Reference: Greeks, Implied Volatility & Options Mechanics

Educational reference only. Nothing here is financial advice or a recommendation to trade. Options involve substantial risk of loss and are not suitable for all investors.

This is the theory/reference module of the manual. It defines the vocabulary, sign conventions, and mechanics that the strategy modules assume you already understand. Read it once end-to-end, then use it as a lookup.

Global conventions used throughout the manual:

1 contract = 100 shares. A quoted premium of $2.50 costs $250 per contract; a Greek of 0.30 delta means the position behaves like 30 shares.
SPX is cash-settled, European-style, and Section 1256–taxed (60/40 long/short blend); no early assignment, no shares ever change hands.
SPY / QQQ / IWM are American-style, physically settled ETF options with genuine early-assignment risk.
IV Rank reference bands: low < 30, high > 50 (the in-between zone is “neutral”).
Sign convention: a positive Greek means the position gains when that input rises. Greeks are quoted per-share unless noted; multiply by 100 for per-contract, then by the number of contracts for position-level.

1. The option price: intrinsic + extrinsic

Every option premium decomposes cleanly into two parts:

Option price = Intrinsic value + Extrinsic (time) value

Intrinsic value is the amount by which the option is in-the-money right now — the value you’d capture by exercising immediately. It can never be negative.

Call intrinsic = max(0, S − K)
Put intrinsic = max(0, K − S)

where S = underlying price, K = strike.

Extrinsic value (a.k.a. time value) is everything else: Premium − Intrinsic. It is the market’s charge for the optionality you still hold — the chance the option moves further into the money before expiration. Extrinsic value is driven by time remaining and implied volatility, and it is the part that decays to zero at expiration.

Moneyness describes where the strike sits relative to spot:

Term	Call condition	Put condition	Composition of premium
ITM (in-the-money)	`S > K`	`S < K`	Intrinsic + extrinsic
ATM (at-the-money)	`S ≈ K`	`S ≈ K`	Almost all extrinsic; maximum time value
OTM (out-of-the-money)	`S < K`	`S > K`	100% extrinsic (zero intrinsic)

How extrinsic decays: time value bleeds away continuously but non-linearly. For an ATM option it decays roughly with the square root of time remaining, so the loss accelerates sharply into the final weeks and days (this is the Theta story in §2.3). Deep ITM and far OTM options carry little extrinsic value to begin with, so they decay slowly. At expiration, extrinsic value is exactly zero and the option is worth only its intrinsic value.

A useful mental model: when you buy an option you pay for extrinsic value and fight decay; when you sell an option you collect extrinsic value and decay works for you.

2. The Greeks (first order)

The Greeks are partial derivatives of the option price with respect to one input, holding the others fixed. They are local, instantaneous sensitivities — accurate for small moves, approximate for large ones (which is why second-order Greeks in §3 exist).

2.1 Delta (Δ) — directional exposure

Definition: the change in option price for a $1 change in the underlying. Calls have delta 0 → +1; puts have delta 0 → −1.

Sign: Long call +, long put −. Short call −, short put +.
Magnitude: deep ITM → |Δ| ≈ 1; ATM → |Δ| ≈ 0.50; far OTM → |Δ| ≈ 0.
What changes it: spot moving (via Gamma), time passing (via Charm), and IV changing (via Vanna). ATM delta sits near 0.50 but is the most sensitive to spot moves (gamma is highest ATM); deep-ITM (~1.0) and far-OTM (~0) deltas are the most stable because their gamma is low.

Delta as a hedge ratio: to hedge one long call with delta 0.40, short 0.40 × 100 = 40 shares to be delta-neutral. Position delta tells you “how many shares of directional exposure do I effectively hold.”

Delta as a probability proxy: an option’s delta roughly approximates the risk-neutral probability it finishes ITM (a 0.30-delta OTM call ≈ ~30% chance of expiring ITM). Caveat: this is an approximation, not an equality. It’s a risk-neutral probability (not real-world), it ignores the volatility skew that makes the true probability differ across strikes, and it drifts as time and IV change. Use it as a quick gauge, not a precise statistic.

Rule of thumb: sell premium around the 0.16–0.30 delta strikes (≈1 standard deviation OTM and closer) when you want a high probability of profit with defined directional risk.

2.2 Gamma (Γ) — the rate of change of delta

Definition: the change in delta for a $1 move in the underlying. It is the “acceleration” of your directional exposure.

Sign: Long options (calls or puts) are long gamma (+); short options are short gamma (−). Gamma has the same sign for both calls and puts on the same side of a trade.
Magnitude: largest ATM and near expiry; small for deep ITM/OTM and for long-dated options.

Why largest ATM and near expiry: near expiry an ATM option’s delta has to swing violently from ~0.50 toward 0 or 1 over a tiny price range as the outcome resolves to all-or-nothing — so a small spot move flips delta hard. That sensitivity is gamma.

“Gamma risk” for short options near expiry: if you’re short a near-expiry ATM option, a small adverse move blows your delta up against you fast, and your losses accelerate — you can’t hedge fast enough. This is why short-dated short-premium positions (e.g., 0DTE/weekly short straddles) are the most dangerous: high theta income, but brutal gamma if the underlying moves. Long gamma is the mirror image — your winners accelerate and losers decelerate, paid for via theta.

Rule of thumb: long gamma = pay theta to profit from movement; short gamma = collect theta but be exposed to sharp moves. Watch gamma in the last week before expiration.

2.3 Theta (Θ) — time decay

Definition: the change in option price for the passage of one calendar day, all else equal. Almost always quoted as a negative number for a long option.

Sign: Long options − (you lose value daily); short options + (you collect daily).
Magnitude: largest for ATM options; accelerates as expiration approaches.

Acceleration into expiry: because ATM extrinsic value decays with roughly √(time), the daily decay rate rises as expiration nears — modest at 60+ DTE, steep inside 21 DTE, severe in the final week. Deep ITM/OTM options have little extrinsic value, so their theta is small and flatter.

Theta is the premium-seller’s friend: sellers of extrinsic value are paid theta every day the underlying behaves. This is the engine behind credit spreads, iron condors, and covered calls. The trade-off is short gamma and short vega — you are paid to decay in exchange for taking movement and volatility risk.

Rule of thumb: premium sellers often favor the ~30–45 DTE window — meaningful theta without the worst of the near-expiry gamma. Theta and gamma are two sides of one coin: you cannot collect one without taking the other.

2.4 Vega (ν) — volatility sensitivity

Definition: the change in option price for a 1 percentage-point change in implied volatility (e.g., IV moving from 20% to 21%). Vega is not a Greek letter; it’s a sensitivity to IV.

Sign: Long options + (gain when IV rises); short options − (gain when IV falls).
Magnitude: largest for ATM options and for longer-dated options. Vega grows with time to expiration — LEAPS are highly vega-sensitive; 0DTE options barely respond to IV changes.

Who’s long vs short vega: option buyers and calendar/diagonal buyers are long vega (want IV up). Premium sellers — short straddles/strangles, iron condors, credit spreads — are short vega (want IV down, i.e., they profit from “IV crush,” §8).

Rule of thumb: sell vega when IV is high (IV Rank > 50), buy vega when IV is low (IV Rank < 30). A 30-day option might carry ~$0.05–0.15 of vega per share per IV point; a 1-year option, several times that.

2.5 Rho (ρ) — interest-rate sensitivity

Definition: the change in option price for a 1 percentage-point change in the risk-free interest rate.

Sign: Long calls +, long puts − (higher rates raise call values, lower put values, via the cost-of-carry on the forward). Short positions flip the sign.
Magnitude: usually the smallest and most ignored Greek for short-dated options. It matters for LEAPS and other long-dated options, where a rate change compounds over a long horizon and can move the premium meaningfully. Rate moves also subtly shift the forward price used to price all options.

Rule of thumb: ignore rho for weeklies and monthlies; account for it on 6-month-plus positions, especially in a changing-rate environment.

2.6 First-order Greeks summary

Greek	What it measures (sensitivity to…)	Sign if LONG the option	Sign if SHORT the option
Delta (Δ)	`$1` move in underlying	Call `+` / Put `−`	Call `−` / Put `+`
Gamma (Γ)	Rate of change of delta	`+` (call & put)	`−` (call & put)
Theta (Θ)	Passage of one day	`−`	`+`
Vega (ν)	+1 pt of implied volatility	`+`	`−`
Rho (ρ)	+1 pt of interest rates	Call `+` / Put `−`	Call `−` / Put `+`

Mnemonic for a long option holder: you are long gamma, long vega, short theta — you pay decay every day to own movement and volatility.

3. Second-order Greeks (brief, practical)

These measure how the first-order Greeks themselves move. You rarely trade them directly, but they explain “why did my delta change when nothing obvious happened.”

Vanna — sensitivity of delta to IV (equivalently, vega to spot). Why you care: your position’s delta shifts as IV moves even if spot is still — a vol spike can quietly hand a “delta-neutral” book real directional exposure.
Charm (delta decay) — sensitivity of delta to the passage of time. Why you care: it’s the delta bleed over a weekend or overnight — an OTM option’s delta drifts toward 0 (and an ITM’s toward ±1) just from time passing, so a hedged position needs re-hedging Monday morning.
Vomma (volga) — sensitivity of vega to IV; the “convexity” of vega. Why you care: it tells you how much your vega exposure grows as IV rises — long-vomma positions get more long-vega in a vol spike, which is what makes some long-volatility trades pay off explosively.
Speed — sensitivity of gamma to spot (the third derivative of price w.r.t. spot). Why you care: near expiry it warns you how fast your gamma itself is changing, so your hedge ratio can become unstable faster than gamma alone suggests.

4. Position Greeks & portfolio Greeks

4.1 Greeks add up

A position’s Greeks are the signed sum of its legs’ Greeks, scaled by quantity and the 100× contract multiplier. To get position delta: Σ (leg delta × ±contracts × 100). The same additivity holds for gamma, theta, vega, and rho. This is what lets you reason about a multi-leg structure as a single risk object.

4.2 Net Greeks of common structures (qualitative)

Structure	Net Delta	Net Gamma	Net Theta	Net Vega
Long call vertical (debit spread)	`+` (directional bullish)	slightly `+` near long strike	slightly `−` (pays decay)	slightly `+`
Iron condor (short strangle + protective wings)	~`0` (neutral)	`−` (short gamma)	`+` (collects decay)	`−` (short vega)
Calendar spread (sell front, buy back month, same strike)	~`0` at the strike	`−` near front expiry	`+` (front decays faster)	`+` (net long vega via back month)

Reading the table: the iron condor is the canonical neutral, short-gamma, positive-theta, short-vega premium-selling trade — it wants quiet markets and falling IV. The calendar is unusual because it’s positive-theta and long-vega, so it likes time passing and rising IV — the profile you want when IV is cheap but you expect a future vol expansion.

4.3 Beta-weighted delta

Raw deltas across different underlyings aren’t comparable — +50 delta in a low-beta utility ETF is not the same risk as +50 in a high-beta tech name. Beta-weighting restates every position’s delta in terms of an index equivalent (usually SPY):

Beta-weighted delta(position) = Δ_position × β(underlying vs index) × (S_underlying / S_index)

Summing beta-weighted deltas across the whole book gives a single number: “if SPY moves $1, my entire portfolio is expected to move $X.” It’s the standard way to see — and hedge — net directional risk at the portfolio level. Caveat: beta is an estimate from historical correlation and breaks down in stress (correlations converge toward 1 in a crash), so treat beta-weighted delta as a planning tool, not a guarantee.

5. Implied volatility

Implied volatility (IV) is the volatility input that, fed into an options pricing model, makes the model’s theoretical price equal the option’s observed market price. It is implied by the price — the market’s forward-looking, priced-in estimate of the underlying’s annualized volatility over the option’s life. Expressed as an annualized percentage standard deviation of returns.

IV vs historical/realized vol:

Historical / realized volatility (HV/RV) is backward-looking — the actual annualized standard deviation of returns the underlying already printed over some window (e.g., 20- or 30-day).
Implied volatility (IV) is forward-looking — what the market is charging for future uncertainty right now.

They frequently diverge. IV is a price (set by supply/demand for options), not a forecast guaranteed to come true.

The volatility risk premium (VRP): across most underlyings and over time, implied vol tends to run above subsequently realized vol. Option buyers systematically overpay (on average) for protection and lottery-like payoffs, and sellers earn a premium for bearing that risk. This structural edge is the reason premium-selling strategies have an expectancy tailwind — but it is an average, and it gets paid back violently during volatility spikes (the seller’s tail risk). The VRP is compensation for taking that risk, not a free lunch.

Expected move: the market’s priced-in one-standard-deviation range over a given horizon. The cleanest read is the ATM straddle (ATM call + ATM put):

Expected move ≈ ATM straddle price                      (rough, slightly overstates)
Expected move ≈ 0.85 × ATM straddle price               (common refinement)
Expected move ≈ S × IV × √(DTE / 365)                    (1-SD from IV directly)

The straddle price is the quickest field estimate (it bakes in the skew and the actual prices you’d trade).
The 0.85 × factor corrects for the straddle slightly overstating the true 1-SD move.
The S × IV × √(DTE/365) formula gives the theoretical ~68% (1-SD) range directly from IV; use DTE/365 for calendar days (some desks use trading days /252).

Example: S = $400, IV = 25%, DTE = 30 → expected move ≈ 400 × 0.25 × √(30/365) ≈ 400 × 0.25 × 0.287 ≈ $28.7, i.e., roughly a $371–$429 1-SD range over the month.

6. IV Rank vs IV Percentile

Both put current IV in context against its own trailing history (standard window: the past 252 trading days ≈ 1 year). A raw IV of “30%” is meaningless without knowing whether that’s high or low for this underlying.

IV Rank (IVR) — where current IV sits between its 1-year low and high, as a fraction of the range:

IV Rank = (IV_current − IV_low_52w) / (IV_high_52w − IV_low_52w) × 100

IV Percentile (IVP) — the fraction of days over the trailing year on which IV was below today’s level:

IV Percentile = (# trading days with IV < IV_current) / (total trading days) × 100

	IV Rank	IV Percentile
Measures	Position of current IV within its 52-week min–max range	Share of days IV was lower than now
Computation	One subtraction + division vs the year’s extremes	Count days below current, divide by total
Sensitivity	Dominated by the extremes — one spike year warps it	Reflects the full distribution of readings
Reads “high” when…	Current IV is near the year’s top	IV is higher than most days, even if not near the peak
Best for	Quick “are we cheap or rich vs the range?”	More robust “how unusual is today’s IV?”

How to use them (with the manual’s bands): treat IVR > 50 (or high IVP) as a green light to sell premium (short strangles, iron condors, credit spreads — collect rich extrinsic, short vega). Treat IVR < 30 (or low IVP) as a cue to buy premium or use debit/long-vega structures (calendars, long options) since options are relatively cheap.

Limitations of both:

Single-spike distortion (IVR especially): one extreme print (e.g., a crash) sets the 52-week high, so IVR can read “low” for months afterward even when IV is objectively elevated. IVP is more robust here because it uses the whole distribution.
Backward-looking window: a fixed 1-year lookback can miss regime changes; what was “high” last year may be normal now.
No directional or event context: a high IVR before a known binary event (earnings, FDA, election) is expected — selling into it without sizing for the event is how sellers blow up. Neither metric tells you why IV is where it is.
Underlying-specific: never compare IVR/IVP across tickers as if equal; each is relative to its own history.

7. The volatility surface: term structure & skew

Real markets do not price every strike and expiration off a single IV. The volatility surface is IV plotted across both strike (skew/smile) and expiration (term structure).

7.1 Term structure (IV across expirations)

Contango (normal/upward-sloping): longer-dated options carry higher IV than near-dated. This is the default calm-market shape — more time means more uncertainty, so more vol is priced in. Calendar spreads (long back month) are natural here.
Backwardation (inverted/downward-sloping): near-dated IV exceeds longer-dated. This signals stress or an imminent event — a market selloff, or a front-month spike ahead of earnings where the expiration capturing the event is bid up far above later cycles. It implies the market expects a near-term shock that subsides afterward.

Reading the slope tells you when the market expects turbulence. A steep front-month bump that flattens after an event date is the fingerprint of a scheduled catalyst.

7.2 Vertical skew / smile (IV across strikes, same expiration)

Plot IV against strike for one expiration and you rarely get a flat line:

Equity index put skew (the classic shape): OTM puts trade at higher IV than ATM, which in turn is higher than OTM calls — a downward-sloping “smirk.” In equities/indices, downside puts are systematically richer.
Why it exists: persistent demand for crash protection (portfolio hedging), the empirical fact that equities fall faster than they rise (vol and price are negatively correlated — markets gap down, drift up), and the leverage effect. Buyers pay up for tail insurance, so OTM put IV stays elevated.
Smile vs smirk: some assets (commodities, FX, single stocks with takeover/upside potential) show a more symmetric smile (both tails bid). Equity indices show a put smirk.

How skew affects spread pricing and strategy choice:

Selling a put credit spread below the market means you’re selling the richer (higher-IV) put strikes — skew is in your favor, you collect more premium for the same distance.
Risk reversals / ratio structures are built specifically to harvest or hedge skew (sell the rich OTM put, buy the cheaper OTM call, or vice versa).
Broken-wing butterflies and asymmetric condors lean on skew to take in extra credit or eliminate one side’s risk.
When you buy an OTM put for protection, recognize you’re paying the skew premium — it’s expensive because everyone wants it.

8. Earnings & IV crush

Around scheduled earnings (and other binary events), IV behaves predictably enough to be its own playbook:

IV ramp into the event: as earnings approach, uncertainty about the post-report move is concentrated into the front expiration, so front-month IV inflates in the days/weeks beforehand (this is the term-structure backwardation of §7.1). Extrinsic value swells even though the underlying may be quiet.
IV crush after the event: the moment results are released, the uncertainty resolves and IV collapses — often dropping the bulk of the run-up in a single session. Extrinsic value evaporates regardless of which way the stock moved.

Why short premium / calendars like the crush:

Short premium (short straddle/strangle, iron condor) sold before earnings collects the inflated extrinsic and profits from the post-event vega collapse — provided the actual move stays inside the expected move. The danger is that the realized move exceeds the priced-in move (gamma risk on a binary event).
Calendars sell the crushed front-month while owning the steadier back month, profiting from the differential IV collapse across expirations.

Why long single options usually suffer: a trader who buys a call or put before earnings pays the inflated IV. Even if the stock moves the right direction, the IV crush can wipe out the vega loss faster than delta gains it back — the stock has to move more than the expected move just to break even. This is the classic “I was right on direction and still lost money” earnings trap.

Tie to expected move: the pre-earnings ATM straddle is the market’s expected move (§5). Long-option buyers need a move larger than that straddle to win after crush; short-premium sellers win if the move is smaller. The straddle price is the breakeven the whole event trades around.

9. Reading an option chain

Field	Meaning
Bid	Highest price a buyer will pay — where you sell (the “natural” sell).
Ask (offer)	Lowest price a seller will accept — where you buy (the “natural” buy).
Mid	`(Bid + Ask) / 2` — the theoretical fair midpoint; your initial limit target.
Mark	The broker’s estimated fair value (often = mid, sometimes model-adjusted); used for P&L and margin.

Natural vs mid fills: paying the natural (lift the ask / hit the bid) guarantees a fill but pays the full spread. Working a mid (or just inside it) gets a better price but may not fill — you’re negotiating with the market maker. On multi-leg orders, price the net debit/credit at mid and work it.

Spread width as a liquidity signal: a tight bid/ask (a few cents, or a small % of premium) signals a liquid, competitively-quoted strike. A wide spread signals illiquidity — you’ll lose more to slippage on every entry and exit, and mid prices are less trustworthy.

Open interest (OI) vs volume:

Open interest = total contracts currently outstanding (cumulative, updated next day). High OI = an established, liquid market at that strike.
Volume = contracts traded today (resets daily). High volume = active interest right now.
You want both healthy at the strikes you trade. High OI with thin volume can still be tradable; low OI and low volume is a red flag.

Spotting illiquid strikes: wide bid/ask, low/zero OI, low volume, and “stale” quotes that don’t update. Far OTM strikes, far-dated expirations, and non-standard strikes are usually the thinnest. Avoid them, or expect poor fills and difficulty exiting.

Slippage and limit orders: slippage is the gap between your expected price and your actual fill. Market orders on options are dangerous — a wide spread means a market order can fill far from mid, and a single bad fill can erase the edge of a whole trade. Always use limit orders (net-debit/credit limits for spreads). The wider the spread, the more this matters.

10. Assignment, exercise & settlement mechanics

10.1 Exercise style

American (most US equity/ETF options — SPY, QQQ, IWM, single stocks): can be exercised any time before expiration → real early-assignment risk for short options.
European (most cash index options — SPX): can be exercised only at expiration → no early assignment.

10.2 Automatic exercise-by-exception

At expiration, the OCC automatically exercises options that are ITM by at least $0.01 (“exercise by exception”), and most brokers follow this default. If you’re short, you can be assigned on anything that finishes a penny ITM. Implication: close or roll positions you don’t want exercised/assigned before expiration — don’t rely on a near-the-money option expiring worthless.

10.3 Early-assignment drivers (American options)

Early assignment is driven by the option’s extrinsic value going to ~zero, making exercise rational for the long holder:

Short ITM calls before an ex-dividend date: if the dividend exceeds the call’s remaining extrinsic value, long holders exercise early to capture the dividend → you get assigned and are short the shares, owing the dividend. This is the single most common early-assignment event; watch ex-div dates on any short ITM call.
Deep-ITM short puts: when a put is deep ITM with negligible extrinsic value (and as carry/rate dynamics favor it), holders exercise early to realize cash → you’re assigned and buy the shares at the strike.
General rule: the less extrinsic value a short ITM option has, the higher its early-assignment risk.

10.4 Pin risk

Near expiration, when the underlying sits right at a strike, a short option holder doesn’t know whether they’ll be assigned (it could close fractionally ITM or OTM, and assignment is somewhat unpredictable at the pin). You can end expiration weekend unsure whether you’ll have a stock position Monday — an unhedged, unexpected long/short share position with gap risk over the weekend. Manage by closing at-the-strike short options before expiration.

10.5 Settlement: cash vs physical

Physical settlement (SPY, QQQ, IWM, single-name options): exercise/assignment delivers actual shares. Assigned short call → you deliver 100 shares (or go short 100). Assigned short put → you buy 100 shares at the strike. Your account shows the share position plus the cash for the strike value.
Cash settlement (SPX and other index options): no shares change hands. At expiration the ITM amount is paid/charged in cash against the settlement value, and the position simply closes. No pin risk in the share sense, no early assignment.

10.6 AM vs PM settlement

PM-settled: settlement value is based on the close on expiration day (standard for ETF options and most equity options, and for SPX weeklys/EOM).
AM (a.m.-settled): settlement value is based on a special opening quotation (SOQ) built from each component’s opening price on expiration morning — used for the traditional 3rd-Friday SPX contract and some other index settlements. The SOQ can differ materially from where the index actually opens or traded, creating “settlement risk”: your final mark is set by prints you never saw and can’t trade against. Know which settlement your index contract uses before holding it into expiration.

10.7 What actually happens to your account on assignment

Assigned short put (physical): cash is debited for strike × 100 × contracts; 100 shares per contract appear long in your account. If you lacked the cash, you incur a margin debit / margin call.
Assigned short call (physical): you deliver 100 shares per contract at the strike; cash is credited for strike × 100. If you didn’t own the shares (naked/short call), you become short 100 shares per contract.
Covered call assigned: your existing 100 shares are called away at the strike; you keep the premium and any gain up to the strike.
Cash-settled (SPX) ITM at expiry: account is credited/debited the cash intrinsic difference; nothing else happens.

11. Margin, buying power & the PDT rule

11.1 Account types

Cash account: every position must be fully paid for in cash; no leverage. You can buy options and sell cash-secured puts or covered calls, but cannot sell naked/undefined-risk options. Proceeds from a sale aren’t available until settlement, and there’s no PDT rule — but you must respect settlement (no “good-faith”/free-riding violations).
Reg-T margin account: the standard leveraged retail account under Federal Reserve Regulation T. Allows naked/undefined-risk option selling and uses strategy-based margin — fixed formulas per position type. Buying-power reduction is computed position-by-position. Most retail option sellers operate here; subject to the PDT rule.
Portfolio margin (PM): a risk-based margin regime (typically requires ~$125k+ equity and approval) that computes buying-power reduction from the net risk of the whole portfolio under a range of simulated market moves, rather than per-position formulas. It is far more capital-efficient for hedged/diversified books (offsetting positions reduce the requirement) — but the leverage cuts both ways, and PM accounts can take large hits in a fast, correlated selloff.

11.2 Buying-power reduction: defined vs undefined risk

Defined-risk positions (debit spreads, iron condors, butterflies — anything with a long protective leg capping the loss): buying-power reduction ≈ the maximum possible loss = (spread width − net credit) × 100 per contract for a credit spread, or the net debit for a debit spread. Predictable and capital-light.
Undefined-risk positions (naked short puts/calls, short strangles): buying-power reduction is formula-based and much larger, sized to a worst-case move rather than a known max loss. A typical Reg-T naked-option requirement is roughly:
```
BPR ≈ max( 20% × underlying value − OTM amount, 10% × underlying value ) × 100 + premium
```
(broker formulas vary; for short puts the “underlying value” leg is often based on the strike). The takeaway: an undefined-risk short can tie up several times the capital of a comparable defined-risk spread, and the requirement grows as the position moves against you (potential margin calls). This is the core reason defined-risk structures dominate retail premium selling.

11.3 The Pattern Day Trader (PDT) rule

A day trade = opening and closing the same position on the same trading day. Under FINRA rules, an account flagged as a Pattern Day Trader — 4 or more day trades within 5 business days on a margin account — must maintain at least $25,000 in equity. Fall below that and you can be restricted from day trading (and may receive an equity call) until you’re back above the threshold or 90 days pass.

How it bites options traders specifically:

Each option leg opened and closed same-day can count as a separate day trade — closing both legs of a spread you opened that morning can burn two day trades, so the 4-trade budget vanishes fast.
Getting assigned and then selling the resulting shares same day can count as a day trade.
It applies to margin accounts under $25k; a cash account sidesteps PDT entirely (at the cost of leverage and settlement timing).
Practical effect for sub-$25k accounts: you must plan to hold overnight or strictly ration in-and-out trades — clumsy management of a multi-leg position can trip the flag unintentionally.

How to use this reference with the rest of the manual

Treat this module as the shared vocabulary the strategy modules build on. Before evaluating any specific strategy, anchor on three things from here: (1) the IV regime — is IV Rank < 30 (favor buying/long-vega, debit and calendar structures) or > 50 (favor selling/short-vega, credit spreads and condors)?; (2) the position’s net Greeks — what is its delta, theta, vega, and gamma exposure, and does that match your thesis and the IV regime?; and (3) the mechanics that govern the exit — assignment style, settlement (cash vs physical, AM vs PM), early-assignment triggers, and the margin/PDT constraints of your account. The strategy modules will tell you what to trade and when; this module tells you why the Greeks and IV behave as they do and what will actually happen to your account when a position resolves. When a strategy module cites “expected move,” “IV crush,” “short gamma,” “beta-weighted delta,” or “early assignment,” the precise definition lives here.