Option Buyer and Option Writer: Where the Choice Sits

The buyer of an option holds a right and has paid for it. The writer holds an obligation and has been paid for it. The right and the obligation are the only difference between the two sides, and every other difference follows from it: who pays at the start, who decides at the end, who can be made to perform, and which of the two lodges collateral against what they might owe.

The second of those two sentences carries a stronger claim than it looks. Not one of several differences. The only one. Everything below about premiums, about ceilings and floors, about who lodges what with whom and who gets picked out on the last day, is downstream of a single fact: two parties cannot both hold the right to decide the same thing. One of them holds it. The other is bound by whatever the first one decides. Once that is accepted, the rest is arithmetic, and the arithmetic is unusually clean. The side that gave up the decision has to be paid for giving it up, and the side that is bound has to show it can perform.

One pair of contracts runs underneath everything below. There is one reference asset, quoted at a spot priceWhat the reference asset changes hands for today, as against any figure fixed now for settlement at a date further out. of Rs 2,000.00/-. There is one call, struck at Rs 2,000.00/- and running for a year. The spot and the strike carry the same figure deliberately and not through an editing slip: this pair was struck at the moneySaid of a contract whose fixed level sits on top of the current price of the thing it references, so the two figures match because they were set to match rather than by accident., and struck at the money is precisely the phrase for two figures landing on top of one another that way. Money costs 6.50 per cent a year to finance. The reference asset pays out nothing whatever over the holding period. A payout would move every carried figure below, so the absence of one matters. The call premium is Rs 180.00/-, a figure given rather than produced by a model. Pricing an option is covered separately.

What does the buyer of an option actually hold?

Start with the buyer alone, and resist for the moment the urge to look across at the other side. The buyer holds one thing: a right to do something at a fixed level, at or by a fixed date. The right may be used and may equally be ignored. The buyer paid Rs 180.00/- for it on day one and that payment is finished business. It is gone. The premium does not come back if the right turns out to be worth nothing, and it is not topped up if the right turns out to be worth a great deal.

Consider a deposit left with a hall for a wedding date eighteen months out. The wedding is not booked. The deposit buys the right to book at the rate quoted today, and if the wedding does not happen the deposit stays with the hall. The shape of an option is the same. The payment buys a decision that did not previously exist, and it buys nothing else. Nobody can come back later for a second payment because the hall turned out to be in demand.

Two properties fall straight out of that and both are needed in every block below: the buyer's largest possible loss is what they paid, and the buyer's decision at the end is taken with the answer already visible. The abstract version of the first property hides a detail, so state it in the exact figure. The buyer paid Rs 180.00/- on day one. Money paid on day one and money settled a year later are not the same money, so put that Rs 180.00/- through a year at 6.50 per cent and it stands at Rs 191.70/- by the end date. Rs 191.70/- is the buyer's floor, and it is a floor in the strict sense: there is no arrangement of prices, no run of events, nothing the reference asset can do, that takes the buyer below it.

The second property is quieter and readers skate past it. On the last day the buyer is not guessing. The price is on the screen. The strike is written into the contract. The comparison is one subtraction, and the decision that follows from it is mechanical. Deciding after the uncertainty has resolved is a genuinely unusual position to be in, and it is what the Rs 180.00/- bought: not an outcome, but the right to decide once the answer is already visible.

Neither of those two properties says anything about what is likely. A floor at Rs 191.70/- says how far down the buyer can go. Whether the buyer ends up at that floor is a different question, and answering it would take a history, a spread of possible levels and a weight attached to each one. The working example holds none of the three. A floor is arithmetic; a likelihood is a claim about the future, and the two are not the same kind of statement.

And what does the writer hold?

Now the other side, defined in its own right and not as a hole where the buyer used to be. The writer is a party who has sold that right to somebody. The writer received Rs 180.00/- on day one. In exchange they shoulder an obligation that runs the full term, and on the last day, if they are called on, they perform. There is no step in the arrangement at which they get asked whether they would rather not.

Take the hall again and stand behind the counter. Somebody has left a deposit against a date eighteen months out. The hall has that money now, and it can spend it now, and it does not have to give it back. The hall has given up the ability to do anything else with that date until the customer says. If the date turns out to be the most sought after Saturday of the season, the hall watches it go at the rate quoted eighteen months ago. The writer's position has that shape, and the discomfort in it is exactly right.

Two properties mirror the buyer's, one for one: the writer's largest possible receipt is the premium and nothing the reference asset does can improve on it, and the writer's outcome is settled by somebody else's decision taken later. The first is Rs 191.70/- once the Rs 180.00/- is carried to the end date at the same 6.50 per cent, and it is a ceiling in the strict sense. There is no price, no path, nothing at all, that pays the writer more than Rs 191.70/- on this contract. The best day of the writer's life on this trade is the day the buyer walks away, and even that day pays Rs 191.70/- and not one paisa more.

The second is the harder one to sit with. The writer's result is not in the writer's hands. The result is fixed on the last day by a person the writer has never met, acting on information the writer also has, in that person's own interest and not the writer's. Everything the writer can control was decided on day one, when the premium was agreed. After that the writer is a passenger.

A third property has no mirror on the buyer's side whatever: the writer lodges collateralSomething of value lodged with a third party so that a promise can be relied on by somebody who has no other hold over the promiser. with whoever stands in the middle of the arrangement, and it is the existence of that requirement, rather than its size, that separates the two roles in practice. A buyer can never owe anything, so a buyer lodges nothing anywhere, ever. A writer lodges something before writing anything at all. How much, and how it is worked out, is set out in the section below.

What is the one difference the rest come out of?

Here it is, in one line. One side may walk away at the end and the other side may not. The right to walk away is not one difference among several, it is the generator of all of them, and the others can be watched being produced from it in four steps.

Step one. Because the buyer may walk away, the buyer's payoff can never be less than nil. Payoff here means what the contract itself pays on the last day, before anything paid for it is counted. If the right is worth nothing the buyer simply declines to use it and the contract pays nil. Declining is always available and declining costs nothing further, so nothing the reference asset does can push the payoff below nil.

Step two. Because the buyer's payoff can never be less than nil, the writer's can never be more than nil. The second step is not a second fact. A contract with two sides pays one side exactly what it takes from the other, so the second step is the first one restated. If one column is fenced below at nil, the other is fenced above at nil. There is no arrangement in which both sides get a payoff above nil, and a description that seems to offer one has left something out.

Step three. Because the writer's payoff can never be more than nil, the writer has to be paid at the start. Read the arithmetic of that rather than the sentiment: a position whose best possible payoff is nil and whose worst is unbounded below is one that nobody would take for nothing, and no part of the contract itself ever pays the writer anything. So the payment happens outside the payoff, at the beginning, once, and it is the premium. The premium is not a fee for a service and it is not a deposit; it is the entire consideration for accepting a position whose payoff cannot be positive.

Step four. Because the writer might owe something later and has already been paid, somebody has to hold collateral against what the writer might owe. The buyer, having already handed over everything they will ever hand over, needs no such arrangement. The asymmetry in collateral is not a rule bolted on from outside. The collateral asymmetry is generated by the same walking away that generated the other three.

What actually changes hands on day one?

A reader who has just met a contract written on Rs 2,000.00/- of reference asset frequently believes that Rs 2,000.00/- went somewhere. It did not. Exactly one amount moves on day one and it is Rs 180.00/-, from the buyer to the writer, once. The day one settlement is that single payment and nothing else.

The Rs 2,000.00/- is exposureThe size of the thing a contract is written against. Nobody has handed over that amount and nobody owes it. It is the yardstick the contract measures itself with., not a payment and not a debt. The exposure is the size of the thing the contract measures itself against, and it stays exactly where it was, in the hands of whoever had it. Distinguish it from a notionalA stated size that a percentage gets applied to. It is a multiplier inside a calculation and it never travels from one side to the other.. The word notional is used where the reference is a rate rather than an asset: same idea, a figure that a calculation is performed on rather than a figure anybody hands over. Whenever a large number is attached to a contract, the first question worth asking is whether it is a quantity somebody owes or a quantity something is being measured in. Here it is the second.

The strike of Rs 2,000.00/- is a third thing again, and it is neither paid nor owed on day one. The strike is a level written into the contract. The strike becomes an amount that actually moves only if the buyer chooses to buy at the end, and even then only where the contract settles by delivery rather than in cash. Whether a given contract settles one way or the other is a specification belonging to the Securities and Exchange Board of India (SEBI), published at sebi.gov.in, and is covered separately.

The writer has the Rs 180.00/- in hand from day one, and that is exactly why a written position feels finished long before it is. The money arrived. The screen shows a credit. Nothing further happens for months. The obligation, meanwhile, is doing what obligations do: sitting there costing nothing and being worth a great deal of attention nobody is paying it.

What can each side end up owing?

Now the arithmetic, and it is worth doing in two stages rather than one. The two stages carry different words, and mixing them is the commonest slip in this whole subject.

The first stage is the payoff. The payoff is what the contract itself pays on the last day, before anything paid for it is counted. For a call struck at Rs 2,000.00/- the payoff to the buyer is the settlement price less Rs 2,000.00/- where that difference is above nil, and nil otherwise. The writer's payoff is the same figure with the sign reversed, always, at every price, without exception.

The second stage is the profit. The profit is the payoff after the premium has been counted, and counted properly means carried forward to the same date the payoff arrives at. Rs 180.00/- paid on day one is Rs 191.70/- by the end of a year at 6.50 per cent. The Rs 11.70/- of carry is not a rounding artefact and it is not decoration. Leaving it out compares an amount paid today against an amount settled a year later, the same error as adding this month's rent to next year's.

Put four settlement prices through both stages and the shape appears. The four are not chosen at random: Rs 1,600.00/- and Rs 2,400.00/- are the ends of the range this guide works over, Rs 2,000.00/- is the strike, and Rs 2,130.00/- is the forward price arrived at by carrying the spot of Rs 2,000.00/- at 6.50 per cent for the year. Every figure below is recomputed here rather than carried over from anywhere.

Look down the third column and then down the fourth. The buyer's four profits have a floor and no ceiling, and the writer's have a ceiling and no floor, and that is the asymmetry a table makes visible where a sentence does not. The buyer's column stops at minus Rs 191.70/- and stays there for the whole lower half of the range, then rises without any limit the table can show. No settlement price is high enough to cap it. The writer's column stops at plus Rs 191.70/-, sits there for the same lower half, then falls without any limit either. Push the last row to Rs 3,000.00/- and the buyer's profit is plus Rs 808.30/- against the writer's minus Rs 808.30/-. Push it to Rs 10,000.00/- and neither column has met a wall.

One detail from the table worth naming because it comes up in a moment. The two lines cross at Rs 2,191.70/-, the strike plus the carried premium, and that crossing is settled under the call itself. The crossing is the price at which both sides finish at nil. The crossing is not a prediction of anything, it is a feature of the arithmetic, and it matters only because it is the one place on the whole range where the two sides finish level.

Which side has to lodge something, and how much?

The buyer lodges nothing, with anybody, ever. Not on day one, not while the contract runs, not at the end. Lodging nothing is not a concession granted to buyers, it is a consequence: a buyer can never owe anything, so there is nothing for anybody to hold security against. The premium was handed over on day one and the buyer's obligations were complete at that moment.

The writer lodges collateral with the middle party, the one whose whole function is to stand between two people who have no reason to trust each other, and may be called for more of itA demand, made while the contract is still running, that more value be lodged than was lodged at the start. while the contract is still open. Three things about that arrangement do not date, and they are the three worth carrying away: that collateral is lodged at all, that it moves while the contract is open rather than being fixed once at the start, and that a writer who does not meet a demand for more of it can have the position closed without being consulted.

Sit with the third one: it is the sharpest of the three, and readers routinely assume the opposite. The writer's position is not protected by the writer's own view that the price will come back. If more collateral is required and it is not lodged, the position can be closed out, and the writer's opinion about what happens next is not part of the procedure. The obligation the writer took on was to perform, and the collateral arrangement is what makes that promise something the other side can rely on without knowing anything about the writer at all.

Now the requirements themselves. How much collateral, how often it is recalculated, what triggers a demand for more, and what follows when a demand is not met all sit with SEBI, published at sebi.gov.in, and every one of them changes. A figure printed today would become the most quoted and most wrong number in the subject within a season, and a reader who had memorised it would be worse off than a reader who had memorised where to look. The card below has its rows labelled and its values empty. The rows themselves are worth remembering, not what sits in them on any one day.

Who decides at the end, and who is decided against?

On the last day the buyer chooses. The writer is assigned, meaning selected to perform against a right somebody else has exercised. Choosing and being assigned describe one event seen from its two ends, and the gap between the two words is the whole difference between the roles.

Here is the part that surprises readers, and it is worth stating without softening: the writer does not choose whether to be assigned, does not choose when, and does not choose against which particular exercise. A writer cannot ring anybody on the morning of the last day and withdraw. A writer cannot argue that the price is unrepresentative. A writer who has decided, quite reasonably, that the whole thing was a mistake has exactly the same obligation as a writer who is delighted with it. The procedure by which one writer rather than another gets selected belongs to SEBI at sebi.gov.in and is covered separately.

Think about a queue at a government counter where the token numbers are drawn rather than issued in order. Everybody in the queue has agreed to be served when their number comes up. Nobody in the queue decides when that is. The person on the other side of the counter decides when to call, and the drawing decides who. The queue is close enough to the shape, with one difference that matters. In the queue everybody eventually gets served. Under an option the buyer may never exercise at all, and then the writer is never called on for anything.

Which gives the plainest sentence available about what the premium actually buys: the writer is paid for accepting that somebody else decides, and that is the entire economic content of the payment. Not for taking a view. Not for skill. Not for being right about anything. For accepting that the decision belongs to another party, will be taken later, and will be taken with the answer already visible.

Do the two sides add up to anything?

The two profits add to nil, at every price, with no exception anywhere on the line. The last column of the table above carries Rs 0.00/- four times. Four zeroes in a row are not four coincidences, and they are not a market maxim of the sort people repeat at conferences. The nil is forced arithmetic, and exactly where the force comes from is set out below.

And there is one qualification that stops the sentence being glib: the addition is exact only when both sides are counted from the same premium at the same financing cost over the same period. The arithmetic here does that. A great many published comparisons do not, usually by carrying the premium forward on the buyer's line and leaving it uncarried on the writer's, or by using a different date on each side. The moment the two sides are counted differently, the columns stop adding to nil and the difference between them is not a fact about the contract at all. The difference is a fact about the inconsistent counting.

The chain worked across once with the control at its opening setting gives the whole argument in one line of arithmetic. Rs 2,400.00/- less the strike of Rs 2,000.00/- is a payoff of Rs 400.00/-, floored at nil so it can never go below. The carried premium of Rs 191.70/- comes off, leaving the buyer with plus Rs 208.30/-. The sign turns around and the writer has minus Rs 208.30/-. The two add to nil, where they were always going to land. Then drag the control anywhere at all and notice that only the first four cells change: the last step, the addition, has the same answer at every one of the eight hundred and one settings the control can take.

Where does this get used by somebody who is only reading?

Most people who need this distinction are not writing options. A reader is working through a set of accounts, or a fund factsheet, or a treasury note, and needs to work out what a written position in the document actually commits somebody to. The buyer and writer distinction is the tool that does that, and it does it in three questions.

First: which side is this. If the entity paid a premium, its worst case is already known and already spent, and no future line item can come out of that position beyond what has been paid. If the entity received a premium, the reverse holds, and the receipt sitting in the accounts is the ceiling on that position rather than a result. An analyst who reads a received premium as income and stops there has read the writer's ceiling and called it a floor.

Second: is there a collateral line, and is it moving. A written position generates a collateral requirement that changes while the position is open. The collateral requirement consumes cash that cannot be used for anything else, and it can grow at exactly the moment the entity is least comfortable. A lender assessing an entity with written positions is not primarily worried about the payoff. The lender is worried about the cash the collateral arrangement can demand at short notice, and about what follows if that cash is not there.

Third: whose decision settles it. If the entity is the buyer, the timing is theirs and can be planned. If the entity is the writer, the timing belongs to a counterparty who will act in their own interest, and the cash requirement then arrives on somebody else's schedule. For a household the same three questions come out as: what was paid, what can still be asked for, and who picks the moment. A person who has paid a non refundable booking deposit has answered all three: they paid it, nobody can ask for more, and the moment is theirs. A person who has taken a deposit and blocked a date has answered all three the other way.

So which side is better off?

Ranking the two sides of an option is not possible here, and the refusal is not caution: a ranking needs something the working example does not contain. A refusal without a reason is just a shrug, so say precisely what is missing.

There are two versions of the question and they need two different missing things. To say which side did better on a particular contract requires knowing where the reference asset actually went. The working example carries no outcome at all. Nothing settled. Nothing happened. The four settlement prices in the table are four places on a line, not four events, and none of them is more real than any other.

To say which side is likely to do better requires considerably more: the spread of levels the reference asset could reach between now and the last day, together with the weight attaching to each one of them. The spread and the weights together are a distribution, and the working example holds none. The example also holds no history, no realised series and no probability of any kind. So both versions of the question are unanswerable here, rather than merely unanswered, and the difference between those two words is the whole content of this block.

There is a third thing missing as well, and it is the one that most often gets skipped in discussions that manage to acknowledge the first two. Even with an outcome and a distribution in hand, better off is a question about a particular person's circumstances: what else they hold, what they can afford to have go wrong, what the arrangement costs them to hold and what it would cost to get out of it partway through. None of those three is present here either, and none of them can be supplied by anybody who does not know the person asking.

The two lines on the diagram describe, completely and exactly, what each side owes at each price, and neither line is a prediction of any price. A complete description of what each side owes is a genuinely useful thing to hold. The shape of the commitment on both sides of a contract is what anybody needs before a sensible question about it can be put.

The reference asset, its spot price of Rs 2,000.00/-, the strike of Rs 2,000.00/-, the financing cost of 6.50 per cent a year and the call premium of Rs 180.00/- are invented.
Educational material. Not advice on any investment, tax, budget or market position.