Options in depth

Delta: the share-equivalent

An option’s delta puts a number on the exposure Lesson 16 described but did not measure: how much this ticket actually moves when the stock moves a dollar? A call with a delta of 0.40 gains roughly forty cents for the stock’s first dollar up — it behaves, for small moves, like owning 40 shares. Delta is therefore an exposure translator: ten contracts of that call are not ‘ten options’, they are approximately 400 shares of the underlying’s movement, with the premium as the stake. Position sizing (Lesson 19) that ignores delta is sizing the ticket instead of the exposure.

Delta also moves — it grows as the stock rises toward and past the strike, shrinks as it falls away — and that movement has a name (gamma) and a character: options accelerate. The practical consequence for this desk’s readers is simpler than the Greek: the exposure you bought is not the exposure you hold a week later. Delta is a reading to re-take, not a fact to file.

Why this matters on a work schedule: an option’s exposure is not printed on its ticket the way a share count is — it has to be computed, at a desk you are not sitting at. A position whose real size you have not computed is a position you sized by accident.

Implied volatility reprices the ticket

Lesson T2’s second half, now with money on it. Premium = intrinsic value (what the ticket is worth if exercised now) plus time value, and time value is mostly implied volatility wearing a suit. When IV rises — into an earnings print, a market scare — tickets inflate with the stock standing still; when it collapses after the event, tickets deflate the same way. A buyer can therefore be right about direction, right about timing, and still lose: they bought the pre-print premium, and the crush (T2) returned the insurance portion to the seller the morning after.

The working rule this produces is not ‘avoid options’; it is ‘know which part of the ticket you are paying for’. Long-dated options (the LEAPS read of Lesson 16) carry more IV exposure, not less — vega grows with time — but they carry it over far more time, so a single event’s crush is a smaller fraction of a two-year ticket than of a two-week one: one honest reason the desk’s options vehicle is the slow one.

Spreads: construction, not courage

A vertical spread pairs two tickets: buy a call, and sell a further call against it, same expiry. The sold call’s premium offsets part of the bought call’s cost, and in exchange the gain is capped at the higher strike. What the construction produces, mechanically, is a position whose maximum loss and maximum gain are both known to the dollar on day one — at expiry, with both legs settled as planned: the loss can never exceed the net premium paid (the debit), and the gain can never exceed the strikes’ width minus that debit. Defined on both sides — which is why this lesson teaches spreads as construction: a way of fencing an idea, taught as mechanics, never as a recommendation of any particular fence.

Contrast the naked ticket of Lesson 16, whose buyer’s loss is also capped (at the premium) but whose gain is open. The spread trades some of that open gain to buy down the stake and soften the IV and time-decay exposure (the sold leg suffers the same decay the bought leg does, in the holder’s favor for once). It is a different instrument built from the same parts, and understanding the trade — less stake, less decay, capped gain — is the entire lesson. Which construction fits a given idea is the trader’s process (Lesson T6), not this page’s business.

Three precisions ride with every figure in this lesson. The multiplier: one listed contract covers 100 shares, so every per-share number — debit, width, maximums — multiplies by 100 per contract. The maximums are expiry values: the table below prices the spread at expiration, with both legs intact; before expiry its market price also breathes with implied volatility and the calendar. The mirror construction is the credit spread: sell the nearer ticket, buy the further one, and take money in instead of paying it out — its maximum gain is the credit kept, its maximum loss the width minus that credit. Same fences, entered from the other side; which structure is debit and which credit is decided by which leg is bought and which sold, never by optimism.

And two limits the fences do not remove. The sold leg can be assigned early — American-style options may be exercised by their holder at any time, most often around dividends or when deep in the money — which can leave the spread holder owning or owing shares mid-flight. And at expiry, a stock closing between the strikes (pin risk) can see one leg exercised and the other lapse, converting a fenced spread into an open stock position over a weekend. Defined risk describes the construction at expiry with both legs settled as planned; the path between here and there is the operator’s to manage.

The Greeks are a dashboard, not a cockpit

Delta, and its siblings the desk will name without worshipping — gamma (delta’s speed), theta (Lesson 16’s time decay, measured per day), vega (the ticket’s sensitivity to IV) — are best understood as a dashboard: gauges that tell you what your position is exposed to, in numbers, before the market tells you in dollars. A reader who can say ‘this ticket is 40 shares of exposure, loses $11 a day to the calendar, and is long the crush’s wrong side into a print’ understands their option. A reader who cannot is holding a lottery ticket with a syllabus.

That sentence is the track’s whole ambition for options: not tactics, but the ability to read the instrument’s exposures in plain language and price them against the risk plan. The plan page (Lesson 22) does not care which vehicle expressed the idea. It cares that the planned maximum loss was known, sized, and survivable. On that standard, an honest spread and an honest stock position are the same citizen.

Where this breaks

Every maximum in this lesson is an expiry value with both legs settled as planned — and expiry is not the only way a spread ends. The sold leg can be assigned early, most often around dividends or when deep in the money; a stock closing between the strikes (pin risk) can leave one leg exercised and the other lapsed, converting the fence into an open stock position over a weekend. Before expiry, the spread’s price also breathes with implied volatility and the calendar, so its live value can sit well away from the expiry table.

Practice

One fictional spread, on paper. With a stock at $52: buy the $50 call for $4.20, sell the $55 call for $0.70 — one contract of each. (1) Is the construction a debit or a credit spread, and what is the net per share? (2) At expiry, with both legs settled as planned: the maximum loss and the maximum gain, per contract. (3) The long call’s delta is 0.40: roughly how many shares do three contracts of it behave like, for small moves? (4) In one sentence: name a way the realized result can escape the tidy expiry maximums.

Answers: (1) A debit spread — you pay to open it: $4.20 − $0.70 = $3.50 a share. (2) Maximum loss = the debit × 100 = $350; maximum gain = the $5 width minus the debit, × 100 = $150. (3) 0.40 × 100 shares × 3 contracts = about 120 shares. (4) Early assignment on the sold leg, or pin risk at expiry, can settle one leg differently than planned and convert the fence into an open stock position.