Options are the first instrument most candidates meet where the payoff is not a straight line, and the mathematics arrives before the intuition. It does not have to. The contract is short, the two payoff shapes can be drawn from memory in under a minute, and the reason the price moves when nothing has happened to the share is a single idea about uncertainty. This page builds that intuition on one worked contract and carries the same numbers all the way through.
The one-line answer
An option is a contract that gives its buyer the right, but not the obligation, to buy or sell an agreed quantity of an asset at an agreed price, on or before an agreed date. The seller, usually called the writer, takes the other side and has no choice in the matter: if the buyer exercises, the writer must deliver.
That asymmetry is the whole product. The buyer pays for it up front, and the amount paid is the premium. Everything else on this page is a consequence of a right on one side, an obligation on the other, and a payment that has already left the buyer’s account before anything happens.
Options sit inside the wider family of derivatives, contracts whose value is derived from something else rather than from a direct claim on a business. What separates them from the rest of that family is the optionality itself. A future or a forward obliges both sides to transact, and a swap exchanges two agreed sets of cash flows, while among the common derivatives only an option lets one side simply walk away.
What the contract actually specifies
Five things define an option, and an interviewer will expect all five without prompting. Read them as the fields on a term sheet rather than as vocabulary.
Exercise style is a sixth detail and a smaller one here. A European option can be exercised only at expiry; an American option can be exercised at any point up to it. Listed equity options are usually American and index options frequently European. The distinction matters for early exercise around dividends rather than for the payoff shapes below.
The example carried through this page is a single contract: the share trades at £50 today, the strike is £55, expiry is three months away, and the call premium is £2.00 per share. Options are quoted per share and traded in contracts covering a fixed number of shares, so cash amounts scale by the multiplier in the contract specification.
| Term | What it fixes | In the worked example |
|---|---|---|
| Underlying | The asset the contract references | One ordinary share, trading at £50 |
| Call or put | Whether the right is to buy or to sell | A call, so the right to buy |
| Strike | The price at which that right is exercised | £55 |
| Expiry | The date the right ends | Three months from today |
| Premium | What the buyer pays the writer for the right | £2.00 per share, paid now |
The buyer and the writer are not mirror images
Buying the call costs £2.00 and that £2.00 is gone. In exchange the buyer holds a right they will use only when it is worth using, so the worst case is losing the premium and the best case is bounded only by how far the share can rise. Writing the same call collects £2.00 and accepts the reverse: the most the writer can make is the £2.00 already received, and the loss grows for as long as the share keeps rising.
The risk conversation about options is therefore a conversation about which side you are on. A long option position has a known, paid-for maximum loss. A short one has a known maximum gain and a loss that is uncapped for a call, and capped only by the share reaching zero for a put. The premium is compensation for accepting that shape, not a profit.
| Buyer (long call) | Writer (short call) | |
|---|---|---|
| Right or obligation | The right to buy at £55 | The obligation to sell at £55 if exercised |
| Cash at the start | Pays £2.00 | Receives £2.00 |
| Maximum gain | Unbounded as the share rises | £2.00, the premium |
| Maximum loss | £2.00, the premium | Unbounded as the share rises |
| Wants the share to | Rise above £57 | Stay below £55 |
What a call is worth at expiry
At expiry the option is worth whatever exercising it is worth, and nothing else. For a call that is the share price minus the strike when the share is above the strike, and zero otherwise. Written once and remembered: payoff equals the greater of zero and the share price less £55.
Profit is a different line. The payoff ignores the £2.00 already paid; the profit does not. So the buyer’s profit line is the payoff line shifted down by £2.00, which puts breakeven at £57 rather than at £55. A candidate who says the call "makes money above the strike" has described the payoff and called it profit, and the follow-up question is usually built precisely on that gap.
| Share price at expiry | Payoff | Buyer’s profit | Writer’s profit |
|---|---|---|---|
| £45 | £0.00 | −£2.00 | +£2.00 |
| £50 | £0.00 | −£2.00 | +£2.00 |
| £55 | £0.00 | −£2.00 | +£2.00 |
| £57 | £2.00 | £0.00 | £0.00 |
| £60 | £5.00 | +£3.00 | −£3.00 |
| £65 | £10.00 | +£8.00 | −£8.00 |
What a put is worth at expiry
A put is the same contract with the direction reversed: the right to sell at the strike. Its payoff is the strike minus the share price when the share is below the strike, and zero otherwise. The shape is the call’s reflection, with one asymmetry that is real rather than cosmetic. A share cannot fall below zero, so the put’s payoff has a ceiling at the strike while the call’s has none.
Take the put on the same share, at the same £55 strike, expiring on the same date. With the share at £50 that put is already worth something at expiry if nothing changes, and it prices at £6.45 against the call’s £2.00. The two premiums are not independent: put-call parity ties them together, and at a 4% risk-free rate over three months the present value of the £55 strike is £54.45. The call price minus the put price equals the share price minus that discounted strike, which is £50.00 less £54.45, or −£4.45. That is exactly £2.00 less £6.45.
The put buyer’s breakeven is £48.55, the strike less the premium, and the most that buyer can make is £48.55 per share, reached only if the company is worthless at expiry. The writer collects £6.45 and is obliged to buy at £55 however far the share has fallen, which is why writing puts is described as being paid to agree to buy.
| Share price at expiry | Payoff | Buyer’s profit | Writer’s profit |
|---|---|---|---|
| £40 | £15.00 | +£8.55 | −£8.55 |
| £45 | £10.00 | +£3.55 | −£3.55 |
| £48.55 | £6.45 | £0.00 | £0.00 |
| £50 | £5.00 | −£1.45 | +£1.45 |
| £55 | £0.00 | −£6.45 | +£6.45 |
| £60 | £0.00 | −£6.45 | +£6.45 |
Intrinsic value and time value
Any option premium splits into two parts. Intrinsic value is what the option would pay if expiry were now, so it is the payoff formula applied to today’s share price and it can never be negative. Time value is the rest of the premium, and it is what the market charges for everything that can still happen before expiry.
The two contracts in this example split very differently, which is the useful thing about pricing them side by side. The £55 call is out of the money with the share at £50, so its intrinsic value is zero and the entire £2.00 premium is time value. The £55 put is in the money by £5.00, so £5.00 of its £6.45 premium is intrinsic and the remaining £1.45 is time value. Same share, same strike, same expiry, and the composition of the price is almost the opposite.
Time value decays toward zero as expiry approaches, which is why an option is a wasting asset for its buyer and a decaying liability for its writer. It also sets up the commonest trap: moneyness describes where the share sits relative to the strike and says nothing about whether the position is making money.
Why implied volatility moves the premium
An option pays off only on one side. The buyer of the call keeps every pound above £55 and never pays a penny below it, so a wider range of possible outcomes is worth more to them even though it is symmetric in the share price. That is the intuition behind volatility being a price input at all: uncertainty has value when the downside has already been paid for.
Implied volatility runs that logic backwards. A pricing model takes the share price, the strike, the time to expiry, the risk-free rate and a volatility assumption and returns a price. Since the price is the thing that is actually observable in the market, traders invert the model and solve for the volatility that reproduces it. In this example, a £2.00 premium on the £55 call with three months to run and a 4% rate implies a volatility of about 36.7% a year.
It is a quoted opinion, not a measurement. Realised volatility is calculated from prices that have already happened; implied volatility is what has to be assumed today to explain the price someone is paying today, and it changes when nothing about the share has changed. The sensitivity is easy to feel with one number: hold everything else and push implied volatility five points higher, to 41.7%, and the call goes from £2.00 to £2.47. Nothing happened to the share. The market simply repriced how much could happen.
Delta, the first Greek
Delta answers the question every desk asks first: if the share moves by one, how much does this option move? For the £55 call in this example, priced at £2.00 with three months left, delta is about 0.35. For the matching put it is about −0.65, and the two are related by the same parity that tied the premiums together, since the call delta less the put delta is one.
The practical use is hedging. Delta is a hedge ratio: a position with a delta of 0.35 behaves, for a small move, like holding 0.35 of a share, so selling that fraction of a share against each option leaves a position that is roughly indifferent to the next small move. Multiply by the number of contracts and the contract multiplier to get the share equivalent the desk actually trades.
Two qualifications matter more than the number. Delta is local: the £2.00 call here gains £0.375 when the share rises a full pound from £50 to £51, against the £0.35 predicted, because delta itself rose on the way. The rate at which delta changes is gamma, and it is why a hedge set once is wrong as soon as the share moves. Delta is also not the probability of finishing in the money. The two are related under the standard model and diverge as volatility, time to expiry and skew increase, so treating one as the other is defensible on a short-dated near-the-money option and unreliable elsewhere.
Who uses options for what
The same contract is doing a different job in each of these seats, and interviewers listen for whether a candidate knows which job they are describing. A structuring answer given in a long-only investment interview reads as borrowed.
| Seat | What the option is for | What gets discussed |
|---|---|---|
| Options market maker | Quoting two-way prices and managing the resulting risk | Implied against realised volatility, gamma, hedging costs, inventory |
| Hedge fund | Expressing a view with a defined loss, or hedging one already held | Asymmetry, catalyst timing, the cost of carrying protection |
| Long-only equity investor | Shaping an existing holding rather than replacing it | Covered calls, protective puts, the return given up to buy protection |
| Corporate finance team | Options embedded in securities rather than traded on their own | Convertible bonds, warrants, employee options and the diluted share count |
What interviewers ask, and what candidates get wrong
Options questions in markets interviews are rarely about pricing formulas. They test whether a candidate can hold a payoff, a premium and a direction in mind at once and stay consistent under a follow-up. The reliable failures are all versions of collapsing two ideas into one word.
- Quoting the payoff as the profit. The payoff ignores the premium that has already been paid; the profit does not, and breakeven sits one premium away from the strike.
- Saying the writer of a put has unlimited risk. The share can only fall to zero, so the put writer’s worst case is the strike less the premium received. It is the call writer whose loss is unbounded.
- Treating in the money as making money. A call bought for £2.00 that is one penny in the money at expiry has lost £1.99. Moneyness is a statement about the strike, not about the position.
- Describing implied volatility as a forecast that was measured. It is backed out of a traded price, so it is the market’s assumption rather than an observation, and it moves on supply and demand for the option itself.
- Reading delta as a probability and a permanent hedge ratio. It is a local sensitivity that changes as the share moves, as volatility changes and as expiry approaches.
- Forgetting the contract multiplier when converting a delta into shares. A 0.35 delta on a contract covering 100 shares is 35 shares of exposure, not 0.35.
What to learn next
Three steps follow from this page. First, draw both payoff diagrams from memory, then draw the profit lines underneath and mark the breakevens. It takes ten minutes and it is the highest-return thing to rehearse before a markets interview, because every structure question is built out of those two shapes.
Second, learn what the other Greeks measure, in the order a desk uses them: gamma for how delta moves, vega for sensitivity to implied volatility, theta for the decay of time value. Each one is a derivative of the same price with respect to a different input, and knowing which input is the point.
Third, combine the legs. A spread, a straddle and a collar are all built by adding the payoff lines above, and once the single-leg shapes are automatic, the combinations are arithmetic rather than a new topic.
Frequently asked questions
What is the difference between a call option and a put option?
A call gives its buyer the right to buy the underlying at the strike price; a put gives its buyer the right to sell at the strike. A call buyer gains as the underlying rises above the strike, with no upper limit. A put buyer gains as it falls below the strike, up to a maximum of the strike itself, because the underlying cannot fall below zero. In both cases the buyer holds a right and the writer holds the matching obligation.
Is the payoff of an option the same as the profit?
No, and the gap between them is the premium. The payoff is what the contract pays at expiry, which for a call is the underlying price less the strike when that is positive and zero otherwise. Profit subtracts the premium the buyer already paid. A £55 call bought for £2.00 has a payoff of £2.00 with the share at £57 and a profit of zero, so breakeven is £57 rather than the £55 strike.
What is the maximum loss on an option?
It depends entirely on which side you are on. A buyer of either a call or a put can lose no more than the premium paid, because the right is never exercised at a loss. A writer of a call faces a loss that grows with the underlying and has no upper bound. A writer of a put faces a loss capped at the strike less the premium received, reached if the underlying goes to zero.
What does implied volatility actually mean?
It is the volatility figure that, put into an option pricing model alongside the observable inputs, returns the price the option is currently trading at. It is derived from the price rather than measured from history, which is what separates it from realised volatility. A £2.00 premium on a £55 strike call with the share at £50, three months to expiry and a 4% risk-free rate implies roughly 36.7% annualised volatility.
Is delta the probability that an option expires in the money?
Not exactly, though it is often used as a rough proxy. Under the standard model the probability of finishing in the money is a closely related but distinct quantity, and the two diverge as volatility, time to expiry and skew increase. Delta’s primary meaning is a sensitivity: how much the option price moves for a one-unit move in the underlying, which also makes it the hedge ratio.
Now try it
Options Payoff Lab
The four single-leg option positions at expiry, drawn as two lines rather than one: what the contract settles for, and what it settles for after the premium. Move the strike, the premium or the share price and watch breakeven, maximum gain and maximum loss follow.
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