Option Spreads: How Two Legs Join Into One Obligation

An option spread is two option legs held together, usually one bought and one written, differing in the level they are struck at or in the date they end. The legs do not merge. Each keeps its own obligation, and what the pair pays at the end is the two payoffs added with their signs. The name describes a shape. The obligation is whatever the legs say.

Two contracts held at once are still two contracts. Nothing about holding them together changes what either one obliges, and nobody nets them off on the holder's behalf. The picture changes. Add the two payoff lines and a third shape appears, flat where one leg cancels the other and sloping where only one of them is doing anything. The third shape is the whole reason people give these pairs names, and it is also how a reader ends up trusting the name instead of the legs.

What is a leg, and how is one written down?

A legOne contract held inside a larger position. A leg is complete on its own and keeps its own obligation however many other contracts sit beside it. is one contract inside a larger position. A leg is complete on its own. Nothing about placing a second contract beside it changes what the first one says, and no settlement system merges the two into a third contract with an average of their terms. So the first job with any pair is to write each contract down separately, in a form that can be read rather than recognised.

The form has four fields and never more. A signed primitiveOne leg written out as four fields: a plus or a minus, a call or a put, one level, and one end date. The word primitive means it cannot be broken down further. is a plus or a minus, a call or a put, one level, and one end date. Plus one call at Rs 2,000.00/- for one year is a complete instruction, and minus one call at Rs 2,200.00/- for one year is another, and an assemblyThe legs held together and read as one position. An assembly is a stack of signed primitives, not a new kind of contract. is nothing more than those rows written one under the other. An assembly is read as its legs, every time, before anything else.

The sign is not decoration and it is not bookkeeping. A plus means the contract was bought, and the buyer may walk away from it once the premium is paid. A minus means the contract was written, and the writer must honour it and cannot walk away. Buying and writing are opposite positions in the same contract, so a row with the sign missing describes two obligations at once and settles neither. Here is the everyday version. Two tickets bought at two separate windows for the same evening, one that admits the holder and one that obliges the holder to admit somebody else, do not merge into a third ticket. Both are held, and each says what it says.

What can differ between two legs, and what happens where they meet?

How Option Spreads Combine Options with Different Strikes or Expiries

Two legs written in the four-field form can differ in exactly two ways that matter here. Two legs can differ in the level they are struck at, and they can differ in the date they end. Everything a two-leg position does follows from which of those two is different, so the reading habit is fixed and mechanical. Group the legs by level and by date, then see what cancels. That single step is the whole of the method, and it is done before the position is given any name at all.

Three outcomes are possible and they are worth separating. Two legs at the same level and the same date with opposite signs cancel completely, and the holder is left with nothing at all except whatever the two premiums netted to. Two legs that differ in level leave a stretch of prices between the two levels where only one of them is working. In that stretch the joinWhat happens where two legs meet, either at the same level or at the same date. The join is the place a pair starts behaving differently from either leg alone. does its work. Two legs that differ in date leave one leg still alive after the other has settled, and that is a different kind of thing entirely.

What is a vertical spread, and what varies between its legs?

A vertical spreadTwo legs ending on the same date and struck at different levels. The word vertical comes from the way levels are listed one under another on a screen, and it carries no other meaning. is two legs ending on the same date and sitting at different levels. Written as signed primitives the pair used throughout this guide reads: plus one call at Rs 2,000.00/- for one year, minus one call at Rs 2,200.00/- for one year. The date field matches on both rows, the level field does not, and that single difference produces the whole shape.

Now read the pair across the range of prices, and notice that there are three separate stretches rather than one. Below Rs 2,000.00/- neither leg does anything, and the pair pays nothing. Between Rs 2,000.00/- and Rs 2,200.00/- the bought leg pays and the written leg is silent, so the pair behaves exactly as the bought call would on its own. Above Rs 2,200.00/- both legs are working and they move together, so every further rupee the bought leg gains is a rupee the written leg owes, and what the pair pays stops at Rs 200.00/- and stays there however far the price goes.

The flat stretch is worth naming carefully. A flat stretch is not a limit on anything the holder might lose, and it is not a promise about anything. The flatness is the arithmetic consequence of two calls with the same slope pointing opposite ways, and it sits at Rs 200.00/- because Rs 2,200.00/- less Rs 2,000.00/- is Rs 200.00/-. Move the second level and the flat stretch moves with it, rupee for rupee.

One caution about Rs 2,200.00/- before it becomes furniture. Rs 2,200.00/- is a declared levelA level chosen purely to draw a shape. A declared level carries no premium and was not read off any venue., chosen here to draw a shape, and it carries no premium anywhere in this guide. Rs 1,600.00/-, Rs 1,800.00/- and Rs 2,400.00/- are declared in the same way, set at ten and twenty per cent either side of the spot price of Rs 2,000.00/-. The levels at which contracts are actually made available, and the spacing between one level and the next, are set by the Securities and Exchange Board of India (SEBI) at sebi.gov.in.

What is a calendar spread, and what varies between its legs?

A calendar spreadTwo legs struck at the same level and ending on different dates. The word calendar points at the field that differs, which is the end date rather than the level. is the other case: two legs at the same level, ending on different dates. Written out, one version reads minus one call at Rs 2,000.00/- ending at the near date, plus one call at Rs 2,000.00/- ending at the far date. Now the level field matches on both rows while the date field does not, and the change is one of kind rather than degree.

On the near date the written leg is settled and finished, and the bought leg is still alive with time left in it, so the holder does not have a payoff on that date at all: they have a settled amount beside a contract that has not ended. That is why a calendar pair cannot be drawn the way a vertical pair can. A vertical pair has one end date, and at that date every leg is finished and every figure on the diagram is arithmetic on the price. A calendar pair has two dates, and at the earlier one something is still running.

What is a contract with time left in it worth? Answering that needs a price rather than arithmetic, and a price needs a figure for how far the reference asset might move over the remaining life of the contract. No such figure exists anywhere in the record this guide works from, so the calendar pair stops there. A drawn line would look exactly as convincing whether it was right or wrong.

What does the pair oblige that neither leg obliged alone?

Take the vertical pair again and read each leg on its own first. A buyer may walk away, so the bought leg at Rs 2,000.00/- obliges its holder to nothing once the premium is paid. Its payoff climbs with the price and has nothing above it to stop it. The written leg at Rs 2,200.00/- obliges its writer at every price above Rs 2,200.00/-, and it too has nothing above it to stop it: the further the price goes, the more it owes.

Held together, the pair obliges something neither of them did on its own: a ceiling on what the assembly can pay, at Rs 200.00/-, and a limit on what the written leg can cost. The bought leg alone had no ceiling, and the written leg alone had no limit. The join is where the new obligation comes from, and it belongs to the pair rather than to either contract. Take either leg away and the ceiling disappears with it. Removing one row and seeing which properties survive is a useful test on any assembly.

Readers relax at exactly this point, too early, so the ceiling is worth one plain sentence. Nothing about that ceiling makes the pair a sensible thing to hold. A ceiling is a description of an obligation. A ceiling says what the assembly does at each price. It says nothing about whether any price is likely, what the assembly costs to put on, or whether a particular person has any business holding it.

What does a two-leg assembly pay at the end, worked at stated prices?

Put a price on the table and read both legs from their own rows rather than from the picture. The bought call at Rs 2,000.00/- pays the price less Rs 2,000.00/- where that is above nil, and nothing otherwise. The written call at Rs 2,200.00/- owes the price less Rs 2,200.00/- where that is above nil, and nothing otherwise. The assembly's payoffWhat a position pays at the end, worked out from the terms of the contracts and before anything paid to put it on is counted. is the first figure less the second, and a payoff ignores entirely what was paid to put the assembly on.

Here is the whole of it at five stated prices. The reference asset has a spot price of Rs 2,000.00/-, it pays nothing at all while it is held, and financing costs 6.50 per cent a year. Notice that the spot price, the strike that carries the premiums and the exposure the contracts are written on are all Rs 2,000.00/-, and they agree for three separate reasons: the strike matches the spot because this pair is struck at the money, and the exposure matches the spot because exposure is the value of the reference asset a contract is written on rather than an amount anybody has paid.

Two rows in that table are worth pausing on. The Rs 2,130.00/- row gives a payoff of Rs 130.00/-, and Rs 2,130.00/- is a figure already met: the spot price of Rs 2,000.00/- carried for one year at 6.50 per cent, a cost of carry rather than a forecast. The price between the last two rows moved by Rs 200.00/-, and both rows still read Rs 200.00/-. The flat stretch is showing up as arithmetic instead of as a picture, and two equal readings are the strongest evidence that the pair really does stop.

Keep one distinction sharp from here on. A payoff is what the assembly pays at the end. A profitThe payoff after every premium is counted and carried to the same date. A payoff and a profit differ by exactly the cost of putting the position on. is that payoff after every premium has been counted and carried to the same date at 6.50 per cent. Every figure in the table above is a payoff. Not one of them is a profit, and the next block explains why no profit figure appears anywhere in this guide.

Slide it slowly through the twenties and watch two things happen at once. The bought leg's line never stops climbing, and the wedge between it and the assembly opens wider with every rupee past Rs 2,200.00/-. The climbing line and the widening wedge are the same fact seen twice: what the bought leg gains above Rs 2,200.00/- is exactly what the written leg takes back, so the assembly's line has nowhere to go. At Rs 2,600.00/- the bought leg reads Rs 600.00/-, the written leg reads Rs 400.00/-, and the assembly still reads Rs 200.00/-.

What does a spread cost, and can that be worked out from what is here?

Costing an assembly is the same four-field discipline applied to money instead of terms. Add the premiums with their signs, the bought leg's premium going out and the written leg's premium coming in, and carry the difference to the end date at 6.50 per cent for the year. Adding and carrying is the entire procedure, and there is nothing subtle in it. The problem is that this record holds a premium at one level only, Rs 180.00/- for the call at Rs 2,000.00/-, and the premium at Rs 2,200.00/- is not in it.

Precision about what is given and what is not matters here. The one level that carries premiums is Rs 2,000.00/-, where the call premium reads Rs 180.00/- and the put premium reads Rs 57.93/-. Both are given figures in an invented example rather than market prices, and neither was computed here. The two premiums are consistent with each other to the paisa. The strike of Rs 2,000.00/- brought back to today at 6.50 per cent is Rs 1,877.9343/-, so the parity difference is Rs 122.0657/-, while Rs 180.00/- less Rs 57.93/- is Rs 122.07/-. The put has been rounded, so the two agree to the paisa and not exactly. A second level would need a second premium. Producing one needs a figure for how far the reference asset might move over the life of the contract, and no such figure sits in this record.

The missing premium is not the end of what can be said, and the honest arithmetic left over is more than nothing. Three statements survive without the missing premium. First, the assembly costs more than nil. A call at Rs 2,000.00/- pays at least as much as a call at Rs 2,200.00/- at every price and strictly more at some, so the leg being bought is the dearer of the two and the difference goes out rather than in. Second, the ceiling of Rs 200.00/- brought back to today at 6.50 per cent is Rs 187.79/-, and paying more than that today would be paying now for something that cannot pay more later. Third, the written leg can only bring money in, so the assembly cannot cost more than Rs 180.00/-, the premium of the bought leg on its own.

The three statements together are a boundA figure something cannot be above or below. A bound is not a price: it is a statement that holds whatever the price turns out to be. and not a price, and the difference matters more than it looks. Rs 180.00/- is also the tighter of the two upper bounds here, so the cost sits somewhere above nil and at or below Rs 180.00/-, a stretch Rs 180.00/- wide. Only the missing premium would narrow that stretch further.

Why can the payoff be exact while the cost is out of reach?

The two halves of this guide sit on completely different footings, and seeing why is worth more than either half on its own. A payoff at the end date is a statement about what two contracts say. Both legs have finished, both obligations are settled by comparing one price to one level, and the arithmetic needs nothing except the price. A cost today is a statement about what somebody would exchange for a contract that has not finished, and that needs a view about the future the record here does not contain.

Three things follow and they are worth stating plainly rather than apologetically. The second premium is missing, so the cost of any assembly with a leg away from Rs 2,000.00/- stays out of reach. Producing that premium needs a figure for how far the reference asset might move over the life of the contract. A price judgement needs a price, and this record cannot produce the second premium, so no combination is called cheap or dear. Where the price will actually be is a separate matter. Saying how often the flat stretch is reached would take a probability, a distribution or a past run of outcomes, and none of those is arithmetic on two contracts.

Why this matters more than it looks: an assembly drawn with an invented premium in it would look complete, would be wrong, and a reader could not tell the difference from the picture. A payoff line and a profit line look identical on a screen. One of them is arithmetic on two contracts and the other carries a number somebody made up, and a reader who trusts the second because it looks like the first has been taught to stop checking. So the drawings stop at the payoff and the cost stops at two bounds.

How does somebody reading a position statement work through two legs?

Four habits, and each is a direct consequence of something above rather than general advice. The name is the last thing that arrives and the first thing that misleads, so the most useful thing anyone does with a two-leg position is refuse to name it until the rows have been grouped.

1. Write both legs out in four fields before reading anything elseSign, call or put, level, end date. A statement that shows a name and two levels has given half the information, and the missing half is the sign. Reconstructing it from the name is guessing; reading it off the contract is not.
2. Group by level and by date, then look for what cancelsSame level and same date with opposite signs means nothing is held. Different levels with one date means a stretch where one leg works alone. Same level with two dates means one leg outlives the other. Three cases, and the grouping decides which one applies before any shape is drawn.
3. Work the payoff at the two levels and at one price beyond the higher oneThree evaluations settle the shape completely, and each is arithmetic on the rows rather than a reading off a line. For the pair in this guide those are Rs 0.00/- at Rs 2,000.00/-, Rs 200.00/- at Rs 2,200.00/-, and Rs 200.00/- again at Rs 2,400.00/-. The third one is the test: if it has not stopped, the shape is not the shape it was taken to be.
4. Mark the cost as unknown rather than filling it with something plausibleA payoff worked from the rows is exact. A cost needs every premium in the assembly, and a missing premium cannot be replaced by an estimate without the whole line becoming an estimate. Writing unknown in that cell keeps the exact half exact, and a household budgeting around a figure it invented is in the same position as a position sheet doing it.

None of those four is a view about whether the pair is worth holding. Working through an obligation carefully and deciding to take it on are separate acts, and this guide is entirely about the first one.

Should a reader who now understands this assemble one?

An obligation, however carefully it is read, does not answer that question. Three things would have to be known before anybody could answer it, and not one of them appears here. The first is a view on how far the reference asset might move and how likely each move is, and no figure of that kind sits in this record. The second is the reader's own circumstances, invisible from outside. The third is what the assembly would cost to place, to hold and to unwind, and the missing second premium puts that out of reach.

So what has this guide actually handed over? A way of writing two contracts down so they can be read, a rule for grouping them, two named shapes and the field that produces each, an exact payoff at any stated price, an honest pair of bounds on a cost, and a clear statement of the three things that are missing. All of that is a description of an obligation, worked all the way through. A payoff diagram is a description of an obligation, and understanding an obligation is not a reason to take one on.

The reference asset, its spot price of Rs 2,000.00/-, the financing cost of 6.50 per cent a year, the two premiums at Rs 2,000.00/- and the four declared levels either side of it are invented.
Educational material. Not advice on any investment, tax, budget or market position.