How to Map What Moves an Option Premium, Step by Step

Mapping an option's sensitivities means three things done in order: list what can move, name the sensitivity each movement carries, and mark which of them the figures in hand can supply. On the pair worked below, one relationship is exact. A call and a put at one strike have slopes against the reference asset that stand exactly one apart. Every other row needs a figure for how widely the reference asset could swing before the end date, and nobody has written that figure down.

A sensitivity is the answer to a question with a very particular shape. How much does the premium move when one thing moves and everything else stays exactly where it is? That question is the whole of it. So a routine for mapping sensitivities is really a routine for asking the one question once per moving input, in a fixed order, and then being honest in writing about which of the answers can actually be produced.

The eight steps below are the routine. How a sensitivity behaves is covered separately and in full. The eight steps set out what to write down, in what order, and what to put in a box that cannot be filled. A mostly empty sheet that names what is absent is a finding and not a failure, so the routine's output is a sheet that is allowed to come out mostly empty.

What does step one separate, and why does it come first?

Before asking what moves the premium, what is even allowed to move has to be settled. So step one is two columns on a sheet of paper, and nothing else happens until they are written.

The left column holds the fixed terms of the contract, meaning the parts that cannot change while the contract stands: which reference asset, whether it is a call or a put, the strike, the end date, and which side the holder is on. The right column holds everything outside the contract that can shift while the contract carries on standing: the price of the reference asset, the time left, the financing rate, and how widely the reference asset might range before the end date arrives.

The rule of the step is one line long and it decides everything after it. A sensitivity always belongs to something in the right-hand column, and anything in the left-hand column changing gives a different contract rather than a moved figure.

A caterer quoting for a wedding makes the same split without being taught. The hall, the date and the number of courses are written into the agreement, and if the couple move the date, nobody says the quote has changed; everybody says there is a new quote. The price of onions on the morning is a different animal altogether. The onion price moves while the agreement stands, and the caterer's exposure to it is a real thing worth measuring. Contract terms on one side, market movements on the other. Step one asks for exactly that split.

The two tinted cells are worth a moment. The strike on the left reads Rs 2,000.00/-, and on the right the reference asset price reads Rs 2,000.00/- as well. The repetition is not a figure copied across by accident. The pair worked through this guide is struck at the money, and that is precisely what those words mean. One of the two identical figures is a term of the contract. The other is a market reading that will have moved by Thursday. Same number, opposite columns, and the routine treats them as nothing alike.

How does step two turn a moving input into a named sensitivity?

Step two writes one question against each moving input, one row apiece, and writes the question out in full rather than reaching for a letter. Five rows come out of it.

How much does the premium move when the reference asset price shifts by a single rupee? How much does that first answer itself shift as the price carries on moving? How much does the premium move as a single day passes with nothing else changing? How much does the premium move when the figure for the asset's reach is revised? How much does the premium move when the financing rate moves? Five questions, one for each thing in the right-hand column plus one that asks about the first answer rather than about the premium.

Writing them as questions rather than as letters is not decoration. A row that reads as a question can be argued with, and a row that reads as a letter can only be looked up. Anybody who has watched a meeting stall while three people establish which letter somebody meant will recognise the saving. For the letters, the GreeksA shorthand that names the standard premium sensitivities after letters of the Greek alphabet. Every one of them is written out as a question here, so nothing below depends on knowing which letter is which. are the ordinary shorthand for exactly these five, and what each of them measures is covered separately and in full.

The ratio quietly demands something. To divide by a movement, somebody has to say how big the movement could be, and for four of the five rows that somebody is the person holding a figure for the reach of the reference asset. No figure for the reach of the reference asset is available here, and step three is where the routine says so.

What does step three ask of every single row?

Step three asks one question of each row and it asks it before any attempt is made to answer the row itself. Can this response be produced from the figures already written down in step one, or does it need something that is simply not there?

Three inputs are all this working example carries. The reference asset price stands at Rs 2,000.00/-. Financing runs at 6.50 per cent a year, and one year is the entire life of both contracts here. The call premium was supplied at Rs 180.00/-, not produced here. Those three inputs are the lot. Running that price forward twelve months at the financing rate gives the forward price of Rs 2,130.00/-, and the reader can already build it unaided. Nobody holding the reference asset collects a paisa over those twelve months, so nothing subtracts from that carry.

Run the test across the five rows and four of them come back the same way. Each needs somebody to have said how widely the reference asset could swing before the end date, and with what odds, and no such statement exists here. A blank cell reads as an oversight and a marked cell reads as a finding, so step three puts the word waiting into those four cells rather than leaving them blank.

The fifth row comes back differently, and it is worth being precise about why. Neither the call's slope against the price nor the put's slope against the price can be produced from three inputs. The distance between the two slopes can be produced, and that distance turns out not to need the missing figure at all.

How is the one available row filled, and how is it checked?

A row accepted rather than checked is a row somebody else is being trusted with, so step four fills the row that can be filled and then checks it. The claim is narrow and it is exact. Where a call and a put share a strike and share an end date, the call's slope against the reference asset price stands exactly one above the put's, whatever else happens to be true.

Where does that come from? The gap falls out of the arithmetic tying the two premiums to each other, and the reader already has that arithmetic. Taking the put premium away from the call premium leaves Rs 122.07/-, and that has to land on the distance between the reference asset price and the strike pulled back to today, a distance that works out at Rs 122.0657/-. The two figures agree to the paisa. Rounded figures never come closer, and Rs 57.93/- is itself a rounded figure by the time it is used here. A rupee added to the price moves only one term on that side of the arrangement, one for one. So the two premiums have to keep moving one rupee apart from each other, and their slopes have to stay exactly one apart with them.

The check runs without using the arithmetic at all, and a check that leaned on the arithmetic would prove nothing. At the end date a payoff line is a straight line either side of the strike, so its slope can be read straight off the picture. Above the strike the call climbs a rupee for every rupee, so its slope is one, and the put lies flat on the floor, so its slope is nil. Nil taken away from one leaves one. Below the strike the call is the flat one and the put falls a rupee for every rupee, so its slope is minus one. Taking minus one away from nil gives one a second time. Two settings, two readings, the same answer, and no figure for the reach of the reference asset entered either of them.

Move the control to either end and watch the bar on the slope scale. Both markers slide, one line goes flat while the other steepens, and the bar between the two readings comes out the same length every single time. The constant length of the bar is the one filled row, drawn rather than asserted. The relationship worth having on a sheet like this is the one that refuses to move when everything else does.

What goes into a cell that cannot be filled?

Step five is the shortest instruction in the routine and the one most often ignored. Into every cell marked waiting, write the name of what is absent, in words. Not a figure. Not a range. Not a placeholder anybody could mistake for a reading.

On this working example all four cells receive the same entry, and writing it out once and pointing four arrows at it is honest rather than lazy: nobody has written down how widely this reference asset could swing before the end date, nor with what odds. One missing statement stands between the analyst and four of the five rows. The gap is not a small one around the edge of an otherwise complete sheet. The gap is most of the sheet.

Why does the instruction insist on words rather than a careful estimateA figure some method produced out of data somebody gathered. An estimate is a different animal from a figure read straight off the face of a contract, and this routine spends most of its effort keeping the two apart.? Because of what happens next to each kind of entry. A cell holding a plausible figure nobody produced will be used, and a cell holding the name of what is needed will be looked up. That is the entire argument, and it is a claim about human behaviour rather than about arithmetic. The first cell ends a conversation and the second one starts one.

A household running on one salary does this every month without calling it a routine. Rent is a fixed term, and it goes in the left column and stays there. The electricity bill is a moving input. On the month the meter reading has not arrived, the honest budget sheet carries the words waiting on the meter in the electricity row, and the sheet that gets somebody into trouble carries a round number that felt about right. Both sheets look complete by the end of the year. Only one of them can be checked.

How does a sensitivity become a quantity of the reference asset?

Step six only comes into play where a sensitivity has arrived from a source outside this guide. When it does arrive, it is converted into a quantity of the reference asset before it is compared with anything, and the conversion is two multiplications.

The sensitivity is multiplied by the number of contracts held. The product is multiplied again by what one contract covers. The result is what the positionWhat somebody is holding right now, counted in contracts rather than in rupees, together with which side of each contract they sit on. comes to in units of the reference asset.

Two things need saying about the result and the step says both in one breath. The result is an exposure. An exposure measures what the position stands against rather than anything that changed hands. And it is emphatically not a premium. The two premiums used here, Rs 180.00/- and Rs 57.93/-, are amounts that genuinely moved from one party to another on day one. An exposure never moved anywhere.

The routine stops at the third box because lot sizeThe market's everyday phrase for the quantity of the reference asset that a single contract stands for. No figure for it is written anywhere in this guide. is set by an authority rather than here. Lot size differs between contracts, lot size is revised, and SEBI decides it, at sebi.gov.in. So the routine writes a labelled box, to be filled from the source on the day it is needed.

When does the whole sheet have to be run again?

A finished sheet feels finished, so step seven, the maintenance instruction, is the one people skip. A sheet belongs to one contract at one moment. The two events that most often make it worthless are not in the moving column at all.

A different strike gives a different contract with a different sheet. A different end date does the same. Both of those live in the left column from step one. The left column is also the list of things whose change forces the whole routine to be run from the top rather than patched in one cell, and that is why step one was worth ten minutes.

So the step ends with two lines written at the head of the sheet before anything else goes on it: the date, and the price of the reference asset it was drawn at. A sheet with those two lines at the head can be read later as a record; a sheet without them cannot be told apart from a statement about today. The card drawn earlier carries both, and reads Rs 2,000.00/- and 28 August 2026 across its top for exactly that reason. Anybody who finds it in a drawer in March knows what they are holding.

Dating a sheet is a habit worth borrowing wherever numbers get written down. A price list with no date on it is not a price list, it is an argument waiting to happen. Every shop that survives puts the month on the board for that reason. The routine is asking for the same discipline and for the same reason. A figure that cannot say as atThe moment a written sheet is describing. A sheet with no such moment on it cannot be told apart from a sheet that is still current. when it was true is a figure nobody can safely reuse.

What does a finished sheet let anybody do, and what does it not?

Step eight is a reading rather than an action, and it belongs at the end of the routine rather than in small print at the foot of the sheet. A finished sheet says how the premium responds to each input, one input at a time. A response to one input is a statement about a relationship, and relationships are the only thing this routine ever set out to produce.

The sheet says nothing whatever about which way any of those inputs will actually go, and it says nothing because the routine never asked. Go back and read the five questions from step two. Every one of them begins with how much does the premium move when, and not one of them begins with what will happen to. A sheet full of responses is not a view, and it does not become a view because somebody hoped it would.

Somewhere about here a reader starts wondering whether they ought to be holding either of these contracts. No sheet of sensitivities can answer that question, and the reason is worth stating plainly. Three things would be needed and all three are missing. The first is a stated view on the reach of the reference asset over the year, the same figure four rows of the sheet are already waiting for. The second is the holder's own circumstances, and nothing published to everyone can see those. The third is what the contract would cost the holder to carry and what it would cost to unwindTo close a contract out ahead of its end date by taking the opposite side of the same contract, instead of waiting for the date to arrive., and both of those sit with an intermediary rather than with a diagram. A routine that produces a sheet has not gone near any of the three.

One more reading, and it matters because the words get muddled constantly. Not one of the five rows holds a payoff and not one holds a profit. A payoff is the amount a contract hands over on the end date, counted before the premium enters the arithmetic at all. Bring the premium in, carried forward to that same date, and what stands instead is a profit. For the call the profit means taking out Rs 191.70/- rather than Rs 180.00/-. A sensitivity is neither of those. A sensitivity is a rate of change, and the only amounts here that have actually moved between two parties are the two premiums.

Who actually runs a routine like this, and on what?

Almost nobody calls it mapping sensitivities, and almost everybody who handles a number they did not produce runs some version of it.

Take somebody on a risk desk first. A risk desk is where the routine is most nearly literal. A position arrives from a colleague with a set of figures attached. The desk's first job is not to use those figures but to sort them. One figure came off the contract, another came out of a model, and a third came out of somebody's judgement on a Tuesday. Step one is that sort. Model rows and judgement rows can change without anything in the world changing, so the rest of the morning is spent on them. A desk that skips step three ends up defending a number it never checked, usually in front of somebody who did check it.

A lender reading a borrower's hedging arrangements does a shorter version. The lender does not need every response measured. Only the floating parts can surprise a repayment schedule, so the lender needs to know which parts of the borrower's obligation are fixed by contract and which parts float with a market. The sort is step one and nothing after it, and it is often enough.

An analyst writing about a company that carries these contracts has a different problem again, and the routine helps most at step five. The company's own disclosure will carry some of these rows filled and some absent. An absent row in a disclosure is itself information, and a filled row with no source behind it is worse than an absent one, so the analyst's job is to notice which rows are absent rather than to fill them.

Then there is the version everybody runs. A street vendor who buys vegetables every morning and sells cooked food every evening holds a fixed term and a moving input without writing either down. The rent on the pitch is fixed and the vendor knows it to the rupee. The price of onions is the moving input, and the vendor knows something about how far it swings because ten years of mornings have taught it. The vendor's map has the row that cannot be filled here, and the reason is that the vendor gathered the data personally while no such data is available here. That is the whole difference between a sheet with four empty rows and a sheet with none: not intelligence, and not care, but whether somebody went and measured.

The difference reframes what an empty cell means, and it is worth sitting with for a second. An empty cell is not a confession that the routine failed. An empty cell is a precise statement of what somebody would have to go and do before the row could be filled at all.

The reference asset, the call premium, the put premium and the pair of contracts written against them are invented.
Educational material. Not advice on any investment, tax, budget or market position.