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Derivatives, Hedging & Structured Products
1Derivative Fundamentals
DerivativesLong PositionMark to MarketThe UnderlyingThe Derivative ContractHow Derivatives Transfer Financial…
2Forwards and Futures
The Futures ContractLong and Short PositionsThe Spot PriceThe Forward ContractSpot Price vs Forward PriceThe Futures PriceForward and Futures PositionForward vs FuturesHow to Read Futures Margin and Mark-to-MarketHow Futures Margin and Mark-to-Market WorkDeliveryRolloverOpen InterestOpen-Interest ChangeBasis vs Basis RiskHedge Ratio vs Hedge Effectiveness
3Options
OptionsThe Call OptionThe Strike PriceThe Put OptionOption DeltaOption Buyer and Option WriterCollar and Protective PutCall and Put OptionsHow to Map What…How to Take an…Exercise Price and Strike PriceOption Price DriversThe Expiration DateIntrinsic Value and Time Value
4Option Strategies and Payoffs
Option SpreadsOption PayoffVertical and Calendar SpreadsHow to Map an Option PayoffMaximum GainThe Iron CondorThe Covered CallMaximum LossStraddle and Strangle
5Volatility and the Greeks
The Implied Volatility SurfaceThe Option GreeksHow an Option Payoff…What an Implied Volatility…How Delta, Gamma, Theta…How Option Volatility Surfaces…Delta HedgingTime DecayHistorical VolatilityImplied Volatility vs Historical Volatility
6Swaps and Rate Derivatives
The Interest Rate SwapSwap Rate and Forward RateThe SwapThe Currency SwapInterest Rate Swap and Currency SwapThe Payment DateThe Reset DateThe Swap CurveThe Swap Payment CalculatorHow to Map a…Cross-Currency BasisDay Count ConventionsDerivative and UnderlyingExchange Traded and Over the CounterFixed Leg and Floating LegHow to Read a Derivative ContractHow to Map a Derivative ExposureHow to Read Derivatives Market DataHow to Map Derivative…How to Write a Derivative Research NoteHow to Run a…How to Maintain a Derivatives Decision Log
7Hedging Application
The HedgeHedge RatioHedge or SpeculationFraming a Hedge ObjectiveExposureOffsetBasis RiskHedge Risk or Counterparty RiskThe Hedged Item
8Structured Products
What a Structured Product IsStructured Product and Mutual FundHow to Take a…Participation RatePrincipal Protection and Capital Guarantee
9Clearing, Margin and Settlement
The Settlement PriceThe Three MarginsInitial, Variation and Clearing MarginPhysical and Cash SettlementHow a Position Moves…Market SurveillanceCounterparty RiskNettingNetting and SettlementPosition LimitsPosition Limits and MarginMarket ManipulationHow Corporate Actions Can…
10Derivatives Discipline and Cases
Derivative ResearchOpen Interest DataPost-Mortem and Performance Marketing,…Market Observation and Trade SignalScenario Analysis and ForecastReading Derivatives Data When…What a Derivatives Post-Mortem…

The Strike Price: The Level That Defines the Contract

The strike price is the fixed level written into an option contract, and the choice the buyer makes at the end is measured against it. The strike is set when the contract is made and never moves afterwards. The strike is not what anybody paid, and the strike is not a forecast. The strike positions the bend in the payoff line, so moving the strike moves the whole shape.

Everything an option does at the end comes down to one comparison, and the strike is one of the two numbers in it. The other number is whatever the reference asset turns out to be worth on the day. Nobody controls that number and nobody knows it in advance. So the strike priceThe fixed level written into the contract when it is made. The choice at the end is measured against this level, and nothing that happens afterwards changes it. is the only half of that comparison anybody chooses. Choosing it is the one design decision either side of the contract actually makes, and every other number attached to the contract follows from it.

One figure can therefore carry an entire guide. Read a contract description and the strike looks like the least interesting thing in it, a plain number sitting between two dates. The strike is in fact the number that decides three things: the shape the contract has, the side of the comparison the buyer will land on, and what the two parties are arguing about when they argue about price. The pair worked below, an invented call and an invented put on one reference asset, is carried to the last paisa so that every figure can be checked by hand.

What is the strike price of an option?

The strike price is a level written into the contract at the start and left alone for the rest of its life. Not adjusted. Not re-set when the reference asset moves. Not revised because either party would now prefer a different number. Fixed is not a feature of the strike price sitting alongside other features. A comparison against a moving target would settle nothing at the end, and a contract that cannot settle has no way of ending. Fixed is therefore the whole of what a strike price is.

The everyday version is worth carrying through everything that follows. A household booking a hall for a wedding eleven months out signs a form with a rate written on it. Over those eleven months the going rate for halls in that neighbourhood moves. The going rate moves with the season, with how many other weddings fall on the same weekend, with what the hall next door decided to charge. None of that touches the figure on the form. On the day, the household pays what the form says, and the entire value of having signed the form is that the figure on it did not move while everything around it did.

Translate that and the strike price is the figure on the form. The reference asset is the hall. The price of the reference asset on the day is the going rate. And the reason the form is worth anything at all is that one of the two figures in the comparison was pinned down in advance. Every other number connected to an option contract moves, so the strike price is the one number the reader can hold on to while the rest of the arithmetic slides around underneath it.

There is one difference between the hall and the contract worked here, and it matters. The household that signed the form must pay on the day. The buyer of an option need not. The option contract pins the level and then hands the buyer a choice about whether to use it. The choice is what separates an option from an ordinary forward agreement. The strike price does the same job in both, and the choice sitting on top of the strike price is what makes the contract an option.

Try it out

Between the day an option contract is made and the day it ends, how many times does the strike price change?

What is the strike not, and which figures get confused with it?

Three separations, and each of them is a mistake somebody makes in front of a real position report. Collapsing any two of them produces a different wrong answer. Take them one at a time.

The strike price is not the premium. The premiumThe amount the buyer pays the writer at the start of the contract. It changes hands once, on day one, and it does not come back. on this invented pair is Rs 180.00/- for the call, and that amount moved from the buyer to the writer on day one. The premium has already happened, and it is settled, banked and irreversible. The strike price of Rs 2,000.00/- has not moved anywhere and may never move anywhere. The strike is paid only if the buyer decides at the end to buy. One of these two figures is a completed payment and the other is a conditional one, and they are different by a factor of more than eleven on this pair.

The strike price is not an amount anybody has committed. The buyer of this call does not have to find Rs 2,000.00/- on the day the contract is signed, does not have to set Rs 2,000.00/- aside, and may never have to find it at all. The Rs 2,000.00/- is exposureThe value of the reference asset a contract is written on. It is a size, not a payment, and neither side has handed it over.: the size of the thing the contract is written on, not a payment either side has made. The premium is the payment. Adding the two together, or reporting the strike where the reader is thinking about cash, describes an arrangement as roughly twelve times larger than the money that actually changed hands.

The strike price is not a forecast. Writing Rs 2,000.00/- into a contract says nothing whatever about where either party thinks the reference asset is going. The level is the point the comparison is made at, not a prediction about which side of it the price will land on. Two parties who disagree completely about the future can still write the same level into a contract. A forward price attracts the same misreading, and the point is worth naming twice: a number in a contract is a term of the contract, and a term of the contract is not an opinion.

Three figures attached to one contract, and only one of them is money that has moved One call on one unit of the reference asset. Every figure invented for teaching. THE PREMIUM Rs 180.00/- Moves at the start From buyer to writer Already gone It is cash THE STRIKE Rs 2,000.00/- May move at the end Only if the buyer chooses Has not moved yet It is a level THE EXPOSURE Rs 2,000.00/- Never moves at all Nobody pays it, ever Has not moved yet It is a size Two of these three read Rs 2,000.00/-, and they are still not the same quantity. One is a level that may be paid. One is a size that nobody pays. Only the first column is money.
Only the Rs 180.00/- has actually changed hands, while the Rs 2,000.00/- appears twice under two different meanings, once as a level that may be paid at the end and once as the size the contract is written on.

The repetition across the second and third panels is what a careful reader notices and then worries about. Look at the two panels together. Both read Rs 2,000.00/-. The two figures agree because this contract is written on exactly one unit of a reference asset whose price today is also Rs 2,000.00/-, so the level in the contract and the size the contract references land on the same figure. The agreement has a reason and is not a coincidence, and the two figures would stop agreeing the instant the contract were written at a different level or on a different quantity. Two figures printing the same digits are not thereby the same quantity, and a reader who treats them as interchangeable will eventually add one to the other.

Try it out

A reader claims to have committed Rs 2,000.00/- by buying this call. What amount has actually left their hands?

Try it out

On this invented pair the price of the reference asset today is Rs 2,000.00/- and the strike is Rs 2,000.00/-. Why are those two the same number?

How does the strike sit against the price of the reference asset today?

The strike price by itself says nothing. Rs 2,000.00/- is a level, and a level only becomes informative once it is set beside what the reference asset is worth right now. The comparison of the strike against the current price has a name in one word, moneynessThe position of the strike against the current price of the reference asset, expressed in one word rather than as a number., and it produces exactly three positions.

A call is the right to buy at the strike. A strike sitting below the current price means the call would pay something if it ended right now, and that position is called in the moneyWhere the contract would pay something if it ended right now. For a call the strike sits below the current price; for a put the strike sits above it.. A strike sitting above the current price means the contract would pay nothing, and that is out of the moneyWhere the contract would pay nothing if it ended right now. For a call the strike sits above the current price; for a put the strike sits below it.. A put is the right to sell at the strike, and a put reads the same scale backwards. A strike above the current price would pay something, and a strike below it would pay nothing. The two contracts do not have separate scales. One scale is read from opposite ends, and a level that is in the money for one is out of the money for the other at the same instant.

Between the two sits a single point, where the strike and the current price of the reference asset are the same number, and that point is called at the moneyWhere the strike and the current price of the reference asset are the same number. It is a single point on the scale, not a region.. Notice the shape of that. In and out of the money are regions, each running away in one direction for as far as the scale goes. At the money is not a region. At the money is the join between the two regions, one point wide.

One scale, read twice: the call from the left, the put from the right the strike of Rs 2,000.00/- stands on the price of Rs 2,000.00/- OUT OF THE MONEY IN THE MONEY THE CALL IN THE MONEY OUT OF THE MONEY THE PUT AT THE MONEY 1,600 1,800 2,000 2,200 2,400 price of the reference asset, in rupees At the money is a join, not a region. At this one point both contracts pay nothing.
In and out of the money are wide regions running away in opposite directions, while the position where the strike stands on the current price is one point wide and both contracts pay nothing there.

Now put this invented pair on that scale. The price of the reference asset today is Rs 2,000.00/- and the strike is Rs 2,000.00/-. The two figures are the same number on purpose. The pair was written at the money, and standing at the money is exactly what it means for the strike and the current price to be one number. Saying that out loud is better than leaving a careful reader to wonder whether one figure was copied into the other by mistake. A repeated figure that goes unexplained reads as an error, and a reader who suspects one error stops checking the rest.

Work out what that position means as a number rather than as a phrase. If the contract ended right now with the reference asset at Rs 2,000.00/-, the call would let its buyer buy at Rs 2,000.00/- something worth Rs 2,000.00/-. The right to do that is worth exactly nothing, so the call pays Rs 0.00/-. The put would let its buyer sell at Rs 2,000.00/- something worth Rs 2,000.00/-. The right to do that is worth nothing either, so the put pays Rs 0.00/- as well. At the money both contracts pay nothing, and at the money is the cleanest place to start from. Neither contract is carrying anything yet, and every rupee of both premiums is being paid for what might happen rather than for what has already happened.

What happens to the payoff line when the strike moves?

The behaviour of the payoff line is the part almost everybody agrees with when reading it and then draws wrongly when attempting it. A call payoff line has two arms: a flat one where the buyer walks away, and a sloping one where the buyer buys. The two meet at a bend. When the strike moves, exactly one of those three things travels with it.

Try it out

When the strike slides upward with the price of the reference asset held still, what happens to the slope of the sloping arm of the call payoff line?

The answer is that the bend travels and nothing else does. A call gains one rupee for every rupee it is above its own strike, no matter where that strike happens to sit. So the whole payoff line slides sideways with the strike, the bend stays at the strike wherever the strike goes, and the slope of the sloping arm never changes. Slope is a rate, and the rate is written into what a call is rather than into the level it is written at.

Draw three calls on the same reference asset at three different levels and the point becomes visible in one look. Each line is flat until it reaches its own strike, then rises at exactly one rupee for one rupee. The bends land in three different places. The three sloping arms are parallel. Nothing about the second half of the shape distinguishes a call struck low from a call struck high except where it started rising.

Three bends in three places, and one slope shared by all three STRUCK AT Rs 1,600.00/- STRUCK AT Rs 2,000.00/- STRUCK AT Rs 2,300.00/- payoff at the end, in rupees 300 600 900 1,200 0 1,500 1,800 2,100 2,400 2,700 Every grey triangle is the same size: 200 rupees along, 200 rupees up, on all three. All three levels are illustrative settings. Payoffs at the end, before anything paid is counted.
Three calls struck at three levels put their bends in three places while the sloping arms stay parallel, and the three identical triangles show the same rise for the same run on every one of them.

The three triangles are the proof rather than the decoration. Each one is drawn over a stretch of two hundred rupees along the bottom, and each one rises the same two hundred rupees. The three triangles are the same shape because the slope is the same on all three lines. Moving the strike moved the bend and left the geometry of the sloping arm untouched. A strike is therefore described as positioning a shape rather than as changing one.

The price of the reference asset now stays still while the strike moves. The control below does one thing only: it moves the strike, with the price of the reference asset frozen at Rs 2,000.00/-. The bend crosses the frozen price, and one of the two contracts starts paying when it does. The third panel then reports the honest state of what is known.

Play with it

Slide the strike past a price that will not move

One control: the strike of the contract, from Rs 1,600.00/- to Rs 2,400.00/- in steps of Rs 10/-. Both endpoints and every step between them are settings on this control rather than levels anybody has quoted. The price of the reference asset stays at Rs 2,000.00/- throughout.

Rs 1,600.00/-Rs 2,000.00/-Rs 2,400.00/-
Slide the strike. The bend travels with it. The price does not move. STRIKE Rs 2,000.00/- PRICE HELD AT Rs 2,000.00/- payoff at the end, in rupees 200 400 600 800 0 1,600 1,800 2,000 2,200 2,400 price of the reference asset at the end, in rupees CALL PAYOFF NOW Rs 0.00/- PUT PAYOFF NOW Rs 0.00/- THE TWO PREMIUMS AT THIS LEVEL Rs 180.00/- and Rs 57.93/-

The strike
Rs 2,000.00/-
Call payoff now
Rs 0.00/-
Put payoff now
Rs 0.00/-
Premium reading
Rs 180.00/- and Rs 57.93/-

Educational illustration. Not a quotation, not a price, and not a statement of which levels are available anywhere. Assumptions on screen: the price of the reference asset is held still at Rs 2,000.00/-, financing costs 6.50 per cent a year, the contracts run one year, and the reference asset pays nothing at all while it is held. The premiums are shown at Rs 2,000.00/- because that is the one level this worked example carries them at, and the panel goes blank everywhere else on purpose rather than by omission. Which levels are actually made available is set by the Securities and Exchange Board of India (SEBI) at sebi.gov.in. Every figure invented for teaching.

Start at the default and the simulation reproduces the worked example exactly: the strike at Rs 2,000.00/-, the call paying Rs 0.00/- and the put paying Rs 0.00/-, with the two premiums reading Rs 180.00/- and Rs 57.93/-. Drag the strike down to Rs 1,600.00/- and with the price still at Rs 2,000.00/- the call would pay Rs 400.00/- if the contract ended now while the put would pay Rs 0.00/-. Drag it up to Rs 2,400.00/- and the two swap: the call pays Rs 0.00/- and the put pays Rs 400.00/-. Only one of the two contracts pays anything at any strike other than Rs 2,000.00/-, and which one it is depends entirely on which side of the frozen price the bend has landed.

The third panel reads the two premiums at Rs 2,000.00/- and reads nothing at all anywhere else. The shape can be redrawn at any level because the shape is defined by the contract. The premium cannot be redrawn. A premium at any other level is precisely the figure this worked example does not carry.

Try it out

Set the control to a strike of Rs 2,400.00/- with the price of the reference asset held at Rs 2,000.00/-. What does the put pay if the contract ended now, and what does the premium panel show?

What happens to the premium when the strike moves?

The question is the obvious one to ask, and the honest answer has two halves, one of which can be proved and one of which cannot.

The first half is certain and needs nothing to be assumed at all: a call struck higher never pays its buyer more than a call struck lower, at any price of the reference asset whatsoever, so the higher one cannot be worth more. The claim follows from the two contracts alone. Compare a call struck at Rs 2,000.00/- with one struck at Rs 2,400.00/- and check it at five prices. At Rs 1,800.00/- both pay Rs 0.00/-. At Rs 2,000.00/- both pay Rs 0.00/-. At Rs 2,200.00/- the first pays Rs 200.00/- and the second pays Rs 0.00/-. At Rs 2,400.00/- the first pays Rs 400.00/- and the second pays Rs 0.00/-. At Rs 2,600.00/- the first pays Rs 600.00/- and the second pays Rs 200.00/-. The second contract is level with the first at two of those prices and behind it at the other three, and it is never once ahead. Nothing about how far the reference asset might travel was needed to establish that.

The loose version of this claim is common and wrong. Notice the precision in the wording. The higher-struck call does not give strictly less at every price. The higher-struck call gives the same as the lower one at every price at or below Rs 2,000.00/-, where both pay nothing, and less only above it. Never more at any price, and less at some prices, is the exact statement, and it is enough to settle which of the two can be worth more without settling what either is worth.

The second half of the answer is a figure that can be computed to the last paisa, and it is the difference between the two premiums at one level rather than either premium on its own. The buyer of a call who may pay the strike at the end rather than today keeps the use of that money for the year. The saving is the strike less the present value of the strikeThe strike brought back to today at the financing cost, being what a sum due at the end of the contract is worth right now., and on this pair the saving is a figure that can be checked in one division.

The strike brought back to today
$$ \frac{K}{1+r} \;=\; \frac{2000.00}{1.065} \;=\; 1877.9343, \qquad S - \frac{K}{1+r} \;=\; 2000.00 - 1877.9343 \;=\; 122.0657 $$
\(K\)the strike written into both contracts, Rs 2,000.00/- on this invented pair
\(S\)the price of the reference asset today, Rs 2,000.00/- on this invented pair
\(r\)the financing cost, 6.50 per cent for the one year these contracts run
\(K/(1+r)\)the present value of the strike, being what a payment of Rs 2,000.00/- due at the end is worth today
What it says in wordsDividing the strike of Rs 2,000.00/- by one plus the financing cost gives Rs 1,877.9343/-, which is what that payment is worth today. Subtracting it from the price of the reference asset today leaves Rs 122.0657/-, and that figure is the amount by which the call premium must exceed the put premium at this level. Neither premium is produced by this arithmetic; only the distance between them is.
The strike has a second face, and the distance between them is one year of financing Measured from nil, at 6.50 per cent a year for one year. Every figure invented for teaching. nil THE STRIKE paid at the end Rs 2,000.00/- Rs 122.0657/- the financing kept by paying at the end rather than today ITS PRESENT VALUE what it is worth today Rs 1,877.9343/- Rs 2,000.00/- divided by 1.065 is Rs 1,877.9343/-, and the gap is Rs 122.0657/-. That gap is how much more the call premium is than the put premium here, and nothing else.
Dividing the strike by one plus the financing cost produces its second face, and the Rs 122.0657/- between the two bars is a year of financing on a payment that may be deferred to the end.

One caution before that picture is generalised. The gap drawn between those two bars is the strike less the present value of the strike, and the amount by which the call premium exceeds the put premium is the price of the reference asset today less the present value of the strike. On this pair both come to Rs 122.0657/-, and they agree only because the price of the reference asset today and the strike are both Rs 2,000.00/-. Change the strike and the two quantities part company immediately. At a strike of Rs 2,400.00/- the financing on the strike is Rs 146.4789/- and the distance between the two premiums is minus Rs 253.5211/-. The two are not the same figure and do not even carry the same sign. The at the money coincidence has now had to be pointed at three times rather than left standing.

The second quantity moves with the strike by division and subtraction from end to end, so it can be drawn in full. The present value of a larger strike is larger, and it is being subtracted from a price that is not moving, so the distance between the two premiums falls steadily as the strike rises. Somewhere on that fall the distance passes through nothing at all, and the level where it does is worth stopping at.

What can be computed at every level: the distance between the two premiums Price of the reference asset today Rs 2,000.00/-, financing 6.50 per cent a year, one year. Invented for teaching. the call premium less the put premium, in rupees +500 +300 +100 -100 -300 nil At a strike of Rs 2,000.00/- the distance is Rs 122.0657/- The line crosses nil at Rs 2,130.00/- which is the forward price, because Rs 2,130.00/- divided by 1.065 is Rs 2,000.00/- 1,600 1,800 2,000 2,200 2,400 the strike, in rupees Neither premium on its own can be placed on this picture. Only the distance between them.
The distance between the two premiums falls in a straight line as the strike rises and reaches nothing at a strike of Rs 2,130.00/-, which is the forward price because Rs 2,130.00/- divided by 1.065 returns Rs 2,000.00/-.

The crossing point is a genuine result and costs nothing to establish. At a strike of Rs 2,130.00/- the present value of the strike is exactly Rs 2,000.00/-, exactly the price of the reference asset today, so the distance between the two premiums is nothing at all. At a strike equal to the forward price, the call premium and the put premium are the same amount, and that equality holds with certainty even though the amount itself cannot be worked out from the figures this example carries.

Neither premium can be produced at any level other than Rs 2,000.00/- from anything worked above. Producing one needs a figure for how far the reference asset might travel over the life of the contract, and how likely each distance is. The missing figure has a name: volatility. The working example carries none, carries no distribution and carries no probability, and it carries premiums at one level and one level only. Naming the gap is the honest move. A plausible wrong number is harder to catch than an obvious one, so the gap stays a gap.

Try it out

Two calls on the same reference asset with the same end date, one struck at Rs 2,000.00/- and one struck higher. Which of the two cannot be worth more, and what has to be known to decide?

What makes a call and a put at one level a pair?

Two contracts written at the same level with the same end date are not merely similar. The two contracts are locked to each other by arithmetic, and the lock is what makes them a pair rather than two items on a list. Setting the price of the reference asset today against the present value of the level gives a distance, and that distance is the distance between the two premiums. Neither figure comes out of a model. One is a division and the other is a subtraction.

Check it on the given figures rather than taking it. The call premium is Rs 180.00/- and the put premium is Rs 57.93/-, so the call premium less the put premium is Rs 122.07/-. The price of the reference asset today is Rs 2,000.00/- and the present value of the strike is Rs 1,877.9343/-, leaving a distance of Rs 122.0657/-. The two figures agree, and how they agree matters more than that they agree.

Two routes to one figure, and they land 0.43 paise apart WHAT THE TWO PREMIUMS SAY the call premium Rs 180.00/- less the put premium Rs 57.93/- the distance Rs 122.07/- WHAT THE STRIKE SAYS the price today Rs 2,000.00/- less the present value of the strike Rs 1,877.9343/- the distance Rs 122.0657277/- from the rounded put premium Rs 122.07/- worked from the strike, to seven places Rs 122.0657277/- the distance between the two Rs 0.0042723/- 0.43 paise It agrees to the paisa, not exactly, and the 0.43 paise is the put being rounded.
Two routes that share no step reach Rs 122.07/- and Rs 122.0657277/-, and the 0.43 paise between them is the rounding of the put premium rather than a break in the relationship.

The relationship holds to the paisa and not exactly, and saying which is the point rather than a caveat. The exact figure worked from the strike is Rs 122.0657277/-. The figure produced by the two premiums as they are carried here is Rs 122.07/-. The two figures stand Rs 0.0042723/- apart, being forty three hundredths of one paisa. The distance exists because the put premium of Rs 57.9342723/- has been rounded to Rs 57.93/- so that a person can write it down and pay it. An equality announced as perfect when the numbers printed beside it are not teaches the reader that checking the arithmetic is a waste of time.

The same discipline applies the moment either premium is carried forward through time, and it is worth doing once so the habit sticks. The call premium of Rs 180.00/- carried for one year at 6.50 per cent comes to Rs 191.70/- exactly. Rs 180.00/- multiplied by 1.065 terminates. The unrounded put premium of Rs 57.9342723/- carried for the same year comes to Rs 61.70/- exactly. The rounded Rs 57.93/- carried the same way comes to Rs 61.69545/-, nearly half a paisa short of Rs 61.70/-. A rounded figure carried forward produces a rounded answer, and calling that answer exact is how a small approximation gets promoted to a stated fact.

Try it out

Check the pair yourself. Is Rs 180.00/- less Rs 57.93/- equal to Rs 2,000.00/- less Rs 1,877.9343/-?

Which strike levels exist to choose from at all?

The honest answer is that no fixed figure exists to be given. Levels are made available in a pattern rather than freely: spaced apart, over a range sitting around the current price of the reference asset, with both the spacing and the range set by the authority and revised from time to time. Either figure written out here would be wrong rather than merely dated on the morning it changed.

The structure does not change, and the structure is what is worth carrying. Levels come as a ladderA set of levels made available at spaced intervals rather than continuously, so that the levels between two rungs simply do not exist. with rungs rather than as a continuous scale, so the level somebody would have chosen may simply not exist, and the nearest rung is a compromise nobody wrote down anywhere. The compromise is the part readers miss. A position taken at the nearest available rung is not the position that was intended but the closest one the ladder allowed, and nothing in any report will ever say so.

The ladder of levels, drawn with its rungs and without its values Every rung is left blank on purpose. The shape is what teaches; the values are set elsewhere and they move. the price of the reference asset today Rs 2,000.00/-, between rungs 1 How far apart the rungs sit. Set by SEBI at sebi.gov.in. 2 How far the ladder reaches, up and down. Set by SEBI at sebi.gov.in. 3 Whether a rung sits where one is wanted. Often not, and no report will say. 4 What one contract covers at each rung. Set by SEBI at sebi.gov.in. A ladder has gaps. The level wanted may sit in one of them.
Seven rungs are drawn and not one carries a value, and the lime marker lands between two of them, which is what makes the nearest available level a compromise rather than a choice.

Look at where the lime marker falls in that drawing. The marker sits between two rungs rather than on one, and the placement is the whole teaching of the picture. A reader who wanted a level exactly at the current price of the reference asset may find that no such rung exists, and will end up on one side of it or the other, holding a different shape from the one they had in mind. Nothing anywhere in the arrangement flags that the shape was rounded to fit the ladder.

India

What is named here and set by an authority

Four things in an option contract are set by an authority rather than by arithmetic, and each one appears below as a labelled row. The levels at which contracts are made available, and how far apart those levels sit: set by SEBI at sebi.gov.in. How much one contract covers, and in what quantity: set by SEBI at sebi.gov.in. How many contracts one participant may hold: set by SEBI at sebi.gov.in. Whether a contract is settled in cash or by delivery of the reference asset: set by SEBI at sebi.gov.in. Where the reference is a rate or a currency rather than a security, the equivalent arrangements sit with the Reserve Bank of India at rbi.org.in.

Each of the four is set by the authority named inside its own row, and each of them changes, so a figure written out here would be wrong rather than merely out of date on the morning it moved. The first row is the one a reader most wants, and it is also the one that moves most. Which levels exist at all is exactly what changes.

How does anybody read a strike outside a classroom?

Somebody looking at a position report meets a row with several columns that all look like money and are not the same kind of thing at all. There is a level column carrying Rs 2,000.00/-, a premium column carrying Rs 180.00/-, and an exposure column carrying Rs 2,000.00/- again. The first thing anybody competent does with that row is work out which single figure has actually left somebody's bank account, and on this row the answer is Rs 180.00/- and nothing else. Reading the level column as an outlay is the mistake that turns a Rs 180.00/- position into a Rs 2,000.00/- one on a summary nobody re-checks.

The strike and the break-even sit close together and are routinely confused, so separating them is the second thing worth doing. The strike on this call is Rs 2,000.00/-. The break-even is the strike plus the premium carried forward to the same date. Rs 2,000.00/- plus Rs 191.70/- is Rs 2,191.70/-. The two figures are Rs 191.70/- apart and they answer different questions. The strike is where the contract starts paying anything at all. The break-even is where the buyer has recovered what they spent. A reader who quotes the strike when asked where the position turns the corner has given an answer that is short by a full year of financing on the premium.

A lender looking at a borrower that has written option contracts reads the strike for one thing above all others: where the borrower's obligation begins to bite, and how far the current price of the reference asset sits from it. The gap is a distance, measured in the same units as the price, and it is readable straight off the contract without any view about anything. An analyst reading the same row asks a narrower question: was the level chosen, or merely available? A position sitting one rung away from where it was meant to sit behaves differently from the position that was intended.

The household version is the wedding hall form again, held from the other end. When a person is handed a sheet of paper with a level written on it and a choice attached, the two questions that matter are what was paid for the paper and what the level will be compared against on the day. Everything else on the paper is describing the same two things in longer words. The level on the form is not money already spent, and it is not anybody's opinion about what the hall will cost in eleven months.

What does the whole worked pair look like in one place?

Every figure in the table below comes from three inputs and nothing else: a price of the reference asset today of Rs 2,000.00/-, a strike of Rs 2,000.00/-, and financing of 6.50 per cent a year for the one year the contracts run. The reference asset pays nothing at all while it is held. A payout during the year would change the financing arithmetic in every row. The two premiums are given rather than computed, and they are given at one level only.

What is being workedThe arithmeticThe figure
The strikewritten into the contract, unchanged for its lifeRs 2,000.00/-
The price of the reference asset todaygiven, and equal to the strike because this pair stands at the moneyRs 2,000.00/-
The exposure on one unitone unit at Rs 2,000.00/-, which nobody has paidRs 2,000.00/-
The present value of the strikeRs 2,000.00/- divided by 1.065Rs 1,877.9343/-
The financing kept by paying at the endRs 2,000.00/- less Rs 1,877.9343/-Rs 122.0657/-
The call premiumgiven, not computed anywhere in this guideRs 180.00/-
The put premiumgiven, and rounded from Rs 57.9342723/-Rs 57.93/-
The two premiums differencedRs 180.00/- less Rs 57.93/-, against Rs 122.0657277/- exactRs 122.07/-
The call premium carried one yearRs 180.00/- multiplied by 1.065Rs 191.70/-
The break-even on the callRs 2,000.00/- plus Rs 191.70/-Rs 2,191.70/-
The call payoff if it ended nowRs 2,000.00/- less Rs 2,000.00/-, floored at nothingRs 0.00/-
The put payoff if it ended nowRs 2,000.00/- less Rs 2,000.00/-, floored at nothingRs 0.00/-
The call payoff at a strike of Rs 1,600.00/-Rs 2,000.00/- less Rs 1,600.00/-, price held stillRs 400.00/-
The put payoff at a strike of Rs 2,400.00/-Rs 2,400.00/- less Rs 2,000.00/-, price held stillRs 400.00/-
Either premium at a strike other than Rs 2,000.00/-not computable from anything in this guideno reading

The last row across is the row that keeps the other fourteen honest. Every figure above it is a division, a subtraction or a multiplication that can be repeated on a phone. The last row is the one that would need something this working example does not carry, and it is left empty rather than estimated. The four payoff figures in the table are payoffs and not profits. A payoff counts nothing that was paid to hold the contract. A profit counts the premium carried forward to the same date. The premium at a moved strike is the one figure this worked example does not have, so a profit at a moved strike cannot be drawn at all.

The error that gets made, and what it costs

A reader looks at the call struck at Rs 2,000.00/- with a premium of Rs 180.00/-, finds a call struck far above it carrying a premium that is a fraction of that, and concludes that the second is the cheaper way of doing the same thing. The two are not the same thing. The second contract pays its buyer less at some prices of the reference asset and never once pays more. Paying less at some prices and never more is precisely why it changes hands for less. The smaller premium is the arithmetic reporting that the contract gives less, not a bargain being offered on a contract that gives the same.

Who makes it: nearly everybody. Every other purchase a person has ever made trains them to compare two prices and take the lower one, and nobody has yet told them that these two prices are attached to two different rights. The mistake is not a careless error and not a failure of arithmetic. A perfectly sound habit has been applied to a place where the two things being priced are not comparable.

The cost: a position chosen on a number that was never a comparison, and a shape the reader did not mean to take. The cheaper contract does what its own contract says, and that is nothing at all across a stretch of prices where the dearer one was already paying. Nobody discovers this at the moment of buying. The discovery comes at the end, when the reference asset has moved and one of the two contracts has moved with it.

The working example here carries premiums at one level only, so the second premium cannot be printed. The point stands without it, and rests instead on what the two contracts pay.

The fix is one line. Before comparing two premiums, ask whether the two contracts would ever pay differently at any price of the reference asset, and if they would, the two premiums are not comparable at all and the lower one is not cheaper.

Two calls, five prices, and one cell that stays empty Both levels are illustrative settings. Payoffs at the end, before anything paid is counted. Invented for teaching. THE LEVEL THE PREMIUM 1,800 2,000 2,200 2,400 2,600 Rs 2,000.00/- Rs 180.00/- nil nil Rs 200.00/- Rs 400.00/- Rs 600.00/- Rs 2,400.00/- NO READING EXISTS nil nil nil nil Rs 200.00/- Inside the lime outline the two contracts pay the same, so the higher one is not behind at every price, only at some. Never more at any price, and less at three of these five. That is enough to settle which of the two can be worth more, and it needs nothing beyond the two contracts. It is not enough to produce either premium, which is why one cell on this sheet stays empty. A smaller premium reports that the contract pays less. It is not a discount.
The call struck higher pays the same as the lower one at two of these five prices and less at the other three, which is why it cannot be worth more and why the empty premium cell changes nothing about the conclusion.

Can anybody be told which strike to pick?

No, and the reason is worth more than the refusal. The level positions the bend and the bend is the shape, so choosing a level is choosing a shape. Choosing a shape without a view on where the reference asset might go, and how likely each place is, amounts to picking a picture, and no such view comes out of the arithmetic worked above.

Three things would have to be known before anybody could answer the question honestly, and all three are worth naming rather than gesturing at. The first is how far the reference asset might travel over the life of the contract and how likely each distance is. The same absent figure stops a second premium being produced here. The second is the circumstances of the person asking, including what they already hold, what they are exposed to and what they could absorb. The third is what the position would cost to hold from one end to the other and what it would cost to close before the end. None of the three appears anywhere in this guide.

One question, three inputs, and not one of them in this guide WHICH LEVEL SHOULD I PICK? How far the reference asset might travel, and how likely each distance is The circumstances of the person asking, and what they already hold What the position costs to hold, and what it costs to close before the end None of the three is in this guide, and none of the three is anywhere on this platform. So this guide describes the shape each level produces, and stops there.
Three inputs would be needed before anybody could answer which level to pick, and every one of the three is absent, so a shape can be described and nothing beyond it.

One closing distinction, and it is the trap sitting immediately behind the refusal. A smaller premium at a level further away is not a cheaper version of the same contract. A smaller premium buys a different contract, producing a different shape, and the two figures are not on the same scale for the same reason that the two contracts are not the same right. A payoff diagram describes what each side owes at each price of the reference asset. A payoff diagram says nothing whatever about which price will arrive, and reading one as a picture of an outcome is how a description quietly turns into a suggestion.

Try it out

Somebody asks which strike they should pick. Which of these can honestly be given?

The strike, what it is not, and what moving it does to the shape of both contracts are settled above. The right to buy and the right to sell in their own right are covered separately and in full. The name the same level carries at the moment the right is used is covered separately, and it turns out to be this same number under another name. The arithmetic that ties the two premiums at one level to each other is covered separately. The components of a premium, and which of them can be worked out without a figure for how far the reference asset might travel, are covered separately. The deadline and what it does to a premium as it approaches is covered separately. How several contracts are combined into one named structure, how a position is collateralised day by day, and how far a reference asset might move as a measured quantity, are all covered separately. The underlying markets themselves and the assembling of a holding across several instruments are covered separately again. Which levels are made available, how far apart they sit, over what range, what one contract covers, how many contracts one participant may hold and whether settlement is in cash or by delivery all belong to SEBI at sebi.gov.in, with the Reserve Bank of India at rbi.org.in where the reference is a rate or a currency, and their names stand above in place of their values.

References

SourceDocumentWhere
Securities and Exchange Board of IndiaFramework for exchange traded derivative contracts, covering the levels at which contracts are made available and the spacing between them, what one contract covers and in what quantity, how many contracts one participant may hold, and whether a contract is settled in cash or by deliverysebi.gov.in
Reserve Bank of IndiaThe equivalent arrangements where the reference is a rate or a currency rather than a securityrbi.org.in
International Organization of Securities CommissionsCross border conduct principles for securities regulators, standing outside any Indian requirementiosco.org
arXiv Quantitative Finance and the Social Science Research NetworkPreprint and working paper repositories carrying research on option pricing theoryarxiv.org and ssrn.com
Research Papers in EconomicsA bibliographic database of economics research, where a citation can be checked against the actual textideas.repec.org

The reference asset, the strike of Rs 2,000.00/-, both contracts 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.

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