The Expiration Date: The Deadline That Drives Time Value

The expiration date is the last moment at which the buyer's right can be used, and after it the contract is nothing at all. On that date a premium is exactly what the contract pays and no more, so whatever a premium held above its intrinsic value has gone by then, whatever the reference asset did in the meantime.

The deadline does all the work in those two sentences. Start with why a deadline is worth anything at all. A right that never ran out would never have to be used: it could always be left for another day, and nobody pays for something that can be postponed forever. The deadline is what turns a right into a thing that can be priced, and it is also what makes the arithmetic at the end simple: by then the price has already arrived and nothing is left to judge.

The shape is familiar from ordinary life. A hall is held for a wedding on a token paid in advance, and the token holds the booking until a stated day. Up to that day the family holds a choice worth having. On that day the choice stops: either the hall is taken or the token is gone, and nobody is going to argue about it afterwards.

What is the expiration date, and what is left of the contract after it?

The expiration date is the last moment at which the buyer's right may be put to use. The date is fixed when the agreement is struck, it sits among the terms exactly as the strike level does, and it does not shift because one side would prefer it elsewhere. The far side of that moment is what matters most. Past that moment the contract is not a weakened claim, not an asset marked down, and not something a second payment can bring back to life. The contract is nothing whatever, and neither side is left owing the other a paisa on account of it.

The consequence is worth stating bluntly. The end date is a term of the contract in exactly the way the strike is, and the two of them together are what makes one contract different from another written on the very same reference asset. A different strike makes a different contract. A different end date also makes a different contract, not the same contract stretched. Two agreements on the same asset, at the same level, running to different dates, are two separate things, each with its own obligation sitting behind it.

The obligation on the other side runs to the same moment. The writerThe side that accepts the payment at the start and carries the duty for as long as the contract lives. The decision to act is never theirs to make. takes the premiumWhat the buyer pays across to the other side when the contract is opened. It changes hands a single time and never returns, however things turn out. at the start and carries the duty for as long as the contract lives, and when the deadline passes, that duty simply stops. Nothing is handed back. Nothing is settled up. The arrangement had a life, and its life ended on a date both sides agreed to at the beginning.

What does the deadline actually do to the decision?

A date matters for one reason. Before the end date, the buyer holds a choice whose outcome cannot be settled: the number the choice will be measured against has not turned up yet. A view about where the price of the reference asset is going may be a good view, but a view is not the same as a fact and the comparison the choice requires cannot be completed. So all the way through the life of the contract, the buyer holds something genuinely open.

On the end date that openness disappears in one step. The price has arrived. The price is a number sitting on a screen rather than a possibility, and it can be set against the strike written into the contract. The decision to exerciseUsing the right the contract carries. Only the buyer can do it, and only inside the window the contract sets for it. then stops being a judgement and turns into a comparison a school child could finish: use the right where using it pays something, walk away where it does not. The deadline converts a right into a decision, and it is the only event in the life of the contract that does it.

The arrival of the price settles how a premium is to be read during the life of the contract. Whatever anybody is willing to pay for the contract before the end date is a payment for a choice still being open. On the end date there is no choice left to be open, and the answer is visible to both sides.

Intrinsic Value: what would the contract hand over if today were the end?

Now the object the deadline acts on. Intrinsic value answers one question and only one: if the deadline landed at this very instant, how much would the contract hand over? The question hides a condition people drop without noticing. Intrinsic value is not the worth of the contract, and not what somebody would pay for it. Intrinsic value is the amount that would be handed over, on the assumption that the moment of decision is this moment.

For a call, that is however far the referenced price stands above the strike. Where it sits at or beneath the strike, the reading is Rs 0.00/-. For a put, it is however far the strike stands above that price, and where the price sits at or over the strike, the reading is Rs 0.00/- once more. The reading never drops beneath nil, and that is not a convention somebody imposed: nobody puts a right to use at a loss, and leaving it alone is a permanent alternative costing not one paisa more. A right to buy at Rs 2,000.00/- goes untouched while the same asset stands on offer at Rs 1,600.00/-. The right is simply left where it lies, and the line flattens onto the axis.

Three things intrinsic value is not, each of them a mistake that gets made in print, and each dismissed in a line.

What do the two contracts read at four different prices?

The same invented pair carries through this sequence, and here are its figures again. The reference asset has a spot priceWhat the thing being referenced costs for delivery today, as distinct from what it would cost for delivery on some later date. of Rs 2,000.00/-, an exposureA quantity of something a position behaves as though it held, without that amount ever having been handed over by anybody. rather than an amount anybody has handed over, and it throws off no payment of any kind for as long as somebody holds it. Both contracts carry a strike of Rs 2,000.00/-, and matching the price exactly is deliberate rather than a transcription slip: this pair sits at the moneyA contract whose agreed level and the going rate for the referenced thing happen to coincide, leaving neither half of that comparison in front., and the phrase reports that coincidence and nothing more. Both run a single year to one end date. Financing costs 6.50 per cent a year. For the call the premium reads Rs 180.00/-; for the put it reads Rs 57.93/-. Neither was produced by any model: both were handed over as given figures.

Work the intrinsic value today before anything else. Most people guess that reading wrong. The price is Rs 2,000.00/- and the strike is Rs 2,000.00/-. Neither stands above the other. So today the call's intrinsic value reads Rs 0.00/-, the put's reads Rs 0.00/- as well, and both premiums lie wholly outside intrinsic value, down to the last paisa. A reader expecting part of that Rs 180.00/- to be intrinsic was treating the size of a premium as proof that the contract already stands ahead, and standing level is precisely what standing ahead is not.

Now the end date, at four prices. Each figure below is the amount the contract would pay on that date, and that amount is also its payoffWhat a contract pays out at the end, counted before anything spent on obtaining it has been taken off.. The two readings coincide there because a contract with no time left pays what it is worth.

The four rows carry payoffs, never profit figures, and confusing the two is the error this subject produces more often than any other. Reaching a profit means removing what the contract cost, moved forward to the same date so both amounts are read at one moment. Carry the call's Rs 180.00/- across the year at financing of 6.50 per cent a year and it lands on Rs 191.70/-; send the put's Rs 57.93/- along the same road and it lands on Rs 61.70/-. Subtracting produces an entirely different set of numbers.

Along the row for Rs 2,130.00/-, the call's intrinsic value is Rs 130.00/-, a genuine amount handed over, and the call's profit still reads minus Rs 61.70/-. Standing above the strike and finishing ahead are two separate readings, and any account that lets a reader slide from one to the other has taught them to lose money politely.

What does the deadline leave behind?

One of the very few statements in this whole subject can be made without qualification. Come the end date, a premium equals its intrinsic value and stops there. No remainder survives, no residue, and no rounding tucked into a corner of it.

The reason leans on nothing that is missing here. Once the deadline arrives, no interval survives inside which any event could occur. A contract is therefore worth exactly what it hands over, and one handing over nothing is worth nothing. Nobody parts with money for a claim that has already produced everything it will ever produce. The argument calls for no view on the referenced asset, no rate and no measure of the ground prices cover, only the observation that the clock has stopped.

Here is the half that makes the first half interesting. Before the end date a premium can sit well above its intrinsic value, and the whole of that difference is the rest of the premium, obtained by subtraction and never measured on its own. On the pair worked above, the call premium of Rs 180.00/- sits against an intrinsic value of Rs 0.00/-, so the entire Rs 180.00/- is the rest. The common name for that difference is time value. Setting time value against intrinsic value, as two routes to one number, is a comparison in its own right and is covered separately.

What is certain about the rest of the premium?

One thing, and only one thing. The rest of the premium arrives at Rs 0.00/- on the end date.

The arrival at nil holds no matter what the referenced price gets up to between today and then. The same arrival holds whatever the financing rate does, and whatever the missing quantity would have turned out to be. The argument never touched any of them: on the deadline the premium and the intrinsic value are one number, the rest is defined as the premium less the intrinsic value, and on that day the rest is therefore a quantity subtracted from itself. The certainty is about a destination, and it says nothing whatever about a journey.

The difference between a settled destination and a route to it is where nearly every error on this subject lives.

And what is not certain about it?

Everything else. The rest of the premium arrives at nil, and no route to that nil can be drawn without a measure of how far the referenced price could travel.

A fall of the same amount each day does not follow. Nor does a fall that speeds up as the end date nears. On any particular day the rest of the premium need not fall at all: the price of the reference asset may have moved in a direction that leaves the split looking quite different. Establishing any of those calls for a measure of the ground the referenced price could cover between now and the deadline, together with a weight on each of those distances. No measure of that description sits in the working example above. Not a small one, not an approximate one, not a round number offered as an illustration. There is none.

In place of an answer there is a procedure, and the procedure is more useful than the answer would have been. Where a path is what is wanted, the quantity that drawing one would take is named first, and then whoever produced it is asked how. Anybody handed a decay curve by somebody else should ask what it was drawn off, and should read a curve with no answer to that question as a shape somebody chose rather than a result somebody worked out.

What does a frozen premium actually demonstrate?

There is one demonstration worth running, and it needs a warning printed on it rather than under it. Hold the call premium perfectly still at Rs 180.00/- and imagine the price of the reference asset standing at Rs 2,130.00/-. The intrinsic value would then read Rs 130.00/-, being the amount by which Rs 2,130.00/- exceeds the strike of Rs 2,000.00/-. The rest would read Rs 50.00/-, being the premium of Rs 180.00/- less that Rs 130.00/-.

Holding a premium still while the price of the reference asset moves is a fiction, it would not happen, and the only thing this demonstration establishes is that the second figure is reached by taking the first away from the premium. The demonstration is about a subtraction, not about a market. The premium at a price of Rs 2,130.00/- cannot be produced from the figures above, for the reason set out at length, and no arrangement of them would get it there.

The demonstration earns its place anyway by making one thing visible that prose keeps failing to make visible: the rest of the premium is never measured. The remainder is what falls out when intrinsic value is taken off the premium. There is no separate instrument for reading it, no market that quotes it and no column anywhere that contains it before the subtraction is done.

What does the same deadline mean to the writer?

Most accounts of an expiration date describe only the buyer's half, and the writer's half is the one that surprises people. The writer's obligation runs to the very same date and ends with it. Until then it stands, it cannot be handed back, and it cannot be closed by deciding that the arrangement no longer suits. And the choice of when to call on that obligation sits entirely with the other side, never with the writer.

The buyer holds a deadline by which a decision may be made, and the writer holds a deadline until which a decision may be made against them: the same date, and opposite meanings. For one side the date is a limit on a right. For the other it is the length of an exposure to somebody else's judgement. The asymmetry of these contracts, restated in the language of time, explains why a writer's experience of a long deadline feels nothing like a buyer's.

The amount the writer places against that obligation while it runs, and the method for working it out, are set by the authority named below.

Where does a deadline actually get used, and by whom?

Take the ordinary case: somebody sitting in front of a quote for a contract. The holder has a number for what the contract costs and a number for what the reference asset is doing, and the first useful act is not to form a view about the asset. The first useful act is to split the quote. Work the intrinsic value, a subtraction anybody can finish in three seconds, and see what is left over. If the intrinsic value is Rs 0.00/- and the quote is Rs 180.00/-, then the entire quote is a payment for a choice that is still open, and it is scheduled to be worth nothing on a date already written into the contract. The split does not say whether to buy. The split says precisely what would be bought, and that is a different and more useful thing to know.

An analyst handed a sheet of positions does the same split for a second reason: it separates the part of a position's stated value that survives arithmetic from the part that depends on somebody's model. The intrinsic part can be re-derived from two numbers on a sheet. The remainder cannot be rebuilt by anybody lacking a measure of how far the referenced price could travel, a measure covered separately. A reader who can say which half of a figure they could rebuild themselves and which half they are taking on trust has done the most useful thing available to them, and it costs one subtraction.

The household version is smaller and identical in shape. A token paid to hold a hall, a booking fee that secures a slot, a deposit that reserves a seat on a course: every one of them buys a choice that expires. On the day it expires the holder has either the thing itself or nothing, and the amount paid for the waiting is not coming back. People handle these arrangements sensibly every week without calling any of it a premium, and the only thing the finance version adds is that the split can be written down in rupees.

Is a longer deadline better than a shorter one?

The question every reader arrives at is which deadline to choose, and arithmetic cannot rank the two. The reason repays reading, and it names what a ranking would take.

A longer deadline is a separate contract. A longer deadline carries a separate premium, and the working example holds a premium for a single end date, so there are not even two figures to lay beside one another. Producing that second premium would take exactly the quantity named throughout: some measure of the ground the referenced price could cover, with a weight on each outcome. Three things would need settling before anybody could answer, and not one of them is available: a view on the range that price could travel and the weight resting on each part of it, the particular circumstances of the person asking, and the cost of carrying and unwinding each contract.

The mechanism is what can be taken away. A deadline ends a right on one side and ends an obligation on the other. A deadline converts a judgement into a comparison. And a deadline guarantees that whatever a premium held above its intrinsic value has gone by the time the deadline arrives. All three hold regardless of which contract is put in front of a reader.

The reference asset, the call and the put written on it, and every rupee figure above are invented.
Educational material. Not advice on any investment, tax, budget or market position.