Lesson 28

    Macro Events and Expiry: Read the Right Clocks

    Align the release with the selected contract, then separate repricing, hedge exposure, final payoff and settlement funding.

    Maya slides one of three clocks along a brass rail while Mr. Chartist checks the line with a straight-edge: read the right clock for the contract
    Three separate clocks for a hypothetical NIFTY option: the scheduled event release at tE minus 1 hour 15 minutes, the final reference fixing at tF, which equals expiry tE in this example, and the actual fill with its own timestamp. A long straddle bought four hours before expiry costs ₹5,557.50 for the call at ₹85.50 and ₹5,525 for the put at ₹85.00, ₹11,082.50 in total, before costs.

    Which clock changes this contract?

    ₹5,557.50call · 85.50 × 65+₹5,525.00put · 85.00 × 65=₹11,082.50long straddle, bought at tE − 4 h

    Hypothetical NIFTY contract clocks · tE is expiry, tF is final-reference fixing · fictional paper entry fills · 65 units each

    Which contract is still exposed to the news?

    I’m Mr. Chartist. Let’s begin with the selected NIFTY contract and its clocks, then follow what can change in its price, hedge exposure and settlement obligations.

    By the end you will be able to answer

    1. Does this contract still span the announcement?
    2. Can hedging reinforce an event move?

    You open a NIFTY option chain and notice that an important policy announcement is approaching while the selected option is close to expiry. Does that option actually span the news? Seeing both entries on a calendar is like seeing a train departure and an appointment on the same date: the order of the clocks decides whether they can connect.

    For an option, the relevant boundaries include when new information becomes available, when its final payoff reference is fixed and when the position can still be traded. Fixing determines the reference used for terminal intrinsic value; the later payment of that obligation is another process. Expected news can influence prices before publication, while a release after fixing cannot change a reference already determined.

    We will follow hypothetical NIFTY Calls and Puts at a 25,000 strike through relative teaching clocks, alternative model marks and a separate paper-fill ledger. Prices, quantities and model inputs are assumptions, rather than live market observations. The lesson connects event uncertainty, changing Delta and Gamma, terminal payoff and funding without turning a scheduled overlap into a trade instruction.

    Updated

    Chapter 1Contract clocks3 min read

    Does this contract still span the announcement?

    Check if the news arrives before the final reference.

    Maya

    Mr. Chartist, a policy announcement is due today and my NIFTY option expires today. So it must carry the news, right?

    Mr. Chartist

    Same date tells you little. Ask whether the news arrives before the final payoff reference is fixed. A later-expiring option can still carry it after an earlier one has passed that point.

    Maya

    And once the reference is fixed?

    Mr. Chartist

    Later news cannot change that contract's ordinary payoff. Earlier hopes may already have moved its premium, though.

    Maya

    If I guess the direction right, do I win?

    Mr. Chartist

    Not always. In our model rows, a small rise with IV falling left the pair worth less. Direction, IV and time work together.

    Keep a journal of the contract, the clocks and the fills. A model mark is not a fill.

    Say you hold a NIFTY option and a policy announcement is due. The announcement and expiry may fall on the same date, but that alone tells you little. The useful question is whether the news arrives before this contract’s final payoff reference is fixed. A later-expiring option can still carry the announcement risk after an earlier contract has passed that point.

    The official final reference is the value that the exchange and clearing rules use to work out the contract’s expiry payoff. It is not the last traded premium, and not a NIFTY level you saw earlier. Fixing the reference, contractual expiry, the end of trading and the later payment of settlement cash are separate events. Your broker’s access limits add one more boundary: your exposure can remain even when your account can no longer place an exit.

    We follow one hypothetical European, cash-settled NIFTY Call and Put, both with strike 25,000 and the same expiry. European means exercise happens at expiry, and trading before expiry is a separate action. Call and Put name the contract type, while buying or selling names the position. Let tE be contractual expiry and tF the fixing of the final reference. For this example, assume tF equals tE. The relative times below are teaching assumptions, not today’s NSE timetable.

    Four hours before tE, NIFTY is assumed to be at 25,000, and we calculate an opening model value. The event arrives one hour and fifteen minutes before tE. Fifteen minutes later, with one hour left, we calculate alternative after-release values. A model mark is an estimate from stated inputs. An actual fill is a completed trade at a recorded price, quantity and time. A mark, a quote on screen or a submitted order does not prove that a trade happened.

    Teaching sequence, not a current market schedule

    Follow the contract through separate clocks

    Hypothetical clocks drawn to scale in minutes: tE is contractual expiry and tF is final-reference fixing. The last point sits after tE only to show that payment comes later.

    1. InformationThe news you wait for
      • Event release: tE − 1 h 15 min
    2. Model marksCalculated, not traded
      • 1Entry mark: tE − 4 h
      • 2After-event mark: tE − 1 h
    3. PayoffWhat the contract pays
      • Final reference fixed and expiry: tF = tE, by assumption
    4. CashWhen money moves
      • Payment: later, no hour assigned
    1. tE − 4 h

      Entry model mark

      The initial spot and IV inputs give model values. The paper ledger separately assumes entry fills at this same toy time.

    2. tE − 1 h 15 min

      Event release

      New information arrives before the assumed fixing. Its effect on spot, IV and executable quotes is not predetermined.

    3. tE − 1 h

      After-event model mark

      Reprice the same contracts under each alternative spot and IV state. These alternatives are not consecutive market observations.

    4. tF = tE, by assumption

      Final-reference fixing

      The stated final NIFTY reference determines terminal intrinsic value. It is separate from the earlier model spot or option last price.

    5. tE, the same toy instant

      Contractual expiry

      This contract reaches its terminal payoff. Fixing and expiry remain different concepts even when their assumed times coincide.

    6. Later; operational time not assigned

      Settlement payment

      Paying the determined cash obligation follows the applicable clearing process. Fixing a payoff does not establish when funds are available.

    Table view of the same rows
    Follow the contract through separate clocks: numerical comparison
    Relative instantObservation or boundaryMeaning for this example
    tE − 4 hEntry model markThe initial spot and IV inputs give model values. The paper ledger separately assumes entry fills at this same toy time.
    tE − 1 h 15 minEvent releaseNew information arrives before the assumed fixing. Its effect on spot, IV and executable quotes is not predetermined.
    tE − 1 hAfter-event model markReprice the same contracts under each alternative spot and IV state. These alternatives are not consecutive market observations.
    tF = tE, by assumptionFinal-reference fixingThe stated final NIFTY reference determines terminal intrinsic value. It is separate from the earlier model spot or option last price.
    tE, the same toy instantContractual expiryThis contract reaches its terminal payoff. Fixing and expiry remain different concepts even when their assumed times coincide.
    Later; operational time not assignedSettlement paymentPaying the determined cash obligation follows the applicable clearing process. Fixing a payoff does not establish when funds are available.

    News released after tF cannot change this already-fixed reference. It can matter for a later-expiring contract or a continuing hedge; anticipation may already have affected prices before fixing.

    Every relative time here is fictional. Actual release, index-reference, last-trading, broker-access, quote, fill and payment clocks can differ. Verify their relationship for the selected contract rather than treating this sequence as an exchange timetable.

    A scheduled release time is also not proof of when the news was actually published or received. A real reconstruction needs the publisher’s timestamp and timezone, the data version, the underlying and quote timestamps, and any fill timestamps. A calendar shows when news is expected. It does not show what the news will say, or when your screen receives it. These differences matter even when several items share one date.

    Once the final reference is fixed, later news cannot change this contract’s ordinary payoff computed from it. Earlier anticipation may already have moved its premium, and later news can still affect a surviving contract or a hedge. An official correction of a wrong reference is a separate process. Fixing the payoff also does not say when the settlement cash becomes available.

    Chapter 2Pending risk3 min read

    Why a short clock can still carry event uncertainty

    See why a short clock can still carry uncertainty.

    If an announcement is still ahead of the final reference, a sudden NIFTY move remains possible even with little calendar time left. Time value is the part of an option’s value above its immediate intrinsic value. It need not be nearly gone just because the contract expires today. The news that could change the payoff may still be unresolved.

    Implied volatility (IV) is the volatility figure that makes a given pricing model match a given option price. It is usually quoted per year. An annual IV of 40% is not a prediction that NIFTY will move 40% in the next hour, and it is not the premium. In a simple diffusion model, the uncertainty over the time left combines annual volatility with the square root of the time remaining. As time shrinks, that scale can fall even when annual IV rises.

    A separate miniature experiment shows this. It does not follow the release timing of the previous clock: here the same event is still pending at both the four-hour and one-hour points. Keep NIFTY and the strike at 25,000. Ordinary continuous price variation, called diffusion in the model, has annual volatility of 20%. Add an independent Gaussian event log-jump of 0.6%. Gaussian means a normal distribution, and log price measures proportional change rather than raw index points. Event log variance, the square of that scale, is the model’s unresolved event uncertainty. It is not a probability of a profitable trade.

    Before the event at both observations

    A pending event can lift annual IV while premium falls

    A separate miniature experiment keeps NIFTY and strike at 25,000. The same unresolved event remains inside both horizons. Ordinary diffusion volatility is 20%; the independent Gaussian event log-jump standard deviation is 0.6%.

    A pending event can lift annual IV while premium falls: numerical comparison
    Remaining time · event still pendingTotal log variance WAnnualised equivalent IVCall model mark · points per unit
    4 calendar hours0.00005426484≈34.47%≈73.77
    1 calendar hours0.00004056621≈59.61%≈63.60

    The annualised equivalent IV rises from ≈34.47% to ≈59.61%, while the Call mark falls from ≈73.77 to ≈63.60 points. The unchanged event variance remains; only the ordinary diffusion horizon shrinks. Less time does not by itself mean an unresolved event has disappeared from the option.

    This is a synthetic Gaussian event-variance illustration, not observed NIFTY data, a calibrated event forecast or a required IV path. The event log jump has mean −j²/2 so its multiplicative mean is one. After a real release, remaining uncertainty can be revised upward or downward. Both marks use the same fictional 6.5% rate and 1.2% dividend yield.

    See the variance and annualisation calculation

    Total log variance measures accumulated model uncertainty across the remaining horizon; annual IV expresses that same uncertainty per year. Their units and denominators differ.

    1. T = hours / 8,760; diffusion volatility σd = 0.20; event log-jump scale j = 0.006
    2. Fixed event log variance j² = 0.000036
    3. W = σd²T + j² = 0.20²T + 0.006²
    4. Annualised equivalent IV = √(W/T)
    5. 4 h: T = 0.00045662100456621003; W = 0.00005426484018264841; IV ≈34.473178%; Call ≈73.771326 points
    6. 1 h: T = 0.00011415525114155251; W = 0.0000405662100456621; IV ≈59.612079%; Call ≈63.598459 points
    7. Use that equivalent IV in the continuous-yield European BSM formula; retain unrounded values in every calculation.

    In this synthetic model, total remaining log variance is ordinary diffusion variance, which shrinks with time, plus the unchanged event variance. Annualising that total means dividing by the time left and taking the square root. The equivalent annual IV rises from about 34.47% to 59.61%, while the Call’s model mark falls from about 73.77 to 63.60 points. Less total uncertainty and a higher annualised number can coexist, because the time in the denominator has become smaller.

    This builds on the Gaussian scheduled-earnings model studied by Tim Leung and Marco Santoli. The NIFTY inputs and the dividend-yield extension are our teaching assumptions. Federal Reserve research also finds higher option insurance costs around selected US macro releases, which supports the narrower idea that scheduled news can be priced in advance. Neither source gives a NIFTY intraday coefficient or a universal IV path. Once an event resolves, the market can revise remaining uncertainty up or down, so the after-release examples next allow both.

    Chapter 3Full repricing3 min read

    Reprice the same contracts after the release

    Reprice the same contracts after the release.

    Back to the main clock, where the event arrives before the one-hour point. We keep the same NIFTY Call and Put, strike 25,000 and expiry tE. At the four-hour start, NIFTY is 25,000 and annual IV is assumed to be 40%. Black–Scholes–Merton (BSM) is the European option pricing model used here, with a lognormal price distribution and a continuous dividend yield. It gives Call and Put marks of about 85.55 and 84.94 points, and an independently rounded pair mark of 170.49 points.

    Every row below reprices both contracts from its own spot, time left and IV. We use a fictional continuously compounded interest rate of 6.5% a year, a dividend yield of 1.2% a year, and remaining calendar hours divided by 8,760 for time in years. One premium point is ₹1 per assumed unit. The quantity is 65 matched units in each leg, for teaching arithmetic only, not a verified current lot size. These assumptions do not reproduce every jump, strike-dependent IV or liquidity change around a real announcement.

    Start with the time-only control. At the same NIFTY level and 40% IV, moving from four hours to one hour lowers the pair mark to about 85.25 points. That isolates the clock inside the model. The other rows are separate alternative states at the same one-hour point. They are not successive moments, and not a forecast of how the event unfolds.

    Model marks · alternative outcomes, not successive trades

    Reprice the whole pair when the event and the clock change

    One hypothetical NIFTY Call and Put share strike 25,000 and expiry tE. The entry model is four calendar hours before tE. The scheduled release is tE − 1 h 15 min; every after-release alternative below is marked at tE − 1 h.

    Reprice the whole pair when the event and the clock change: numerical comparison
    Observation / alternative · spot, time, IVCall model mark · points per unitPut model mark · points per unitPair mark and separate model change
    Before the event · NIFTY 25,000, 4 h, IV 40%≈85.55≈84.94Pair ≈170.49 points · baseline, no fill demonstrated
    Time-only control · NIFTY 25,000, 1 h, IV 40%≈42.70≈42.55Pair ≈85.25 points · change ≈−85.25 points, ≈−₹5,541.01 for 65 units
    Small move · lower IV · NIFTY 25,025, 1 h, IV 20%≈36.22≈11.07Pair ≈47.28 points · change ≈−123.21 points, ≈−₹8,008.83 for 65 units
    Same small move · higher IV · NIFTY 25,025, 1 h, IV 60%≈77.33≈52.18Pair ≈129.51 points · change ≈−40.99 points, ≈−₹2,664.20 for 65 units
    Large move · lower IV · NIFTY 25,200, 1 h, IV 20%≈200.15≈0.00122Pair ≈200.15 points · change ≈+29.66 points, ≈+₹1,927.82 for 65 units

    In the small-move alternative, annual IV rises from 40% to 60%, yet the pair mark falls from ≈170.49 to ≈129.51 points as time also shrinks. The larger +0.80% move raises the pair to ≈200.15 even with lower IV. Neither time decay nor an assumed IV change alone gives the complete result.

    All spots, IVs, rates and clocks are fictional inputs. BSM uses continuously compounded r = 6.5%, dividend yield q = 1.2% and T = calendar hours / 8,760. Sixty-five matched units are a teaching multiplier, not a verified current lot size. These full-precision model-value changes are neither executable quotes nor realised profit. Independently rounded leg marks may differ from the rounded pair by 0.01; the tiny Put remains positive before expiry.

    See the full-repricing inputs

    Each row prices both European contracts anew. Local Greeks are sensitivities at one snapshot, not a substitute for this finite-change calculation. A real event can involve jumps, skew and different executable quotes.

    1. T = remaining calendar hours / (365 × 24)
    2. d1 = [ln(S/K) + (r − q + σ²/2)T] / (σ√T); d2 = d1 − σ√T
    3. C = S exp(−qT) Φ(d1) − K exp(−rT) Φ(d2)
    4. P = K exp(−rT) Φ(−d2) − S exp(−qT) Φ(−d1)
    5. Pair model change = (new unrounded C + P) − (baseline unrounded C + P)
    6. Whole-position model-value change = pair model change × 65 assumed units
    7. Remaining-horizon scale σ√T: 4 h / 40% ≈0.854748%; 1 h / 60% ≈0.641061%. These are model scales, not promised ranges.

    Say NIFTY rises only 25 points to 25,025 and IV falls to 20%. The pair is marked at about 47.28 points. With exactly the same small move but IV at 60%, it is about 129.51 points. That is higher than the lower-IV case, yet still below the original 170.49. Annual IV rose from 40% to 60%, but the model’s scale for the time left fell from about 0.855% to 0.641% as time shortened. A higher annual IV does not guarantee that a bought pair gains when other inputs change too.

    A bigger rise of 200 points, to 25,200, tells a different story. Even with IV at 20%, the pair mark is about 200.15 points, above its starting model value. The Call now carries substantial intrinsic value, and the Put’s tiny pre-expiry mark stays positive. So “IV fell, so every option buyer lost” leaves out the move in the underlying, the contract and the time horizon.

    The changes shown for 65 units compare unrounded model values with the unrounded opening model value. They are not realised profits, and the opening model mark is not the fictional fill used in the next section. A real early exit needs actual entry and exit fills, the quantities filled and charges. Bid and ask, depth, stale quotes or partial fills can make fills differ from a model estimate. Rounded Call and Put cells can also differ by 0.01 from the rounded pair, since the calculations keep full precision.

    Chapter 4Expiry results4 min read

    At the final reference, recover the premium first

    Recover the premium first at the final reference.

    Now change the question from a model value before expiry to cash results at the final reference. Separately assume fictional paper fills four hours before tE: buy the NIFTY 25,000 Call at ₹85.50 per unit and the matching Put at ₹85.00, 65 assumed units each. Buying both at the same strike and expiry is a long straddle, and selling both is a short straddle. The Call costs ₹5,557.50 and the Put ₹5,525.00, so the long pair costs ₹11,082.50. That opening payment is cash moved, not a profit or loss settled at entry.

    For this terminal ledger, subtract the entry premium from exercise cash, with no financing, interest, dealing charges, taxes or hedges. The Call pays the amount by which the final reference is above 25,000, if positive. The Put pays the amount by which 25,000 is above the reference, if positive. Together, their exercise value per unit is the distance between the final reference and the strike. To recover the pair’s ₹170.50 premium per unit, the final reference must be 170.50 points away in either direction.

    The two cash break-evens are 24,829.50 and 25,170.50. They apply to this pair at its final reference under the stated exclusions. They are not thresholds for an early-exit result, and a one-hour model spot crossing one of them is not an expiry outcome. The figure’s final levels are separate hypothetical terminal scenarios, and we have not projected them from the after-release alternatives in the previous section.

    Separate terminal scenarios · before dealing costs and financing

    Expiry cash results use the actual assumed fills

    Fictional paper entry at tE − 4 h: buy Call at ₹85.50 and Put at ₹85.00 per unit, both at strike 25,000, 65 matched units each. The long pair pays ₹11,082.50; its matching short pair receives the same opening cash.

    • Long straddle · buys Call + PutSolid line
    • Short straddle · sells Call + PutDashed line

    Pair cash result after entry premium · ₹ before costs and financing

    Pair cash result after entry premium · ₹ before costs and financing against Final NIFTY reference fixed at tF · index pointsExact supplied series. Legend identifies solid and dashed lines. All plotted values are available in the following accessible table. Both curves use the same linear 24,600–25,400 horizontal scale and −₹16,000 to +₹16,000 vertical scale. The zero line separates loss and profit. The finite window is not a risk cap: the long Call tail can gain without bound and the uncovered short Call tail can lose without bound; the Put-side tail is finite at a nonnegative final reference.

    Final NIFTY reference fixed at tF · index points

    Drag the slider to read each line at that point.
    • Lower cash break-even 24,829.50
    • Shared strike 25,000
    • Upper cash break-even 25,170.50

    Both curves use the same linear 24,600–25,400 horizontal scale and −₹16,000 to +₹16,000 vertical scale. The zero line separates loss and profit. The finite window is not a risk cap: the long Call tail can gain without bound and the uncovered short Call tail can lose without bound; the Put-side tail is finite at a nonnegative final reference.

    Complete plotted values: Pair cash result after entry premium · ₹ before costs and financing against Final NIFTY reference fixed at tF · index points
    SeriesFinal NIFTY reference fixed at tF · index pointsPair cash result after entry premium · ₹ before costs and financing
    Long straddle · buys Call + Put24,60014,917.5
    Long straddle · buys Call + Put24,829.50
    Long straddle · buys Call + Put25,000−11,082.5
    Long straddle · buys Call + Put25,170.50
    Long straddle · buys Call + Put25,40014,917.5
    Short straddle · sells Call + Put24,600−14,917.5
    Short straddle · sells Call + Put24,829.50
    Short straddle · sells Call + Put25,00011,082.5
    Short straddle · sells Call + Put25,170.50
    Short straddle · sells Call + Put25,400−14,917.5
    Expiry cash results use the actual assumed fills: numerical comparison
    Alternative final NIFTY reference · pointsExercise cash to the long pair · Call / PutLong pair cash result · ₹ before costsShort pair cash result · ₹ before costs
    24,800.00Call ₹0.00 · Put ₹13,000.00+₹1,917.50−₹1,917.50
    24,829.50Call ₹0.00 · Put ₹11,082.50₹0.00₹0.00
    24,975.00Call ₹0.00 · Put ₹1,625.00−₹9,457.50+₹9,457.50
    25,000.00Call ₹0.00 · Put ₹0.00−₹11,082.50+₹11,082.50
    25,025.00Call ₹1,625.00 · Put ₹0.00−₹9,457.50+₹9,457.50
    25,170.50Call ₹11,082.50 · Put ₹0.00₹0.00₹0.00
    25,200.00Call ₹13,000.00 · Put ₹0.00+₹1,917.50−₹1,917.50

    At 25,000 both legs have zero exercise cash, so the long pair loses ₹11,082.50 and the matching short pair retains that opening premium before costs. At 25,025, ₹1,625.00 exercise cash still leaves a long-pair result of −₹9,457.50. At either 24,800 or 25,200, the long pair gains +₹1,917.50 before costs.

    These are alternative final references, not predictions from the after-release model spots. For arithmetic only, tF = tE; final-reference fixing, contractual expiry and later operational cash settlement remain distinct. One premium point is ₹1 per assumed unit. This cash-result convention deliberately omits interest/financing, charges, taxes and hedges. It is neither an early-exit quote nor a margin or physical-stock delivery funding bound. Counterpart results are exact opposites only under these matched fills and exclusions.

    Reconcile fills, exercise cash and pair result

    Entry cash is paid or received at the fill; it is not profit at entry. The terminal exercise cash is separate from the result after recovering the premium. Model marks above are never substituted for these fills.

    1. Call entry cash = 85.50 × 65 = ₹5,557.50
    2. Put entry cash = 85.00 × 65 = ₹5,525.00
    3. Pair debit per unit = 85.50 + 85.00 = 170.50
    4. Call buyer result = 65 × [max(SF − 25,000, 0) − 85.50]
    5. Put buyer result = 65 × [max(25,000 − SF, 0) − 85.00]
    6. Long pair cash result = 65 × [|SF − 25,000| − 170.50]
    7. Short pair cash result = − long pair cash result under the same fills and exclusions
    8. Pair cash break-evens = 25,000 ± 170.50 = 24,829.50 and 25,170.50

    At a final reference of 25,000, both legs pay nothing and the long pair loses the ₹11,082.50 entry payment. At 25,025, the Call pays ₹1,625.00 and the Put pays zero, leaving a pair loss of ₹9,457.50. The direction was up, but the distance was too small to recover both premiums. At either 24,800 or 25,200, exercise cash is ₹13,000.00 and the pair gains ₹1,917.50 before the excluded costs and financing. The chart’s zero line separates a cash loss from a profit after premium.

    For a matching short pair with the same fills and exclusions, every terminal result has the opposite sign. Keeping the opening premium at 25,000 is one scenario. It is not evidence of dependable income or of a seller’s winning probability. The two sides also carry different risk. An uncovered short Call has unlimited loss as the final reference rises without limit. An uncovered short Put’s terminal loss is finite, because the reference cannot fall below zero. The short pair inherits the unlimited Call tail, and the chart’s finite window is not a loss cap.

    In this example the bought pair’s largest terminal cash loss is its entry premium, before the excluded amounts. These cash-settled calculations do not estimate an early-exit fill, margin needs or physical stock-delivery funding. A realised result needs the recorded fills or the official final reference and the settlement ledger. The event story and the model give neither, and these alternatives cannot say which position wins more often.

    Chapter 5Hedge direction3 min read

    Can hedging reinforce an event move?

    See how hedge trades can add to a move.

    A sudden NIFTY move changes more than the option premium. Delta is the option’s local sensitivity to direction. Gamma is how fast that Delta changes as the underlying moves. For a plain bought Call or Put, Gamma is positive. Selling the option reverses the sign. A whole portfolio adds up the signed sensitivities of all its positions.

    Imagine a trader who rebalances an isolated option position towards Delta neutrality with a linear hedge, one whose exposure moves about one-for-one with its price reference. The target hedge is the opposite of the option book’s Delta. A positive-Gamma book sells linear exposure after a rise and buys after a fall. A negative-Gamma book buys after a rise and sells after a fall. The first kind of flow tends to oppose the initial move, and the second tends to reinforce it.

    Exposure arithmetic · Delta-equivalent units

    The signed book decides the hedge direction

    Four separate hypothetical positions, each with 65 assumed option units. Bought Call Delta changes +0.50 → +0.80 on the assumed rise; bought Put Delta changes −0.50 → −0.80 on the assumed fall. Selling reverses the option exposure.

    • Long Callunderlying rises · positive Gamma

      Signed option Delta · before → after
      +32.5 → +52.0 · bullish exposure
      offset by the opposite sign
      Linear hedge target · before → after
      −32.5 → −52.0

      Sell 19.5 equivalent units−19.5

    • Short Callunderlying rises · negative Gamma

      Signed option Delta · before → after
      −32.5 → −52.0 · bearish exposure
      offset by the opposite sign
      Linear hedge target · before → after
      +32.5 → +52.0

      Buy 19.5 equivalent units+19.5

    • Long Putunderlying falls · positive Gamma

      Signed option Delta · before → after
      −32.5 → −52.0 · bearish exposure
      offset by the opposite sign
      Linear hedge target · before → after
      +32.5 → +52.0

      Buy 19.5 equivalent units+19.5

    • Short Putunderlying falls · negative Gamma

      Signed option Delta · before → after
      +32.5 → +52.0 · bullish exposure
      offset by the opposite sign
      Linear hedge target · before → after
      −32.5 → −52.0

      Sell 19.5 equivalent units−19.5

    Table view of the same rows
    The signed book decides the hedge direction: numerical comparison
    Separate option positionSigned option Delta · before → afterLinear hedge target · before → afterTarget adjustment
    Long Call · underlying rises · positive Gamma+32.5 → +52.0 · bullish exposure−32.5 → −52.0Sell 19.5 equivalent units · −19.5
    Short Call · underlying rises · negative Gamma−32.5 → −52.0 · bearish exposure+32.5 → +52.0Buy 19.5 equivalent units · +19.5
    Long Put · underlying falls · positive Gamma−32.5 → −52.0 · bearish exposure+32.5 → +52.0Buy 19.5 equivalent units · +19.5
    Short Put · underlying falls · negative Gamma+32.5 → +52.0 · bullish exposure−32.5 → −52.0Sell 19.5 equivalent units · −19.5

    A trader choosing to rebalance a positive-Gamma book sells linear exposure after a rise and buys after a fall; a negative-Gamma book does the reverse. These adjustments can oppose or reinforce an initial move, respectively. They do not establish the resulting market price.

    All quantities and Delta snapshots are teaching assumptions. Targets are idealised exposure, not executable fractional futures lots or NIFTY shares. Other legs, IV, time, basis, lot rounding, costs and incomplete fills can leave residual Delta. Public OI alone cannot prove the participant’s net book, Gamma sign, motive or actual hedge trades.

    Check the four signed hedge cases

    Use a positive quantity for a bought option and a negative quantity for a sold option. The target linear hedge is the opposite of the option-book Delta; it is an arithmetic target, not a demonstrated fill.

    1. Option-book Delta D = signed option quantity × bought-option Delta; target hedge H = −D.
    2. Long Call: D +32.5 → +52.0; H −32.5 → −52.0; Hnew − Hold = −19.5 (sell).
    3. Short Call: D −32.5 → −52.0; H +32.5 → +52.0; Hnew − Hold = +19.5 (buy).
    4. Long Put: D −32.5 → −52.0; H +32.5 → +52.0; Hnew − Hold = +19.5 (buy).
    5. Short Put: D +32.5 → +52.0; H −32.5 → −52.0; Hnew − Hold = −19.5 (sell).
    6. 65 × 0.50 = 32.5; 65 × 0.80 = 52.0; 52.0 − 32.5 = 19.5. At each target, D + H = 0.

    The separate cases below use 65 assumed option units. A bought Call’s supplied Delta rises from +0.50 to +0.80, so the book’s exposure rises from +32.5 to +52.0 equivalent units. The target hedge moves from −32.5 to −52.0: sell another 19.5 equivalent units. Selling the same Call reverses the book exposure and calls for buying 19.5. These are assumed exposure snapshots, not observed NIFTY trades.

    For the falling-underlying Put cases, a bought Put’s Delta becomes more negative, from −0.50 to −0.80, so its target hedge becomes more positive and calls for a purchase. The short Put has the opposite, positive Delta, and its target adjustment is a sale. Call and Put name the contract. Whether you bought or sold it decides the signed exposure.

    Equivalent units express sensitivity. NIFTY is an index, so there is no single NIFTY share to buy or deliver. A practical hedge may use whole futures contracts, other options or a basket of stocks. Contract multipliers, lot rounding, gaps between futures and index prices, costs and incomplete fills can leave exposure behind. Time and IV change Delta too, so the target arithmetic does not mean continuous neutrality or a hedging profit.

    Public open interest cannot show who holds the long or short side, what else they hold, their hedge policy or the trades already done. Every outstanding contract has a long and a short. The same displayed OI can therefore sit beside opposite dealer Gamma signs. Cboe’s explanation for the US market supports the hedge mechanism, not a finding about today’s NIFTY dealer book. Whether hedge flow moves a market also depends on its size and the liquidity available.

    Chapter 6Near-strike Gamma2 min read

    High Gamma belongs to a location and a model

    Learn where sensitivity bunches up as expiry nears.

    “Expiry day” does not make every option equally sensitive. At the money means the underlying is near the strike. In a smooth European pricing model with a fixed positive IV, Gamma bunches up around that region as time shortens. Farther from the strike, Delta is already close to its final value, so there is much less Gamma.

    Hypothetical model comparison · 4 hours versus 1 hour

    Near expiry, high Gamma concentrates near the strike

    European BSM comparison at fixed strike 25,000 and fixed annual IV 20%. Each curve varies NIFTY spot while holding its own remaining time fixed. Matched bought Calls and Puts share this positive Gamma; a short leg reverses the sign.

    • 4 hours remainingSolid line
    • 1 hour remainingDashed line

    Gamma · Delta change per index point per option unit

    Gamma · Delta change per index point per option unit against NIFTY spot · index pointsExact supplied series. Legend identifies solid and dashed lines. All plotted values are available in the following accessible table. Shared zero-based Gamma scale. Spot is the horizontal variable; these are alternative model snapshots, not an intraday path or an event prediction.

    NIFTY spot · index points

    Drag the slider to read each line at that point.
    • Fixed strike · 25,000

    Shared zero-based Gamma scale. Spot is the horizontal variable; these are alternative model snapshots, not an intraday path or an event prediction.

    Complete plotted values: Gamma · Delta change per index point per option unit against NIFTY spot · index points
    SeriesNIFTY spot · index pointsGamma · Delta change per index point per option unit
    4 hours remaining24,8000.0006531081
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    Near expiry, high Gamma concentrates near the strike: numerical comparison
    NIFTY spotGamma · 4 hours remainingGamma · 1 hour remaining
    24,8000.000653110.00000653
    25,0000.003733760.00746772
    25,2000.000641990.00000698

    At spot 25,000, the 1-hour Gamma is approximately twice the 4-hour Gamma. At spot 25,200, it is much smaller. Shorter time sharpens the region near the strike in this fixed-IV model; it does not make every option or every portfolio high Gamma.

    All model inputs are assumed: continuous annual rate 6.5%, dividend yield 1.2%, IV 20%, and remaining calendar hours divided by 8,760. A real event can change IV, spot and liquidity. At expiry the payoff has a kink at strike; do not extend this smooth positive-time Gamma formula to zero time.

    How the Gamma geometry is calculated

    Every plotted sample is recalculated from the same European continuous-yield BSM helper. Gamma measures a local Delta response, rather than the price impact of a finite jump.

    1. T = remaining calendar hours / 8,760; d1 = [ln(S/K) + (r − q + σ²/2)T] / (σ√T).
    2. Gamma = exp(−qT) × φ(d1) / (S × σ × √T), where φ is the standard normal density.
    3. S = K = 25,000: Gamma(4 h) ≈ 0.00373376; Gamma(1 h) ≈ 0.00746772 per index point.
    4. S = 25,200: Gamma(4 h) ≈ 0.00064199; Gamma(1 h) ≈ 0.00000698 per index point.
    5. For each signed option leg: book Gamma = signed quantity × per-unit Gamma. The chart shows one bought option unit.

    This separate comparison keeps the NIFTY strike at 25,000 and annual IV at 20%, and changes only the model’s time left, from four hours to one hour, at each spot level. At spot 25,000, Gamma per unit rises from about 0.00373376 to 0.00746772 Delta per index point. At spot 25,200, it falls from about 0.00064199 to 0.00000698. The narrower, taller peak shows why distance from the strike matters.

    The curves are alternative model snapshots, not an intraday price path. Their 20% IV is a fixed assumption, separate from the changing-IV event cases earlier. A real release can move spot and IV together, and a portfolio can mix positive and negative Gamma. A high-Gamma snapshot does not show pending hedge orders and does not predict the size of the next move.

    At expiry, use the final intrinsic payoff directly. Its slope changes abruptly at the strike, a kink, so there is no single ordinary slope there and no finite smooth Gamma. The usual formula for positive time cannot be stretched by setting time to zero. The fixed-IV limit also differs from a model in which unresolved event risk makes annualised IV itself rise as time shrinks.

    Chapter 7Funding needs3 min read

    Payoff, collateral and delivery use different amounts

    Keep payoff, collateral and delivery apart.

    Our NIFTY teaching options settle in cash. A fully paid, standalone bought index option cannot lose more than its premium before costs. That statement is about the option’s economics. It does not describe the funds needed for a physically settled stock option, a hedge or other positions in the account.

    Take standalone in-the-money stock options that reach physical settlement. A long Call or short Put receives shares and pays strike-price funds. A short Call or long Put delivers shares and receives strike-price funds. Paying the premium on a bought stock option does not remove these delivery duties. Eligible offsetting positions can change settlement netting, and the table assumes there are none.

    Settlement and collateral · checked 8 October 2026

    Premium, settlement funding and margin answer different questions

    NSE index options settle in cash. Applicable stock options settle through shares and strike-price funds. The stock directions below assume standalone in-the-money positions reaching settlement, with no eligible offsetting positions.

    Additional expiry-day extreme loss margin (ELM)

    Rule scope
    Expiring short index options

    Applies to relevant shorts open at the start of the day and initiated during that day. It is not a blanket rule for all stock or index positions.

    Assumed underlying notional
    65 × 25,000 = ₹16,25,000

    The rule uses the underlying reference based on its last available closing price. Here 65 units and the 25,000 reference are fictional inputs, not a verified current lot or quote.

    Additional 2% ELM only
    ₹32,500

    Calculated on underlying notional, not option premium or already blocked margin. Other margin and settlement requirements remain.

    Premium, settlement funding and margin answer different questions: numerical comparison
    Contract / positionSettlement obligationWhat must be available
    NIFTY index option · cash settlementITM buyer receives intrinsic exercise cash; assigned seller pays it. No delivery of index shares.Payable cash and applicable margin; premium paid is separate.
    Stock · long Call / short PutReceive the shares and pay strike-price funds.Full required funds; paid premium does not fund the shares.
    Stock · short Call / long PutDeliver the shares and receive strike-price funds.Deliverable shares and applicable margins.

    A premium-limited cash-settled bought-option payoff does not cap stock-delivery funding. The additional ₹32,500 ELM is collateral arithmetic; it is neither the whole margin requirement nor a loss cap.

    Sources checked 8 October 2026: NSE Individual Securities F&O; NCL settlement mechanism (index-specific statements); NCL/CMPT/55330, 20 January 2023 (stock physical obligations); NCL/CMPT/64639, 21 October 2024 (additional index ELM, effective 20 November 2024); NCL margins (underlying-notional definition). Verify the selected contract and current broker/clearing requirements. No universal retail cutoff or funds-release time is assumed.

    Check the additional ELM amount

    This is an isolated calculation using a fictional underlying reference and quantity. It does not calculate total margin, available buying power or maximum loss.

    1. Assumed underlying notional = 65 × 25,000 = ₹16,25,000.
    2. Additional expiry-day ELM = 2% × ₹16,25,000 = ₹32,500.
    3. Physical stock funds: applicable shares × strike price. The premium is a separate payment.

    The extra expiry-day extreme loss margin (ELM), checked on 8 October 2026, applies to expiring short index options. NCL/CMPT/64639, dated 21 October 2024 and effective 20 November 2024, covers shorts already open at the start of the day and those opened during it. The extra 2% is charged on underlying notional based on the last available underlying close, not on the option premium or the margin already blocked.

    With the fictional quantity of 65 and an assumed underlying closing reference of 25,000, that notional is ₹16,25,000 and the extra ELM is ₹32,500. This is only the extra ELM part. Other margin and settlement needs remain, so the amount is neither a loss limit nor a full funding estimate. The assumed quantity is not a verified live lot size.

    A calendar spread uses different expiries. Dated SEBI rules remove the calendar-spread margin offset that involves an expiring leg on its expiry day, and leave pairs of later expiries under their existing treatment. The 1 October 2024 circular covers index contracts. The 5 February 2026 circular extends the same treatment to single-stock derivatives, effective three months from its date. This does not mean every same-expiry vertical spread loses its margin benefit. A vertical’s bounded final payoff still does not guarantee an exit fill, fixed collateral or enough funds for stock delivery.

    The contract you hold, current clearing requirements and your broker’s account limits decide what you can actually do. Fixing the final reference, last trading, automatic exercise and settlement payment are separate processes. Neither this example nor a generic webpage gives a universal retail square-off time or a promise about when money becomes withdrawable. Start lesson 32 on margin covers the mechanics in full.

    Chapter 8Evidence journal4 min read

    Keep an evidence journal for the overlap

    Keep an evidence journal for the overlap.

    Before you explain a result, keep the question as it stood at the time: which contract could still respond to the release, and what position did you really hold? An educational journal records the contract, the dated rules, the news source and the timestamps. It can also record a decision to do nothing. These fields help rebuild the evidence. They are not a universal event-day strategy.

    An evidence ledger

    Keep evidence separate from the explanation

    These record fields help reconstruct what was known and what was executed. They do not prescribe whether or when to trade.

    1. Contract and known schedule

      Retain with its source and time
      Venue, underlying, expiry, strike, Call/Put, position side and quantity; dated contract rules and event publisher’s schedule with timezone.
      What it can establish
      Which contract was held and whether its reference window could span the scheduled news.
      If evidence is missing
      Current contract terms, exact timing or actual quantity remain unknown; a remembered weekday is insufficient.
    2. Release and data vintage

      Retain with its source and time
      Original release or file, initial/revised status, actual publication or receipt evidence, timezone and retrieval time; contemporaneous expectation source if available.
      What it can establish
      What information was available then. Actual minus expectation differs from actual minus the prior reading.
      If evidence is missing
      Do not substitute later revisions for the original information or assign a surprise magnitude without a comparator.
    3. Spot, quotes and IV/model inputs

      Retain with its source and time
      Underlying and quote timestamps, feed identity/delay, bid/ask and available depth; IV’s price/model convention and remaining-time assumption.
      What it can establish
      A timestamped observation or a labelled model estimate. Quote, last trade and model value are different references.
      If evidence is missing
      An unrecorded quote side, depth or model convention stays unknown; a mark cannot demonstrate an executable price.
    4. Orders and actual execution

      Retain with its source and time
      Submission and each fill timestamp, fill price and quantity, contemporaneous bid/ask, charges, partial fills and outstanding or cancelled orders.
      What it can establish
      The position actually filled and the cash exchanged. Requested size or a submitted order is not filled size.
      If evidence is missing
      No fill evidence means no realised-trade claim. A fictional paper fill must retain its assumption label.
    5. Official final reference and funding

      Retain with its source and time
      Official reference and its source/date; actual settlement statement, premium/cost ledger, margin and cash or share-delivery obligations where applicable.
      What it can establish
      A reconciled expiry outcome and separate funding needs. Final reference, net result, collateral and payout answer different questions.
      If evidence is missing
      A model terminal result does not prove an actual settlement, available funds or completion of delivery.

    Record observations before assigning a cause. Spot, IV, elapsed time, concurrent news, spreads and costs may all matter; one later outcome cannot establish that the event alone caused a result.

    Preserve “unknown” where evidence is absent. Label paper results and counterfactuals as hypothetical, retain their assumptions, and separate ordinary fixed-payoff settlement from any official reference-correction process.

    A real, now-past event shows the clock conversion. The Fed released its FOMC statement on 28 October 2026 at 2:00 p.m. EDT (read on the Federal Reserve’s own site on 6 November 2026). On that date Eastern Time was EDT, UTC−04:00, and IST is UTC+05:30, so the release came at 23:30 IST on 28 October. The Fed’s calendar had also scheduled a press conference half an hour later, at 00:00 IST on 29 October. The statement held the target range at 3¾ to 4 percent, with two members preferring a quarter-point rise. We use it only for the clock arithmetic. Compare any such time with the rules of your own option. This example does not invent a matching NSE expiry date or fixing hour, and it says nothing about how NIFTY options priced the news.

    Keep the original release and its information vintage, the version available when you decided. The BLS, for example, revises payroll estimates as new information comes in and keeps vintage tables. A revised value downloaded later is not the earlier information. Actual minus the previous reading measures a change. Actual minus a pre-release expectation measures something else. Without a recorded source for the expectation, the size of the surprise stays unknown.

    Record the timezone, the source timestamp and your own receipt time separately. A data provider can publish or refresh later than the original publisher. FRED’s release calendar uses US Central Time and separates source releases from availability on FRED. A quote’s timestamp, a last trade’s timestamp and a model calculation’s timestamp are also different evidence. Bid, ask and available quantity describe a quote, and only an actual fill shows what was executed.

    Record requested and filled quantities, every fill price and time, partial or rejected orders, and charges counted once. An order submission is not a fill, and a chart or model mark does not show execution at your size. If there is no fill evidence, write “unknown” and do not present a realised result. The fictional premiums and the 65-unit paper ledger in this lesson stay labelled as assumptions.

    Reconcile an expiry outcome with the official final reference and the settlement statement, keeping premium, dealing costs, collateral and delivery funding apart. A what-if such as holding longer needs the same starting position and a stated horizon, price convention and costs. Label it a counterfactual, not an observed trade. Spot, IV, time passing, other news and execution can all matter. One later outcome does not prove a single cause or a winning frequency for buyers or sellers.

    The next lesson uses position-sizing maths to connect a contract’s exposure with the capital you have. Carry forward the contract, the filled quantity, the funding duties and the reconciled outcome, because they define what is being sized. The aim here was to see which clocks and exposures interact. It is not a rule to buy, sell, wait a fixed time or always exit because an event and an expiry share a date.

    Before you go

    Check yourself

    5 questions from this lesson. Pick an answer to see why, then slide on to the next.

    Question 1 of 5

    A release arrives after a selected option’s ordinary final payoff reference has already been fixed. What follows?

    Questions readers ask

    Common questions

    Does a macro announcement on expiry day affect every NIFTY option?

    The selected contract’s timing matters. A release before its final reference is fixed can affect the remaining reference exposure; an earlier account cutoff can still limit trading access. A release after fixing cannot change that already-fixed payoff, although anticipation may have influenced earlier prices and later contracts or continuing hedges may remain exposed.

    Can annualised IV rise while an option premium falls near expiry?

    Yes. Annualised IV and remaining-horizon uncertainty are different quantities. A still-pending event can retain a variance contribution while the ordinary time horizon shrinks. In the lesson’s separate synthetic event model, annualised equivalent IV rises while the Call mark falls. Real quotes also reflect spot, carry, price convention and liquidity; neither IV nor premium follows a compulsory expiry-day path.

    Does an IV fall after a release guarantee that an option buyer loses?

    No. Reprice the whole position when spot, time and IV change together. In the hypothetical small-rise, lower-IV case, the pair model mark falls; in the separate larger-rise, lower-IV case, it rises. A model-value change is not an executed profit. Actual results require fills or settlement, quantity, premium and the stated treatment of costs and financing.

    Are all options high Gamma immediately before expiry?

    No. In the lesson’s fixed-positive-IV European model, Gamma concentrates near the strike as time shrinks, while an option away from the strike can have very low Gamma. Position side reverses its sign and other legs change portfolio Gamma. At expiry, evaluate the kinked intrinsic payoff directly instead of applying a smooth positive-time Gamma formula at zero time.

    Can large option-chain open interest prove dealer Gamma hedge direction?

    No. Outstanding contracts have matched long and short positions, and ordinary OI does not identify who holds them, the rest of a participant’s book or its actual hedge trades. A trader rebalancing a positive-Gamma book sells after rises and buys after falls; a negative-Gamma book does the reverse. Knowing that mechanism does not establish the observed market’s net dealer position or price impact.

    Is the additional 2% expiry-day index option margin calculated on premium?

    No. The checked rule applies additional ELM to expiring short index options on underlying notional based on the last available underlying close. With fictional 65 units and a 25,000 reference, notional is ₹16,25,000 and the extra 2% is ₹32,500. It is an additional margin component, not total margin or a maximum loss; it is not a blanket rule for every stock or index position.

    Does paying a stock option premium remove physical-delivery funding?

    No. For standalone in-the-money stock options reaching settlement with no eligible offsets, a long Call or short Put receives shares and pays strike-price funds; a short Call or long Put delivers shares and receives strike-price funds. Premium, collateral and delivery obligations are separate. A premium-limited bought index-option payoff does not provide a general stock-delivery funding bound.

    What was the Indian time of the 28 October 2026 Fed announcement?

    The Fed’s FOMC statement was released on 28 October 2026 at 2:00 p.m. EDT, as read on the Federal Reserve site on 6 November 2026. Eastern was EDT on that date, so the release came at 23:30 IST on 28 October. The press conference was scheduled half an hour later, at 00:00 IST on 29 October. This is a clock conversion only, not a statement about how options priced the news or a matching NSE expiry.

    Sources for further reading

    25 sources

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