What is a call option (simple definition)
– A call option is a contract that gives its buyer the choice — not the obligation — to purchase a specific underlying asset (for example, a stock, bond, or commodity) at a pre-agreed price (the strike) before a set date (the expiration). The buyer pays a fee for that choice called the premium. If the buyer exercises the option, the seller of the call must sell the underlying at the strike price.
Key terms (brief definitions)
– Underlying: the asset the option references (e.g., a share of stock).
– Strike price (or strike): the price at which the buyer can buy the underlying.
– Expiration date (expiry): the last date the option can be exercised.
– Premium: the upfront price the buyer pays to acquire the option.
– In-the-money (ITM): when the underlying’s market price is above the strike for a call.
– Out-of-the-money (OTM): when the underlying’s market price is at or below the strike for a call.
– Long call: buying a call option (the right to buy).
– Short call: selling (writing) a call option (the obligation to sell if exercised).
How a call option works — step by step
1. Choose an underlying asset, a strike price, and an expiration date from available contracts.
2. Pay the premium to buy the call contract (this is your maximum possible loss as the buyer).
3. Between purchase and expiry you can:
– Hold the option until expiry and exercise it (buy the underlying at the strike) if it’s profitable;
– Sell the option contract in the market before expiry; or
– Let it lapse unexercised (worthless) if it’s not profitable.
4. If the buyer exercises, the seller must deliver the underlying at the strike price.
Why investors buy or sell calls
– Buyers (long calls) are typically bullish: they expect the underlying price to rise above the strike by enough to cover the premium.
– Sellers (short calls) earn the premium up front and profit if the option expires worthless. Sellers who already own the underlying can use calls to generate income (covered calls). Sellers who do not own the underlying face potentially large losses if the price spikes (naked short calls).
Payoff and profit formulas (at expiration)
– Call buyer payoff (intrinsic value) = max(S − K, 0)
where S = underlying price at expiration, K = strike.
– Call buyer profit = max(S − K, 0) − premium
(loss is limited to the premium; upside is potentially large).
– Call seller profit = premium − max(S − K, 0)
(maximum gain is the premium; potential loss can be large if the seller is naked).
Worked numeric example
– You buy one call contract (representing 100 shares) on stock ABC with:
– strike K = $50
– premium = $2 per share
– expiration = Nov. 30
– Break-even for the buyer at expiry = strike + premium = $50 + $2 = $52.
– If ABC is $60 at expiry:
– Buyer payoff = max(60 − 50, 0) = $10 per share
– Buyer profit = $10 − $2 = $8 per share → $800 total for the contract (100 shares)
– Seller profit = premium − intrinsic = $2 − $10 = −$8 per share → $800 loss
– If ABC is $48 at expiry:
– Buyer payoff = 0 → buyer loss = premium = $2 per share ($200 total)
– Seller profit = premium = $2 per share ($200 total)
Practical uses (common strategies)
– Speculation: buy calls to gain leveraged upside when you expect the price to rise.
– Income (covered calls): own the underlying stock and sell calls against it to collect premiums; you may have to sell the stock if exercised.
– Tax management and timing: options can sometimes be used to defer or accelerate transactions, but tax rules vary and require professional advice.
Checklist before trading a call option
– Confirm the underlying and liquidity of the option series.
– Note the strike price, expiration date, and premium.
– Calculate break-even (strike + premium).
– Decide exit plan: exercise, sell the contract, or let it expire.
– For sellers: determine whether the call is covered (you own the underlying) or naked (you do not).
– Understand maximum loss (buyer = premium; naked seller = potentially large) and margin/assignment implications.
– Consider transaction costs and tax consequences.
Simple analogy (ELI5)
– Buying a call is like paying a small deposit to reserve the option to buy a bike at a fixed price within a month. If bike prices go up, you can buy at the cheaper reserved price or sell your reservation. If prices fall, you lose only your deposit.
Bottom line
– A call option transfers the opportunity to benefit from price increases from the seller to the buyer, for a fee (the premium). Buyers trade limited, known downside for potential upside; sellers collect premiums but assume obligations that can be risky if uncovered.
Sources
– Investopedia — Call Option: https://www.investopedia.com/terms/c/calloption.asp
– U.S. Securities and Exchange Commission (SEC) — Options: https://www.sec.gov/fast-answers/answersoptionshtm.html
– Chicago Board Options Exchange (CBOE) — Options Basics: https://www.cboe.com/learncenter/default.aspx
– Options Clearing Corporation (OCC) — Options Education: https://www.theocc
Options Clearing Corporation (OCC) — Options Education: https://www.theocc.com
Key formulas and payoffs
– Buyer (long call) payoff at expiration (per share): payoff = max(S_T − K, 0) − premium.
– S_T = underlying asset price at expiration.
– K = strike price.
– premium = price paid for the option (per share).
– Seller (short call) payoff at expiration (per share): payoff = premium − max(S_T − K, 0).
– Breakeven price at expiration (per share) for the call buyer: S_BEP = K + premium.
Worked numeric example (one standard U.S. option contract = 100 shares)
– Setup: buy 1 call contract (100 shares) — strike K = $55, premium = $2.50 per share, current underlying ≈ $50. Total premium paid = $2.50 × 100 = $250.
– If S_T = $65 at expiration: intrinsic value per share = $65 − $55 = $10 → contract value = $1,000. Profit = $1,000 − $250 = $750.
– If S_T = $56 at expiration: intrinsic per share = $1 → contract value = $100. Profit = $100 − $250 = −$150 (loss). Note breakeven S_BEP = 55 + 2.5 = $57.50.
– If S_T ≤ $55: option expires worthless; loss = premium = $250 (limited downside).
Covered call vs. naked call (brief examples)
– Covered call: own 100 shares and sell 1 call on those shares. Example: buy shares at $50 and sell a $55 call for $2. Premium income cushions downside but caps upside if shares rise above $55. If called away at $55, total gain = (55 − 50) × 100 + premium × 100.
– Naked (uncovered) call: sell a call without owning the underlying. Premium collected is limited gain; losses are potentially large/unlimited if the underlying rallies strongly.
American vs. European style
– American option: can be exercised any time on or before expiration. Common for equity options in U.S. markets.
– European option: can be exercised only at expiration. Common for some index options and most academic pricing formulas.
– Exercise style affects early-exercise decisions (e.g., to capture dividends) and pricing.
Pricing basics and Black‑Scholes (overview, not a how-to for trading)
– Black‑Scholes–Merton (BSM) call price (no dividends): C = S0·N(d1) − K·e^{−rT}·N(d2)
– d1 = [ln(S0/K) + (r + σ^2/2)T] / (σ√T)
– d2 = d1 − σ√T
– S0 = current underlying price; K = strike; r = risk‑free interest rate; σ = volatility (annualized); T = time to expiration (years); N(·) = cumulative standard normal distribution.
– If the underlying pays a continuous dividend yield q,