Option Price Drivers: What Can Be Read and What Cannot

Reading option price drivers means naming what can move a premium and in which direction, then marking which of those movements the figures in hand can account for. Almost none of those movements can be accounted for here. Accounting for one would need a figure for the ground the reference asset could cover, and this working example carries no such figure. One thing does hold: the gap between a call premium and a put premium at one strike is set by financing alone.

A driver is something sitting outside the contract that can change while the contract is still standing, and reading one means saying what its movement did to a premium. The definition hides two requirements. A driver is a claim about a change, and a change needs a before and an after, so reading one wants two premiums observed at two separate moments. Several drivers move at once, so reading one also wants some way of dividing that change between whichever of them moved in between. The reader has to say which did what. The figures worked below come to one premium, taken at one moment, with no way of dividing anything. The routine below says so at the step where it bites, rather than walking politely around it.

A routine with eight steps follows instead, and a routine of this kind has a definite job. The routine is not a way of producing a premium. The routine holds a premium so that the questions it can answer stand apart from the questions it cannot, and leaves a written record of that distinction for the next person who picks the sheet up. The output of this walkthrough is a card with most of its direction column marked unavailable, and that card is the finding rather than a gap in the finding.

Which of the numbers on the card is a driver supposed to move?

Start with a household case that has nothing to do with contracts. A household planning a move next month pays a tempo operator Rs 500/- today to lock a rate of Rs 4,000/- for a Sunday four weeks away. Four separate numbers are now in play. There is what tempos actually cost on that Sunday when it arrives. There is the Rs 500/- that has already left the house and is not coming back. There is the value of the booking once that Sunday arrives: whatever tempos cost that morning less the Rs 4,000/- locked in, and nothing at all where tempos come cheaper. And there is the household's overall position once the Rs 500/- is counted in.

Ask which of those four responds to anything, and the answer is only the second one, and only while it is still being negotiated. Once the Rs 500/- has been paid it is history. The value of the booking on the Sunday depends on the tempo rate that day and on the Rs 4,000/- written into the booking, and on absolutely nothing else: no amount of arguing about fuel prices in week two changes the arithmetic of week four.

The contract version has the same four numbers and the same answer. A spot priceThe price for taking the reference asset now rather than on some later date. It is what the thing costs today, before any contract is written on it. is what it takes to buy the reference asset today. A premium is what the contract itself costs, handed over once at the start by the buyer to the writerThe party who takes on the obligation side of an option and receives the premium for doing so. The buyer chooses whether to use the right; the writer has to live with that choice.. A payoff is what the contract hands back on the end date. A profit is that payoff net of the premium, brought forward to the same date at the financing rate so that two amounts from two dates can be compared honestly. Only the premium is still being decided while the contract stands, so of those four numbers only the premium has drivers at all.

Look at what that rules out. A payoff at the end date is settled by whatever the reference asset costs that day, set against the strike the contract carries. There is no third input. The financing rate never enters it, the time left never enters it, and nothing anybody believes about what comes next enters it either. Once the end date arrives the waiting is over, and a belief has nothing left to attach itself to. So a reader who says the payoff moved because a driver moved has not made a small error of degree. The reader has applied a list to a quantity the list was never about.

What has to be written down beside a premium before it can be read?

A premium on its own is a number. Somebody says Rs 180.00/- and it goes down on the sheet. Four digits with no context attached are worth about as much as a temperature with no place and no date beside it. Twenty six degrees is a mild afternoon in one city and a heatwave in another, and it means nothing at all without knowing which reading it was.

The premium of Rs 180.00/- becomes a reading when five things are written beside it, and the five are not a matter of taste. Each one appears in the arithmetic that ties premiums together, so each one has to be recorded or the arithmetic cannot be run. The five are what the reference asset was costing at the moment the premium was observed, the time left to the end date, the financing rateThe cost of holding money for a period, always quoted with the period it covers. Six and a half per cent a year and six and a half per cent a month are not the same rate and never behave alike. together with its period, whether the reference asset pays anything out while it is held, and the strike.

On this working example those five read as follows. The reference asset carries a price of Rs 2,000.00/-. The price counts as exposureHow much of the reference asset a position tracks. It scales what the position follows, and it is not money anybody handed across. rather than an amount anybody handed over. The time left is one year. Financing is 6.50 per cent a year. The reference asset hands nobody a single paisa over the course of that year. And the strike is Rs 2,000.00/-.

Two of those five numbers are the same, and that is deliberate rather than a copying slip. A reference asset priced at Rs 2,000.00/- meets a strike that also reads Rs 2,000.00/-. The pair of contracts is therefore struck at the moneyA contract whose strike sits level with the current price of the reference asset. Struck above or below it, the same contract would be described differently.. A reader who spots two identical figures in a table usually assumes somebody pasted one into the other. The repetition is exactly what the phrase means.

A premium with none of those five beside it is not a reading, it is a number, and nothing in the rest of this routine can be done to it. The claim is stronger than it looks. Every later step of the routine reaches back into this list: the split in step three needs the price and the strike, the check in step five needs the price, the strike, the rate and the time, and the empty rows in step four are empty precisely because a sixth thing that would have belonged on the list is not written down anywhere.

Which part of the premium could a driver even be touching?

Saying what moves a premium means first breaking the premium into parts, and there is exactly one place to cut it that requires no assumption from anybody. The cut is at what the contract would pay if the end date were today. For the call that is the price less the strike where the price stands higher, and nothing at all where it does not. For the put it runs the other way. The cut is arithmetic on two numbers already in hand, and two readers doing it separately will get the same answer every time.

Whatever is left over after that is the remainder. The remainder is a subtraction rather than a figure anybody produced, and that is the only reason it can be printed here. Nobody produced it from a model, priced it, or estimated it. The remainder is the premium less the part that is arithmetic, and it is knowable for the simple reason that both of the other two numbers are known. The meaning of each part, and how each behaves as conditions change, is covered separately. The step takes the split and stops.

Run it on the working example and something awkward happens. The reference asset sits at Rs 2,000.00/- while the strike also reads Rs 2,000.00/-, so what the call would pay if the end date were today is Rs 0.00/-, and so is what the put would pay. The arithmetic part of both premiums is nil. Every paisa of the call's Rs 180.00/- and every paisa of the put's Rs 57.93/- therefore sits in the remainder.

The split is the simplest one available and also the least helpful. Being struck at the money makes the arithmetic trivial and leaves the whole of both premiums parked in the part where, as the next step works out, no direction can be established from anything already set down. A reader hoping the split would carve off something readable gets a clean cut and nothing on the useful side of it.

What are the five drivers, and which way does each one push?

Five things can be written down as rows. The cost of the reference asset. How much time is left before the end date. The financing rate. The room the reference asset has to move in before that date arrives. And anything paid out on the reference asset to whoever is holding it. Almost every printed list of option price drivers contains those five rows, and writing them down is the easy half of the step.

The hard half is the rule that separates this routine from a memorised list. A direction may be written against a driver only where the reason can be given from arithmetic already set down. Not because the direction has been seen printed elsewhere, not because it sounds right, and not because it is almost certainly true. If the reason cannot be pointed at, the cell is marked unavailable and left that way.

Apply that rule to the part of the premium that is arithmetic, and the rows sort themselves out quickly. The arithmetic part asks what the contract would pay if the end date were today. The comparison sets the price against the strike and asks nothing else. So the price row takes a direction, and it is derived rather than recited: push the price up and the call's arithmetic part rises with it. The put's falls, straight off the shape of what each side owes. The other four rows take a direction too, and it is the same one in each case. Time left does not appear in that comparison. The financing rate does not appear in it. How far the price could move does not appear in it. Payouts on the reference asset do not appear in it. Each of those four has no effect whatever on the arithmetic part, and saying so is a derived answer rather than an empty cell.

Applied to the remainder, the rule fails every row. The remainder was defined as a subtraction, so nothing set down here says how it responds to anything. Establishing a direction for the time left, or the financing rate, or the price itself against the remainder would need a way of producing the remainder from conditions, and producing it needs the input this working example does not hold. So all five cells in that column are marked unavailable, in words, and not one of them gets a direction copied in from memory.

A direction recited from memory and a direction derived from the arithmetic look identical once they are written down, and only one of them can be checked. The rule exists for exactly that reason. Six months later, a reader picking up a card somebody else filled in cannot tell by looking whether a row was worked out or remembered. Marking the unworked rows unavailable is what keeps the two apart, and it costs nothing except the discomfort of a card that looks half finished.

One row is empty twice over, and it is worth naming. A payout changes what holding the reference asset actually costs, and therefore feeds into the arithmetic tying premiums together. So anything the reference asset pays out while it is held would matter in general. Here it is silent for two separate reasons. No payment reaches a holder of this reference asset during the year, so the row is nil on this example. And this working example carries no case in which one does, so there is nothing to swap in and nothing to demonstrate against. The row stays on the card because leaving it off would suggest that payouts never arise.

Which reading in this walkthrough is exact, and what does it cost to run?

After a step that fills almost nothing in, the rest might fairly be expected to be apologies. One reading here is exact, needs nothing this working example lacks, and can be reproduced in four lines by anybody with a calculator.

For a single strike on a single end date, a call premium net of a put premium comes to the reference asset's price with the strike's present valueAn amount due later brought back to what it is worth today, by dividing it by one plus the financing rate for the period involved. taken out of it. The relationship falls out of what each contract obliges its two sides to do at the end date rather than out of any model of how prices behave, so it holds no matter what the absent figure would have been. Holding a call and writing a put at the same strike commits the holder to taking the reference asset at that strike on that date, whatever the price does. An agreement to buy forward at that strike carries the same commitment. The gap between the two premiums is what that commitment costs, and what it costs is the delay in paying the strike.

Worked through on the pair carried here: the strike of Rs 2,000.00/- set against one plus 6.50 per cent falls back to Rs 1,877.9343/- in today's money. Taking that away from the price of Rs 2,000.00/- leaves Rs 122.0657/- standing. The difference between the two premiums is required to be exactly that. The two premiums actually in hand are Rs 180.00/- and Rs 57.93/-, and Rs 180.00/- less Rs 57.93/- comes to Rs 122.07/-.

The check passes to the paisa rather than to an exact equality. The two answers stand 0.43 paise apart, forty three hundredths of one paisa, and the reason is not a flaw in the arithmetic. A premium has to be expressed to the paisa before a person can hand it over, so the put premium of Rs 57.93/- is the rounded form of Rs 57.9343/-. Writing the check to demand exact agreement would reject almost every honestly quoted pair in existence, and a check that fails on correct inputs teaches a reader to stop running it.

How much of that check survives when one condition is moved?

Two of the five drivers act on that gap in a way that can be computed to the last place, and it is worth seeing why. Look at the right hand side of the relationship: the price of the reference asset, and the strike brought back to today. The financing rate and the time left are the only two things that touch the second of those, and nothing else in the driver list appears on that side at all. Move either one and the gap moves with it, exactly, with no missing input anywhere in the calculation.

Consider the time left. Both contracts worked here run one year, so a longer setting has to be declared as a control rather than smuggled in as a second contract that somebody wrote. At two years, with financing held at 6.50 per cent a year, the strike of Rs 2,000.00/- falls back to Rs 1,763.3186/-, or Rs 1,763.32/- once rounded to the paisa. The required gap between the two premiums becomes Rs 236.6814/-, or Rs 236.68/- to the paisa, against Rs 122.0657/- at one year.

The control establishes the gap between the two premiums at both settings, and neither premium itself at the second one. The boundary is easy to slide past. A call and a put struck at Rs 2,000.00/- for two years are required to stand Rs 236.6814/- apart. Whether the call is Rs 300.00/- and the put Rs 63.32/-, or the call Rs 500.00/- and the put Rs 263.32/-, the relationship cannot say, and no figure of this kind ever will. The distance is knowable; the position is not.

Why can this working example not show a premium moving?

Here is the honest position, and it is two separate holes rather than one. Patching either one would still leave a reader unable to read a driver off these figures. Both holes are written in separately for that reason rather than collapsed into a single line.

The first hole is a second reading. Attribution is a statement about a change, and a change needs two dated observations of the same thing. The working example carries the call at Rs 180.00/- and the put at Rs 57.93/-, both observed at one moment, with nothing before them and nothing after. There is no earlier premium to compare against and no later one. So no premium has moved. There is nothing to attribute, and no amount of skill with the driver list changes that.

The second hole is the input itself. Suppose two dated readings did exist, a month apart, and the premium had gone from Rs 180.00/- to Rs 195.00/-. Dividing that Rs 15.00/- between the drivers that moved in the meantime needs a way of turning conditions into a premium, and that machinery needs a figure for the band of prices the year could end inside, together with how much weight each part of that band carries. Nothing of the kind is written down anywhere in this working example, in any form: not as a percentage, not as a range, not as a round number offered for illustration.

The cell gets the name of what is absent, written in words, and never a plausible number. The reason is about what happens to the sheet afterwards rather than about tidiness. A plausible number gets used. Somebody copies the cell into a note and the note into a summary, and by then the caveat has been left behind. Four steps later a figure that nobody produced is sitting in a document with an air of authority. A named absence gets looked up. A named absence is a question in written form, and questions in written form get answered eventually.

Naming the absence is the finding rather than a gap in it. Naming the absence is the half readers skip, and the half that matters. A card with three cells reading unavailable is a complete and accurate record of what these figures support. A card with three cells filled in would be a record of an attribution nobody carried out, dressed up to look like work.

What does a driver never tell anybody?

Naming what a driver never says stops the whole list from being read backwards, so it belongs in the routine as a step rather than as a caution tacked on at the end. Three things a driver does not say, and every one of them is an error that turns up regularly.

A driver does not say which way it will itself go. The relationship on a card runs like this: if this moves, the premium responds in that direction. Read the sentence carefully and notice that it opens with a condition. Nothing in the routine asked, at any step, whether the financing rate will rise, or whether the price of the reference asset is heading anywhere in particular. Neither question was ever put, so no answer to either is hiding in a filled-in row.

A driver does not cause a payoff. A payoff at the end date is settled by the closing price of the reference asset and by the strike the contract carries, and the driver list has already been shown not to reach it. So a sentence beginning with the words the payoff rose because is a sentence about the price of the reference asset, whatever noun follows the word because.

And a premium is not a forecast. A premium that is larger than another premium is not somebody's view about direction hiding inside a number. The claim is worth stating flatly, and the failure block below works it out in full with the two figures this working example actually carries.

What does the finished card actually say?

Read the output back and it comes to six lines. Which quantity was held, and it was a premium rather than a price, a payoff or a profit. The conditions it was read against, and there were five of them written down beside it. Which part of it a driver could be moving, and on this pair that is the whole of it, the arithmetic part being Rs 0.00/- on both contracts. Which directions were derived rather than recited, and that is one row on one side of the split. The output of the exact check, Rs 122.0657/- against Rs 122.07/- in hand, agreeing to the paisa. And what is missing: a second dated reading and a figure for the travel available to the reference asset before the end date.

Beside that sits everything the card leaves unsaid. The card does not say whether the contract should be held, entered into or closed. Answering that would need three things in hand first. A view on how widely the price could swing before the deadline, with the odds attached to each part of that swing. The reader's own circumstances, recorded on no card of this kind. And what the arrangement would cost to hold from now until the end date and to unwind before it. Not one of those three is available, and no arrangement of the five rows produces any of them.

Where does a card like this actually get used?

A routine that mostly writes the word unavailable sounds like an academic exercise until somebody uses one. Consider an analyst inside a firm that has written a small number of these contracts and now has to explain, at a monthly review, why the amount carried against them changed. The instinct is to reach for a story: the price moved, so the premium moved. The card stops that. The card asks which quantity moved and against which conditions, and it asks for the readings to be dated. Half the time the honest answer turns out to be that the conditions were recorded once and never recorded again, so nobody can say anything at all, and finding that out in the review is enormously cheaper than finding it out in an audit.

Take a lender who has accepted a position of this kind as part of a borrower's asset list. The lender never asks what a premium is worth in the abstract. The lender asks what the position amounts to if things go badly. Answering that means separating notionalA quantity that a contract's payments are worked out against, which never itself changes hands. It scales the arrangement without ever being an amount anybody pays. from what could actually be lost, and separating the premium already paid from the carryGrowing an amount forward at the financing rate so that two figures from two different dates can be compared on the same date. of holding the position on to the end date. The five standing conditions are exactly the list a lender asks for, and a borrower who cannot produce all five has told the lender something useful before any number is discussed.

And take a household that has been offered something with an option embedded inside it, wrapped in a product with a name. The routine here does not price that. The routine gives the household six lines instead: what am I holding, against what conditions, what part could move, what directions can actually be defended, what checks out exactly, and what is missing. The last line is where an unanswered question gets written down and kept, and most of the value of a card like this comes from that line rather than from the filled ones.

Does any of this establish whether to hold the contract?

Nothing in the routine settles that, and the reason is worth stating rather than leaving as a disclaimer. Whether an arrangement suits a particular person is a question about that person, and these figures could not begin to answer it. No event in this working example was ever written down as having occurred. No run of past prices stands behind the Rs 2,000.00/-. Nobody put a band of possible endings around the year, or weights on the parts of that band. There is no realised outcome anywhere, so there is nothing to compare one choice against another with.

The silence is a stronger position than a caution. An account that carried outcomes could at least be tempted to rank two arrangements and would then have to resist. Here there is nothing to rank with, so the silence costs nothing and reads as a description of the figures rather than as legal noise at the foot of a lesson.

The reference asset with its price of Rs 2,000.00/-, the call and the put, and the premiums of Rs 180.00/- and Rs 57.93/- are invented.
Educational material. Not advice on any investment, tax, budget or market position.