Derivatives: What They Are and What Each One Obliges

A derivative is a contract whose value comes from the price of something else, called the underlying. A forward and a future oblige both sides to trade at an agreed price on an agreed date. An option obliges one side and gives the other a choice. A swap exchanges one set of payments for another. The contract is the promise, and the payoff follows from it.

Every derivative is a promise made now about a transaction later. Buying the thing now and holding it until that date has a cost anybody can compute, so a promise about a later transaction can be priced today. Everything below follows from that one sentence: what each shape obliges, where the price agreed today for a later date comes from, and why two positions that look nothing alike on a screen can be the same obligation.

What has actually been agreed when a derivative is struck?

Begin with what a derivative is not. A derivative is not a thing held in a vault, not a share of any business, and not a claim on an issuer. A derivative is a contract, and like every contract it is a set of promises between two sides about what happens on a stated date. One thing only makes that contract a derivative: the amount that changes hands on that date is worked out from the price of something else. The something else has a name, the underlyingThe thing whose price a contract's value is read from. The underlying sits outside the contract and is unaffected by it..

Taken apart, one has three parts and no more. There is the referenced thing. There is the date. And there is a rule saying what is owed once the referenced price on that date is known. Holding the contract gives its holder no ownership of the underlying at all, and nothing about the underlying changes because the contract exists. The reference asset does not know the contract is there.

The same promise gets made on an ordinary street. A stall outside one office building agrees today what it will pay for its flour in three months. No flour has moved. The stall holds none and the mill has delivered none. But something real has been agreed, and if flour costs more in three months than the agreed price, the stall is in a different position from the shop next door that agreed nothing. The agreement is the whole of the arrangement. The flour is only the thing it is read against.

Who has promised what, and who may walk away?

Who is bound comes before any drawing. Two arrangements are possible and there is no third. In the first, both sides are bound: each has promised, and neither may decline when the date arrives. In the second, one side may choose and the other may not, and the side holding the choice paid for that privilege at the start.

Read the obligation before the payoffWhat a contract delivers on its date, ignoring anything that was paid for it earlier.. A payoff drawing shows what happens at each price. Only the obligation says whether a holder had to be there at all, and whether the other side may hand over something never asked for. Two positions can produce very similar drawings and place entirely different duties on their holders, and the drawing is silent about which is which.

Two neighbours agree to swap cars in a month. Both are bound: on the day the swap happens, whether or not either of them has changed their mind. Now change one thing. One neighbour pays the other a sum today for the right to decide in a month. The sum handed over is spent the moment it is paid. The neighbour who took it must swap if asked, and may not ask. The right to decide is the whole difference between the two structures, and it deserves more attention than any payoff curve.

Which contract shapes exist, and what does each one oblige?

Four shapes, and the useful way to hold them is by what each one obliges rather than by what anybody uses it for. A forward binds both sides to trade at an agreed price on an agreed date, and nothing changes hands when it is struck. A future carries the same obligation, with the gain and the loss recognised as the price moves rather than only at the end, and with a party standing between the two sides so that neither is relying on the other. An option binds one side and leaves the other holding a choice: a call is the right to buy at an agreed price, a put is the right to sell at one, and the side that granted the right may not decline. A swap binds both sides to exchange one set of payments for another, computed on an agreed amount that never changes hands.

The option is the only shape here where money moves at the start, and that money is the premiumWhat the side holding the choice paid for it at the start, before anything else happens.. The premium is what the choice cost. On the other three, nothing is paid on day one. The premium is also why an option needs a number the other three do not, and why an option is the one shape whose obligation can be set out in full while its price stays out of reach.

One warning about the swap. The misreading it invites arrives fastest and travels furthest. The agreed amount that the payments are computed on is called the notional, and the notional never changes hands. Two invented parties, Chitrakoot Cements Limited and Saranga Capital Limited, agree a swap on a notional of Rs 1,000 crore. Not one rupee of that Rs 1,000 crore moves anywhere, ever. The notional is a multiplier. The money that moves is the difference between two computed payments: with a fixed rate of 7.20 per cent a year against a floating benchmark reading 6.00 per cent a year for the first period, the difference is 1.20 percentage points, and 1.20 percentage points of Rs 1,000 crore is Rs 12.00 crore. Dividing that Rs 12.00 crore back by the notional of Rs 1,000 crore gives 1.2 per cent. Reporting the notional without saying this tells the reader the arrangement is roughly eighty three times larger than the cash it actually produces.

Where does the forward price come from?

Everything from here runs on one invented reference asset, whose figures are set for teaching rather than read from anywhere. The reference asset has no issuer, no market and no name in any exchange listing. Its spot priceWhat the underlying costs to buy today, for delivery now rather than on a later date. is Rs 2,000.00/- today. Financing costs 6.50 per cent a year. The asset also pays nothing at all while it is held, and that belongs in the same sentence as the price. A payout during the holding period would change every forward figure below.

Now work the forward priceThe price agreed today for a purchase that happens on a stated later date. rather than quoting one. To have the asset in a year, it can be bought today at Rs 2,000.00/- and the cost of that money borne for twelve months. Rs 2,000.00/- multiplied by one point zero six five is Rs 2,130.00/-. The carryThe cost of holding the underlying from today until that later date, financing included. is Rs 130.00/-, and it is the whole of the gap between the two numbers.

Nothing is subtracted anywhere in that build, and the reason is that this asset pays nothing while it is held. The absence of a subtraction is not a footnote. The same arithmetic on an asset that does pay something during the holding period carries a subtraction where this one has none, and the forward price can then sit below the spot price. With no payout to work with here, that case is named and covered separately.

Is that number a prediction?

No, and this is the block the rest of the subject rests on. Rs 2,130.00/- does not say the price is expected to rise by 6.50 per cent. The forward price says that buying the underlying now and borrowing the money to do it costs Rs 2,130.00/- by that date. Walk it slowly. The four steps are the whole argument.

1. Borrow Rs 2,000.00/-for one year, at 6.50 per cent a year.
2. Buy the underlyingat its spot price of Rs 2,000.00/-, and hold it. The underlying pays nothing while it is held, so nothing comes back in during the year.
3. Deliver it on the dateinto the forward that was sold.
4. Repay the loan,now grown to Rs 2,130.00/-. The position is square, and the Rs 2,130.00/- was fixed on the first day.

Followed through, the consequence is immediate. If somebody offers to sell forward at less than Rs 2,130.00/-, taking the other side of the four steps above yields the difference for nothing. The free difference is why the forward price sits at Rs 2,130.00/- and not somewhere else. The forward is a cost, not an opinion.

Set the financing rate to nil and the forward price becomes Rs 2,000.00/-, exactly the spot price, and nobody would call that a prediction that the price will not move. The nil-rate test settles the argument in one line, and the control below runs it. If a gap can be sent to nil by changing a financing rate and nothing else, the gap was never a view about anything.

There it is, in one drag. At nil financing the ladder collapses to a single line and the forward price is Rs 2,000.00/-, the spot price itself. Back at 6.50 per cent a year, the shaded block reappears at Rs 130.00/- of carry, the worked build above reproduced exactly. At the top of the range the forward price reads Rs 2,260.00/-. The last readout holds throughout: the carry as a share of the spot price is the financing rate every single time, the claim of the block above restated as a ratio.

What did the choice cost, and can that cost be worked out here?

Now the option, and the number it needs that the other three shapes do not. At a strikeThe price written into an option, at which the side holding the choice may exercise it. of Rs 2,000.00/- on the same invented reference asset, the call premium is Rs 180.00/- and the put premium is Rs 57.93/-. Both are given rather than worked out here, and the paragraph after the drawing says why that distinction matters more than the figures do.

A premium is paid at the start whatever happens afterwards, it is not a payoff and it is not a profitThe payoff net of what was paid for the contract. A different number from the payoff., and it is spent whether or not the choice is ever used. Keep those three words apart and most of the confusion in this subject never arrives. A long call struck at Rs 2,000.00/- has a payoff of Rs 130.00/- when the price on the date is Rs 2,130.00/-. Rs 180.00/- went out at the start, so its profit at that same price is minus Rs 50.00/-. A reader who reads the first number as the second has just recorded a gain on a losing position.

So where does Rs 180.00/- come from? Not from anything here. Working a premium out from scratch needs a measure of how much the underlying price moves about, and that measure has not been established anywhere above: not a small one, not an assumed one, none at all. The two premiums here are given rather than derived, they are consistent with one another, and that consistency is the only thing they support. Reaching for a pricing model at this point would mean inventing its single most important input, and inventing it silently. The two premiums still do one thing between them, worked immediately below. Deriving a premium is covered separately, where the input it needs is available to be discussed properly.

Why do a call and a sold put add up to a forward?

Buying the call struck at Rs 2,000.00/- and selling the put struck at Rs 2,000.00/-, to the same date, leaves a long forward struck at Rs 2,000.00/-. Not something that behaves like one on most days. The same obligation, at every price.

The reason is easier than the result. Below the strike, the put that was sold is exercised against its seller, so the purchase happens at Rs 2,000.00/- while the price is lower. Above the strike, the call is worth exercising, so the purchase happens at Rs 2,000.00/- while the price is higher. One of the two is always live, so the buying happens at Rs 2,000.00/- at every price. A forward struck at Rs 2,000.00/- obliges precisely that.

The result is worth checking rather than taking. At Rs 1,600.00/- the call is worthless and the put costs Rs 400.00/-, so the pair gives minus Rs 400.00/-, and the forward gives Rs 1,600.00/- less Rs 2,000.00/-, which is minus Rs 400.00/-. The other three rows work the same way and can be read off the table.

Two positions that look nothing alike on a screen can be the same obligation, and once that is seen, the question stops being what each contract does and starts being what each one costs to assemble. The shift from what each contract does to what each one costs turns four definitions into a subject worth learning. The relationship is introduced here and shown holding at four prices. Rearranging it into its other forms, and using it to build positions, is covered separately.

Do the printed premiums balance to the last paisa?

Almost, and the word almost is doing real work here, so read this slowly. A careful reader checks the arithmetic at exactly this point, and then either keeps checking everything else or quietly stops.

The relationship says the call premium less the put premium must equal the spot price less the present value of the strike. Discounting the strike of Rs 2,000.00/- once, at 6.50 per cent for the year, gives Rs 1,877.9343/-. Then Rs 2,000.00/- less Rs 1,877.9343/- is Rs 122.0657/-. Taking the two premiums as printed here: Rs 180.00/- less Rs 57.93/- is Rs 122.07/-.

The two sit forty three hundredths of a paisa apart, and that is not an error. The gap is that the put premium has been rounded to the paisa: worked in full it is Rs 57.9343/-, and rounding it to Rs 57.93/- moves the difference by exactly that much. So the relationship holds to the paisa, and not exactly.

The wording matters far more than the amount involved. A claim of exact equality that the printed figures do not produce teaches the reader, quietly, that checking is pointless. The check fails, and the reader concludes the arithmetic was done wrong. A reader who has stopped checking is worse off than one who never started, and there is no way back from it.

Why are the spot price and the strike the same number?

A careful reader has noticed that Rs 2,000.00/- has appeared as the spot price and again as the strike, and is now wondering whether one was copied into the other by accident. It was not. The option pair here is struck at the moneyAn option whose strike is the same number as the current price of the underlying., and at the money is precisely what that phrase means: the strike is the same number as the current price of the underlying. There is a third appearance of the same figure a little further down, where Rs 2,000.00/- is also the exposure a single unit stands against, and that one is the same number for the same reason: one unit of the underlying is what a single contract here references. Nothing in the relationship above depends on the spot price and the strike being equal, and the pair is struck at the money here only because it keeps the arithmetic easy to follow. Move the strike to Rs 2,200.00/- and the call premium, the put premium and the present value of the strike all change, while the relationship between them holds exactly as it did.

What stands behind the promise while the contract is open?

A forward struck today settles a long way off, and in between each side is relying on the other to still be there and still be willing. An amount posted against the position holds that promise up in practice, and it stays posted while the position is open.

Work it on the invented figure, and label it in the same breath. A marginThe amount posted against an open position while it runs, so that the promise is collateralised. of 8.0 per cent of the exposure, invented for teaching and not a requirement of any kind, is Rs 160.00/- against Rs 2,000.00/- of exposure. Now take the two halves together. Either one on its own misleads. A 4.0 per cent adverse move on the exposure is Rs 80.00/-, or 50.0 per cent of the Rs 160.00/- posted. And Rs 2,000.00/- of exposure standing on Rs 160.00/- posted is 12.50 times.

A four per cent move in the referenced thing takes half of what was posted, and that ratio, rather than the exposure and rather than the notional, is what makes these contracts different to hold. Quote the exposure on its own and the position sounds large. Quote what was posted on its own and it sounds small. The pair of figures is the fact, and either alone is a misleading half of it.

Stating the base of every ratio in the same sentence as the ratio keeps this straight. The 8.0 per cent used above was chosen to keep the arithmetic clean, and it matches no requirement anywhere. The amount actually posted, and the method by which it is worked out, are set by the Securities and Exchange Board of India (SEBI) at sebi.gov.in and by the clearing corporations working under its framework. The requirement varies by contract and by day, and it moves. There is also a stated order in which losses are met when a clearing member fails, and the protection is that the order is fixed in advance rather than decided in the moment. Every step in that order and every threshold in it are set by the authority as well, and the live steps sit with that authority.

Why do these contracts exist at all?

Stated as functions rather than as benefits, and the distance between those two words is the whole of this block. One side wants a price settled now rather than discovered later, and is willing to give up a better price in exchange for the certainty. Another side is willing to take the other end of that. And the arrangement separates a price risk from holding the thing at all, so the risk can sit with somebody who is not holding the asset and never intends to.

The everyday version is easy to find. A caterer has quoted a fixed price for a wedding eight months out. From the moment that quotation is accepted the caterer is carrying the price of onions and oil for eight months, whether they want to or not and whether they know it or not. The quotation was fixed and the cost was not, so settling that price now is worth something to the caterer even in the years when the price later turns out lower.

Every one of those is a description of the function the arrangement performs, and not one of them is a reason for any particular reader to enter into one. The distinction is not pedantry. A function explains why a thing exists in the world. A reason to act would have to rest on one reader's holdings, obligations and capacity to absorb a loss, and a function rests on none of those.

How does somebody actually work with this on an ordinary day?

Picture the treasury of an invented manufacturer being handed two numbers: a spot price, and a forward price for the same thing on a date a year out. The first move is not to form a view. The first move is to carry the spot price at the financing rate for the period and see how much of the gap that accounts for. Ten seconds of multiplication, before any sentence is written.

If the whole gap is carry, then the forward price has said nothing about direction and the note that goes upstairs should say nothing about direction either. If some part of the gap is not carry, that residue is the only part worth a question, and the question is nearly always about a cost the arithmetic missed rather than about anybody expecting anything. A lender looking at the same position does something adjacent, and reads what was posted against the exposure rather than the exposure on its own. The exposure says what the position stands against. The amount posted says how far the price may move before somebody is asked for more.

The practical skill is a habit of asking which of four words applies to the number in view: is it a price, a premium, a payoff or a profit, and if it is a quantity, is it a notional or an exposure. Both questions catch most of the errors that ever reach a written note, and they cost nothing to ask. A household budgeting for a fixed rent has already made the same move without naming it: the rent is settled now for a period, and whether that turns out well is a separate question from whether the arrangement did what it said.

Should anybody enter into one?

Each of the four shapes and what it obliges is now settled. Whether to be in one arrives next, and it arrives for nearly everybody. Knowing what a contract obliges does not answer it, and saying so plainly is more useful than a hedge.

Four things would have to be known before anybody could answer it. The first is what the position would be held against. The second is what could be afforded if the price went the other way. The third is the whole range of outcomes and how likely each one is. The fourth is whether a given party may take such a position at all, and SEBI sets that at sebi.gov.in rather than anybody offering a view.

None of those four things appears here: no probability, no distribution, and no record of what any position anywhere ever returned. A payoff drawing is a description of an obligation. A payoff drawing says what happens at each price and says nothing whatever about which price arrives, and reading one as a forecast is the same error as reading a forward price as one. Understanding a mechanism is not a reason to use it, and having taught the first says nothing at all about the second.

Who sets the terms left unprinted here?

Every value box in the sheet above stands empty. Each of those values is set by the authority named beside it, each of them moves, and a written-out value would be wrong rather than merely old. Each is confirmed at the source named beside it on the day it is needed, and the value is taken from there.

The reference asset, Chitrakoot Cements Limited and Saranga Capital Limited are invented.
Educational material. Not advice on any investment, tax, budget or market position.