Market microstructure

How a listed option is quoted

An option is quoted as a price per share of the deliverable, in a minimum increment set by the exchange, in a size stated per venue and per side. The number a trader thinks in - implied volatility - is not quoted by anyone and is computed downstream from the price by each consumer of the data.

Field	Value
Formula	Cash per contract = QuotedPrice * Multiplier; the cash spread = (Ask - Bid) * Multiplier
Price to cash	A 4.4852 quote on a 100-multiplier contract is 448.52 of cash
Spread to cash	A 0.20 wide market is 20.00 per contract, paid on entry and again on exit
Spread as a share of premium	(Ask - Bid)/Mid, which grows without bound as the option gets cheaper
Worked	Reference inputs: S = 100, r = 0.04, q = 0, sigma = 0.20, T = 0.25, at which the K = 100 call is 4.485236 with a quoted vega of 0.197240 per volatility point. These are inputs chosen to make the arithmetic checkable, not observations of any market. A 0.20 wide market around the 4.4852 mid is 4.3852 bid at 4.5852 offered: 20.00 of cash per contract and 4.46 percent of the premium. The same 0.20 spread around the 125-strike model value of 0.0659 would be 303 percent of the premium and is not quotable, which is why the wing in the table above is shown with a 0.05 spread instead - and that 0.05 is still 75.9 percent of the mid

• Spread as a percentage of premium is the wrong comparison across strikes and the right one across time on a single strike. Across strikes, use volatility points.
• Round-trip cost is two spreads, not one, and on a defined-risk spread it is two spreads on each of two to four legs. Comparing a maximum profit to a single crossing understates the friction by a factor of two or more.
• Displayed size is per exchange. A 10-up market on one venue with fourteen other venues quoting the same series is not a 10-lot market, and it is not a 150-lot market either.

The bid-ask spread expressed in volatility

Dividing the price spread by vega converts it into volatility points, which is the only unit in which spreads are comparable across strikes and tenors. It is also the unit in which market makers set them, which is why the price spread widens on the wings while the volatility spread does not.

Field	Value
Formula	Spread in volatility points = (Ask - Bid) / VegaPerPoint, where VegaPerPoint = Vega/100
First-order accuracy	Exact to first order. The approximation degrades where volga is large, which is on a far wing
Why market makers work in this unit	It removes S, K, T and r, so one quoting rule applies to a whole surface
Worked	Reference inputs: S = 100, r = 0.04, q = 0, sigma = 0.20, T = 0.25, at which the K = 100 call is 4.485236 with a quoted vega of 0.197240 per volatility point. These are inputs chosen to make the arithmetic checkable, not observations of any market. A 0.20 price spread at K = 100 gives 0.20/0.197240 = 1.0140 volatility points, and inverting the two sides directly gives 0.194930 and 0.205070, a difference of 1.0140 points - the rule-of-thumb and the exact inversion agree to four decimals. At K = 125 the model value is 0.0659 and the quoted vega is 0.022862, so a 0.05 spread is 0.05/0.022862 = 2.1870 points by the rule of thumb, while the exact inversion of 0.0409 and 0.0909 gives 0.187298 and 0.209816, a difference of 2.2517 points. The 0.065 discrepancy between the two methods is the volga term, and it is 3 percent of the spread

• The rule of thumb is good to about a hundredth of a point at the money and to a few hundredths on a wing. It is the right calculation to do in your head and the wrong one to publish.
• A wing quoted 0.05 wide and an at-the-money quoted 0.20 wide can be the same spread in volatility terms. Comparing them in cents makes the wing look tight when it is not.
• Because the conversion divides by vega, spreads in volatility terms explode where vega collapses. That is not a market-maker choice; it is the tick grid meeting a small vega.

The tick regime and the Penny Interval Program

The minimum price increment is set by the exchange and is not uniform: series in the Penny Interval Program quote in 0.01 below 3.00 and 0.05 at or above, while everything else quotes in 0.05 and 0.10. The tick is a hard floor on how finely a volatility can be expressed.

Field	Value
Formula	Minimum expressible volatility increment = Tick / VegaPerPoint
Standard increments	0.05 for series priced below 3.00, 0.10 at or above 3.00
Penny Interval Program increments	0.01 below 3.00, 0.05 at or above 3.00
Where the floor bites	Low-vega series: far wings and very short tenors
Worked	Reference inputs: S = 100, r = 0.04, q = 0, sigma = 0.20, T = 0.25, at which the K = 100 call is 4.485236 with a quoted vega of 0.197240 per volatility point. These are inputs chosen to make the arithmetic checkable, not observations of any market. At K = 100 the model price is 4.4852, so the standard tick is 0.10 and the floor is 0.10/0.197240 = 0.5070 volatility points; under penny quoting it is 0.0507 points. At K = 110 the price is 1.1404, tick 0.05, quoted vega 0.144477, floor 0.3461 points standard and 0.0692 penny. At K = 120: price 0.1882, vega 0.049200, floor 1.0163 points standard and 0.2033 penny. At K = 130: price 0.0211, vega 0.009358, floor 5.3431 points standard and 1.0686 penny. The tick floor is ten times larger at the 130 strike than at the 100 strike under either regime

• Note the discontinuity at 3.00: a series that ticks through the 3.00 boundary changes its minimum increment, so the volatility grid coarsens by a factor of two on a price move of one cent.
• The floor at a far wing exceeds a whole volatility point under standard quoting. Any statement about wing volatility finer than that is describing the model used to smooth it, not the market.
• Penny quoting narrows spreads and also narrows the price bands into which a market maker can retreat. Its effect on quoted size, as distinct from quoted spread, is a separate question and is not settled by this arithmetic.

Market-maker inventory and quoted skew

A market maker's quoted volatility for a strike is a function of the price at which it is willing to change its inventory, not of a forecast. Because inventory is held in Greek space rather than in contracts, a position in one strike moves the quoted volatility of every strike that shares its exposures.

Field	Value
Inventory is measured in	Net delta, gamma, vega by tenor, and vanna and volga on a skewed book - not in contract counts
Mechanism	A maker long vega quotes lower to attract sellers and higher to deter buyers, shifting the mid it shows rather than only widening around it
Cross-strike propagation	Vega and gamma are proportional at one expiration, so absorbing gamma at one strike changes the vega inventory that prices every other strike in that expiration
Skew as a quoting artefact	Part of an observed skew is a persistent inventory imbalance across strikes, and part is a distributional view. The two are not separable from quotes alone
Worked	Reference inputs: S = 100, r = 0.04, q = 0, sigma = 0.20, T = 0.25, at which the K = 100 call is 4.485236 with a quoted vega of 0.197240 per volatility point. These are inputs chosen to make the arithmetic checkable, not observations of any market. A maker who has absorbed 100 contracts of the 100-strike call holds vega of 100*19.723967/100 = 1,972.40 per volatility point and gamma of 100*100*0.039448 = 394.48 of delta per point. Because Vega = Gamma*S^2*sigma*T with S^2*sigma*T = 500 at these inputs, that same inventory could be described as 394.48 of gamma or as 1,972.40 of vega, and offsetting it at any other strike in the same expiration necessarily offsets both in the same ratio. Neutralising the vega with the 105-strike call requires 1,972.40/(18.840253/100) = 104.69 contracts, and that position simultaneously removes 104.69*100*0.037681 = 394.48 of gamma - exactly all of it, not a coincidence but the proportionality

• Because vega and gamma cannot be separated within one expiration, a maker cannot hedge one and keep the other. Every intra-expiry hedge is a joint decision, which is why term is where the real inventory management happens.
• Reading a skew as a pure statement about the distribution ignores that the quotes are also the price of transferring inventory. Both are present and neither is observable alone.
• This entry describes mechanics only. Nothing about the direction of any observed skew, or about whether any level is high or low, follows from it.

Open interest and volume are different counts

Volume counts contracts traded in a session. Open interest counts contracts outstanding at the end of it. A trade changes open interest only according to whether each side was opening or closing, so the same volume figure is consistent with any change in open interest between minus that volume and plus it.

Field	Value
Formula	Change in OI = (buy-to-open matched with sell-to-open) minus (buy-to-close matched with sell-to-close); open-with-close pairs leave OI unchanged
Open against open	Creates a new contract. OI rises by the traded quantity
Close against close	Extinguishes a contract. OI falls by the traded quantity
Open against close	Transfers an existing contract. OI unchanged
Bounds	For volume V, the change in OI lies between minus V and plus V
Worked	Stated composition for one series in one session, chosen for checkability: 250 contracts matched open against open, 100 matched close against close, 30 matched buy-to-open against sell-to-close, 20 matched buy-to-close against sell-to-open. Volume = 250 + 100 + 30 + 20 = 400. Change in open interest = plus 250 minus 100 = plus 150. Starting from an open interest of 1,000 the session ends at 1,150 on 400 of volume, a volume-to-opening-OI ratio of 0.4000. The same 400 of volume with all of it close against close would have ended at 600, and with all of it open against open at 1,400

• Open interest is published the following morning, not intraday, because it is a clearing figure rather than a market-data figure. Any intraday open-interest number is an estimate.
• Volume exceeding open interest is often described as unusual. Arithmetically it only requires the same contracts being traded more than once, which is the normal state of a liquid series.
• Open interest is a count of contracts, not of positions or of participants. One account holding 1,000 long and another holding 1,000 short is open interest of 1,000, not 2,000.

Source: OCC

The clearing and margin flow through OCC

Every listed option trade is novated to the clearinghouse, which becomes buyer to every seller and seller to every buyer. The obligation chain therefore runs from the customer to the clearing member to OCC, and margin is collected at each link under different rules at each link.

Field	Value
Novation	After clearing there is no bilateral counterparty. Each side faces OCC
Customer to clearing member	Regulation T strategy-based margin, or portfolio margin for a qualifying account. Broker house requirements may be higher and usually are
Clearing member to OCC	A risk-based margin calculation on the member's whole cleared position, not a per-customer sum
Settlement cycle	Premium settles on the business day after the trade. Exercise settlement follows the underlying's settlement convention
Consequence for the customer	A customer requirement is the maximum of the regulatory formula and the house requirement, and the house requirement is set with the member's own OCC margin in mind
Worked	A short 95-strike put with the underlying at 100 sold for 2.40. The Regulation T customer requirement is 2.40 plus max(0.20*100 minus 5.00, 0.10*95) = 2.40 plus 15.00 = 17.40 per share, 1,740.00 per contract. The customer's maximum loss is 9,260.00, so the requirement is 18.8 percent of the worst case. The clearing member's own requirement at OCC is computed on its net cleared book across all customers under a risk-based method, so it bears no fixed relationship to the 1,740.00 - which is exactly why a house requirement above the regulatory figure is common

• There is no counterparty to research on a listed option, which is the entire economic function of the clearinghouse and the reason listed and over-the-counter structures are not comparable on price alone.
• The three margin layers are computed by different methods on different portfolios. A customer who reconciles a house requirement against the Regulation T formula and finds a gap has found the house layer, not an error.
• Novation is why an assignment arrives from the clearinghouse by allocation and not from the person on the other side of the original trade. The original counterparty is not identifiable and is not relevant.

Source: OCC

Exercise cut-offs and contrary instructions

Automatic exercise happens by exception: in-the-money contracts are exercised unless the holder submits a contrary instruction before the broker's cut-off. The cut-off is earlier than the clearinghouse deadline, is set by the broker, and is the operative deadline for a customer.

Field	Value
Default	Exercise if in the money by the clearinghouse threshold at expiration
Contrary instruction to abandon	Instructs the broker not to exercise a contract that would otherwise be exercised automatically
Contrary instruction to exercise	Instructs exercise of a contract that would not be exercised automatically, which is how an out-of-the-money contract is exercised at all
Cut-off ordering	Customer to broker, then broker to clearing member, then member to the clearinghouse. Each is earlier than the next
Worked	A long 100-strike call with the underlying settling at 100.02. It is in the money by 0.02 per share, so the default is exercise: the account receives 100 shares at a cost of 10,000.00 against a market value of 10,002.00, a 2.00 gain before any commission, and takes on an unhedged 10,002.00 stock position over the weekend. The same contract settling at 99.98 is out of the money by 0.02 and lapses by default, and exercising it by contrary instruction would cost 10,000.00 for 9,998.00 of stock, a 2.00 loss. In both cases the 2.00 is negligible against the 10,000.00 of position the decision creates

• The important consequence of a marginal automatic exercise is not the two dollars of intrinsic value; it is the full notional stock position that appears in the account with no hedge and no decision.
• A broker's cut-off can be an hour or more before the clearinghouse deadline and is not standardised. Confirm it against your own broker's published time rather than against a general rule.
• The threshold for automatic exercise is a clearinghouse parameter, not a law of nature, and it has been changed. Check the current figure rather than a remembered one.

Source: OCC

The closing print and the settlement price are different numbers

The price that determines exercise value is a settlement price computed under a stated rule, not the last trade of the session. For an equity option that rule references the underlying's official closing price; for a cash-settled index option it can reference an opening calculation on the following morning.

Field	Value
Equity option	Exercise is physical and the moneyness test uses the underlying's official closing price on the last trading day
Index option, PM-settled	Cash settlement against a closing index calculation on the last trading day
Index option, AM-settled	Cash settlement against a special opening calculation on the following morning, using each component's opening price
Why it matters	The last option trade can occur minutes before a settlement reference that moves, so the option's final print and its settlement value can differ
Worked	An index option struck at 100 whose last trade of the session is 0.05, on an index printing 99.90 at the close. If the contract is AM-settled and the special opening calculation the next morning is 100.60, the contract settles for 0.60 per unit, twelve times its last traded price, and the holder had no opportunity to trade between the two. If instead the opening calculation is 99.40, it settles at zero. The final trade price carries no information about which of these occurs

• An AM-settled contract stops trading before its settlement reference is determined. That gap is not a liquidity problem, it is the contract specification, and it cannot be traded out of.
• The special opening calculation uses each component's opening price, which need not occur at the same instant. It is therefore not a price at which the index ever traded.
• Reconciling a settlement value against the last option print will always show discrepancies. Reconcile against the stated settlement reference instead.

Source: OCC; CBOE contract specifications

How a spread order is legged, and what the fill does to the profile

A multi-leg order can be filled as a net package or leg by leg. The distinction is not administrative: because every profile figure on a spread is derived from the net price, the fill quality moves the maximum profit, the maximum loss and the breakeven, and the implied spread market is wider than either leg's market suggests.

Field	Value
Formula	Implied spread market: bid = LegBid1 - LegAsk2, offer = LegAsk1 - LegBid2. Width of the implied market = sum of the two leg widths
Net debit at the worst fill	Pay the offer on the long leg, sell the bid on the short leg
Net debit at the best fill	Buy the bid on the long leg, sell the offer on the short leg, which requires both legs to trade against you at your price
Leg risk	Filling one leg and missing the other converts a defined-risk structure into a single-leg position at a price chosen by the market
Worked	A 100/110 call vertical with the 100 call quoted 3.15 at 3.25 and the 110 call quoted 1.05 at 1.15, stated for checkability. Paying the offer and selling the bid: 3.25 minus 1.05 = 2.20 debit, maximum profit 7.80, breakeven 102.20. Mid on both legs: 3.20 minus 1.10 = 2.10 debit, maximum profit 7.90, breakeven 102.10. Buying the bid and selling the offer: 3.15 minus 1.15 = 2.00 debit, maximum profit 8.00, breakeven 102.00. The implied spread market is therefore 2.00 bid at 2.20 offered, 0.20 wide - the sum of the two 0.10 leg widths. The full crossing costs 0.20 of the 2.10 mid debit, which is 9.5 percent of the premium and 2.5 percent of the maximum profit, and it moves the breakeven by 0.20

• The implied spread market is the sum of the leg widths, so a two-leg structure crosses twice the spread and a four-leg structure four times. Comparing a maximum profit to a single leg spread understates the friction proportionally.
• A net-priced complex order can fill inside the implied market, because a single counterparty can take the whole package where no single leg market would. That is the reason to use one.
• Legging deliberately to capture a better net price accepts leg risk in exchange. The arithmetic of the trade-off is the improvement, 0.05 or 0.10 on the net, against the cost of being left with an unintended single-leg position.

Complex order books and the implied spread market

Exchanges maintain a separate book for multi-leg orders in which a package is matched against another package at a net price, or against the individual leg markets, whichever is better for the order. The book therefore has two sources of liquidity and the better of the two sets the executable net price.

Field	Value
Package against package	Two complex orders in the same structure match directly at a net price, with no leg market involved
Package against legs	A complex order executes against the individual leg quotes when their combination beats the complex book
Priority	Rules differ by exchange on whether a leg-market price beats an equal-priced complex order, and this is a rulebook question, not a general principle
Consequence	The best available net price is at least as good as the implied market from the legs, and can be better
Worked	Using the same 100/110 vertical: the leg markets imply 2.00 bid at 2.20 offered. If the complex book holds a resting order to sell the package at 2.12, the executable offer is 2.12 rather than 2.20, an improvement of 0.08 on the net, worth 8.00 per contract and moving the breakeven from 102.20 to 102.12. Against a mid-priced debit of 2.10 that improvement is 3.8 percent of the premium paid

• Sending a multi-leg structure as separate single-leg orders forgoes the complex book entirely. That is a decision with a measurable cost and it is usually made by accident.
• The complex book is thinner and less continuously quoted than the leg markets, so a resting package order can sit unfilled at a price the leg markets would have crossed. Both books have to be read.
• Priority interaction between the two books is exchange-specific and has changed. Treat any general statement about it, including this one, as a pointer to the current rulebook.

Opening and closing procedures in options

Options series open through an exchange procedure rather than by continuous trading from the first quote, and the procedure exists because the option cannot be priced until the underlying has opened. The consequence is a window at the start of the session in which quoted prices are not comparable with the rest of the day.

Field	Value
Why an opening procedure is needed	An option's value depends on the underlying price, so a series cannot be meaningfully quoted before its underlying opens
Sequencing	The underlying opens, the exchange runs its opening procedure for the series, then continuous quoting begins
Consequence for data	Prints and quotes from the opening window can reflect a stale underlying reference, so implied volatilities computed from them are unreliable
AM-settled expiration	For an AM-settled index contract the settlement reference is itself an opening calculation, so the opening procedure and the settlement are the same event
Worked	An option computed from a stale underlying reference: Reference inputs: S = 100, r = 0.04, q = 0, sigma = 0.20, T = 0.25, at which the K = 100 call is 4.485236 with a quoted vega of 0.197240 per volatility point. These are inputs chosen to make the arithmetic checkable, not observations of any market. If the underlying has in fact opened at 101 but the volatility calculation still uses 100, the 100-strike call at a true 0.20 volatility is worth 5.064399 rather than 4.485236, and inverting that true price against the stale spot of 100 returns an implied volatility of 0.229350 instead of 0.200000 - an error of 2.9350 volatility points from a one-point staleness in the underlying reference. That is 2.89 times the entire 1.0140-point bid-ask spread from the table above

• A one-point error in the underlying reference produces a 2.94-point error in the implied volatility at these inputs, against a bid-ask spread of 1.01 points. Underlying staleness, not option staleness, is the dominant data-quality problem at the open.
• Any volatility series built from opening prints will show a spike that is an artefact of the reference price and not a market event. Check the timestamp alignment before interpreting it.
• Exchange opening procedures differ in detail and change. The point that survives any specific rule is the sequencing: the underlying first, then the series.

Source: CBOE contract specifications; OCC