Options trading: premiums, payoffs, Greeks and strategies

Lesson 1 · 6 min

What an option is

A listed option is a contract on a reference, with a strike and an expiration. A call is the right to buy. A put is the right to sell. The buyer pays a premium for that right. The writer receives the premium and accepts the obligation if the buyer exercises.

Listed options are cleared. An over-the-counter option is a different contract, with the provider as counterparty. This academy prices expiration payoffs from figures you type. It does not show a live chain.

Lesson 2 · 6 min

Calls and puts, long and short

A long call gains at expiration if the reference finishes above the strike by more than the premium. A long put gains if it finishes below by more than the premium. The most the buyer loses, if the option is held alone to expiration, is the premium, before you add fees.

The writer’s result is the other side of that payoff before gaps, early exercise and fees. A short call on a stock that can rise without a bound has a loss that is not capped by the premium. Assignment can turn the short option into a share or futures position.

Lesson 3 · 6 min

Strike, expiration and the multiplier

The strike is the price in the right. The expiration is when the right ends. The multiplier turns a premium quoted per unit into cash. A common US equity convention is 100 shares, but index options, futures options and contracts outside that market use other multipliers. Type the one in the specification.

Settlement can be physical or cash. The premium on the screen may be quoted per share, per index point, or per contract. The lab asks for premium per underlying unit and multiplies by the multiplier and the contract count. Do not mix those units.

Lesson 4 · 6 min

Intrinsic and extrinsic value

A call’s intrinsic value is the reference minus the strike, when that difference is positive, and zero otherwise. A put’s intrinsic value is the strike minus the reference, on the same rule. In, at and out of the money describe that comparison. They are not a view on what happens next.

Premium minus intrinsic value is extrinsic, often called time value. Before expiration an option can be worth more than its intrinsic value because of time and volatility. The payoff charts on this page are expiration sketches. They are not a model of today’s premium.

Lesson 5 · 7 min

Expiration payoffs and breakeven

At expiration a long call is worth the greater of the reference minus the strike, and zero, minus the premium. A long put uses the strike minus the reference. Short positions reverse that premium-adjusted result. Scale by the multiplier and the contracts, then subtract fees under the convention that fees are a single cash amount.

A long call struck at 100, bought for 5, breaks even at 105 if the premium is per unit and there are no fees. At 110, one contract with a multiplier of 100 has 1,000 of intrinsic cash, 500 of premium paid, and 500 of expiration profit. Before expiration the contract can be sold for a different amount.

Lesson 6 · 6 min

Implied volatility

Implied volatility is the volatility figure that, inside a pricing model, matches an option’s premium. Different strikes can imply different volatilities. That pattern is skew. Different expirations can imply different volatilities. That pattern is the term structure.

A high implied volatility is not automatically a reason to sell the option. The premium can be high because the market expects a large move, because of demand for protection, or because the model’s assumptions are a poor fit. Implied volatility is not a prediction of the realised move, and this page does not calculate a live figure.

Lesson 7 · 7 min

The Greeks as local sensitivities

Delta is how the model price changes for a small move in the reference. Gamma is how delta itself changes. Theta is how the model price changes as time passes, holding the other inputs still. Vega is the sensitivity to implied volatility. Rho is the sensitivity to interest rates.

Each number is local to a model and to the inputs at that moment. They change when the reference, the volatility or the time changes. They are not a promise of the next fill. This page draws the ideas. It does not invent a live Greek.

Lesson 8 · 6 min

Time decay and expiration risk

Extrinsic value tends to shrink as expiration approaches, if nothing else changes. Near expiry, delta can move sharply for a small change in the reference. That is the gamma of a short-dated option. Liquidity can also thin, and a strike near the reference can be awkward to trade.

The sketch of decay on this page is conceptual. It is not the theta of a particular contract, and it is not a history. An American option can be exercised early. A European option generally cannot. The specification decides.

Lesson 9 · 6 min

Long calls and long puts

A long call is a view that the reference will be far enough above the strike, in time, to cover the premium. A long put is the mirror for a fall. Both lose if the move is too small or too late. Volatility that falls can hurt the premium before expiration even when the direction is right.

The chart shows the expiration result, including a theoretically unbounded upside for the long call. A long put on a reference that cannot trade below zero has a finite maximum. Fees move both results.

Lesson 10 · 7 min

Covered calls

A covered call is long the shares, or another eligible underlying, and short a call. The premium reduces the net cost. Above the strike, further gains in the shares are offset by the short call, and assignment can take the shares away. Below the strike, the shares can keep falling. The premium is only a cushion of that cash amount.

Dividends matter when early exercise of an American call is possible. The lab includes the share position, not the option alone. A covered call does not remove the downside of the holding.

Lesson 11 · 6 min

Protective puts

A protective put is long the shares and long a put. At expiration the put pays when the reference is below the strike, which can offset part of the share loss. The premium is the cost of that shape. If the reference rises, the put can expire worthless and the shares carry the gain, minus that premium.

The floor is only as good as the strike, the multiplier, the number of shares you actually hold, and a fill if you close early. Costs and a mismatch between share count and contract size leave a gap.

Lesson 12 · 7 min

Vertical debit spreads

A bull call spread buys a call and sells a higher-strike call. A bear put spread buys a put and sells a lower-strike put. You pay a net debit. At expiration the most you can lose is that debit, and the most you can gain is the distance between the strikes minus the debit, before fees and assignment complications.

The strikes have to be in the right order. The lab rejects a lower strike entered second. Defined expiration risk is not the same as an easy close: both legs need a market, and early assignment can leave you with one side only.

Lesson 13 · 7 min

Vertical credit spreads

A bull put spread sells a put and buys a lower-strike put. A bear call spread sells a call and buys a higher-strike call. The net credit is the most the spread can gain at expiration. The most it can lose at expiration is the distance between the strikes minus the credit, before fees.

Receiving premium first does not make the position safer than a debit spread. The loss can be larger than the credit. Margin, early assignment and a gap through both strikes sit outside a clean expiration diagram.

Lesson 14 · 7 min

Cash-secured puts and collars

A cash-secured put is a short put with cash set aside for assignment. The premium is income only if the put expires worthless. If it finishes in the money you can be assigned the shares and the loss continues below the strike, cushioned by the premium only. The cash is collateral for that obligation, not a guarantee against a further fall.

A collar is long the shares, long a put and short a call. The put sets an expiration floor. The call caps the upside. The net premium can be a debit or a credit depending on the two prices you type. The two options are not a substitute for owning a different number of shares than the contracts cover.

Lesson 15 · 6 min

Several legs, exercise and assignment

A spread is two or more contracts. They can expire on different days, trade in different sizes, and be assigned one at a time. American exercise can arrive before expiration, especially around a dividend for a short call. European exercise generally waits. Pin risk is the awkwardness of a finish very near a strike, where small moves decide whether the option finishes in the money.

Clearing notices and the broker’s cutoff are operational facts. This page cannot tell you the cutoff. After assignment you may hold shares or a futures position you did not draw on the expiration chart.

Lesson 16 · 8 min

Build an options plan

Choose a long call or put, a covered call, a protective put, a debit or credit spread, or a collar. Enter the strikes, the premiums per unit, the multiplier, the contract count and, where the structure holds shares, the share count and entry. The lab returns the net debit or credit, the result at the price you select, the breakeven crossings it can see, and whether the gain or the loss is unbounded.

The picture is expiration intrinsic value, plus the share result when you included shares, minus fees. It is not the value of the option tomorrow. Completing it is not a recommendation.

Explore trading strategies

Premium received is not evidence that a structure is safer. The comparison uses the lesson’s hypothetical premiums.

Knowledge check

Ten questions. A correct count is not a certificate and is not stored.

Learn, calculate, then review

• Risk and rewardDistances you type. Not a probability.
• Profit and lossA share or contract result from figures you enter.
• Position sizeA cash budget for the underlying, where that is the risk you sized.
• Trading journalA note that stays under the tool’s privacy choice.
• Trading performanceA reading of records you already keep.

The payoff lab uses the options expiration study. The full calculator route is not in the public directory. The curve is an expiration sketch, not a price before expiration.

Related reading

• Risk and volatility
• Strategy research
• Stocks and shares
• Order types
• Volatility