap strike and capture the upside. If it falls, you walk away and the deposit is your only loss. This is the same logic a property developer uses when paying for an option-to-buy on a block of land. The fee is non-refundable, but it caps the cost of waiting to see whether the project becomes viable.

Formulas

Call payoff at expiry
Payoff=max(STK,0)\text{Payoff} = \max(S_T - K, 0)
Zero whenever STKS_T \leq K. Above the strike, payoff rises one-for-one with STS_T.
Long call profit at expiry
Profit=max(STK,0)C\text{Profit} = \max(S_T - K, 0) - C
CC is the premium paid. The position breaks even when ST=K+CS_T = K + C.

Worked examples

Scenario

You buy a 3-month CBA call with strike K=K = 50 for premium C=C = 3. At expiry ST=S_T = 58.

Solution

Payoff per share =max(5850,0)== \max(58 - 50, 0) = 8$. Profit per share =83== 8 - 3 = 5$. On one ASX contract of 100 shares, total profit is $500 against an outlay of $300. Return on premium =5/3167%= 5/3 \approx 167\%, illustrating the leverage built into options.

Scenario

Same call, but at expiry ST=S_T = 48.

Solution

Payoff =max(4850,0)== \max(48 - 50, 0) = 0$. You let the call lapse. Loss is the full premium of $3 per share, or $300 per contract. The stock fell only 4\% from the strike, but your option investment lost 100\%, illustrating that leverage cuts both ways.

Common mistakes

  • A call obligates you to buy at expiry. It gives you the right, not the obligation. You exercise only when ST>KS_T > K, and you can sell the call in the market at any time before expiry.
  • Early exercise of an American call on a non-dividend stock is often optimal. Merton (1973) proved it is never optimal to exercise such a call early. The remaining time value is always worth more than the immediate intrinsic value, so the holder is better off selling the option.
  • A call buyer profits whenever the stock rises. Profit requires ST>K+CS_T > K + C. A small rally above the strike still leaves the buyer with a partial loss if the move does not cover the premium.

Revision bullets

  • Right to buy at strike KK
  • Payoff =max(STK,0)= \max(S_T - K, 0)
  • Profit =max(STK,0)C= \max(S_T - K, 0) - C
  • Bullish position with capped downside
  • Early exercise never optimal if no dividends (Merton 1973)

Quick check

A long call is exercised at expiry when:

You hold a long call with K=K = 40$ and paid C=C = 5$. The stock closes at ST=S_T = 43$ at expiry. Your profit per share is:

Connected topics

In learning paths

Sources

  1. Hull, John C. Options, Futures, and Other Derivatives. 11th ed. Pearson, 2022. ISBN 978-0-13-693997-9.
    Section 10.1 sets out the call payoff function $\max(S_T - K, 0)$ and the buyer-writer relationship that underpins all option strategies.
  2. Merton, Robert C. "Theory of Rational Option Pricing." Bell Journal of Economics and Management Science, vol. 4, no. 1, 1973, pp. 141 to 183.
    Original proof that early exercise of an American call on a non-dividend-paying stock is never optimal. The result still anchors modern option pricing courses.
  3. Cboe Global Markets. Options Trading Glossary. Cboe Options Institute, accessed 2026.
    Industry definition of a call option and its standard contract terms in US listed markets.
  4. Australian Securities Exchange. Online Options Course, Module 2: What are Options. ASX Investor Education, accessed 2026.
    ASX teaching reference for Australian students on call and put basics, contract size, and exercise mechanics.
How to cite this page
Dr. Phil's Quant Lab. (2026). Call Option. Derivatives Atlas. https://phucnguyenvan.com/concept/call-option