Options glossary · 79

Every term from the course, defined the way a market maker uses it

The vocabulary of the Options Course with Sven Hubens, ten years an options market maker at Optiver and Maven. Short definitions in his words, grouped in the order a desk learns them. The worked examples, the desk figures and the full formula sheet are in the course.

Part 1 · Option basics and use cases
Part 2 · Option pricing
Part 3 · Market making
Part 4 · Positional volatility trading
Part 5 · Going for the trading job

Part 1

Option basics and use cases

The contract

Call option: The right, not the obligation, to buy the underlying at the strike. Exercised only when the underlying is above the strike.
Put option: The right, not the obligation, to sell the underlying at the strike. Exercised only when the underlying is below the strike.
Contract size: One option is one hundred shares. A quoted option price is per share, so the cost of a contract is the price times one hundred, and exercising a call means buying one hundred shares at the strike.
American option: Exercisable any time before expiry. Stock options are nearly always American. Early exercise is mostly rational just before a large dividend, because the call holder does not receive the dividend and the stockholder does.
European option: Exercisable only at expiry. Index options typically. The course treats everything as European.
Cash settlement: Settled in cash rather than by delivery, as Eurostoxx options are, since delivering the whole basket of shares would be impractical.
Physical settlement: Settled by delivery of the underlying, or of a future that later becomes stock, as with S&P options.

Value

Intrinsic value: What the option is worth if exercised right now.
Extrinsic value: Everything above intrinsic: what you pay for the chance that the option ends further in the money. Also called time value.
Option value: Intrinsic value plus extrinsic value. Every option price splits into those two parts.
In, at and out of the money: The strike beyond spot in your favour, at spot, or against you. At the money carries the most extrinsic value and the largest Greeks.

The Greeks

Delta: The change in option value per one point move in the underlying. Quoted against the contract size, so a delta of 0.2 is called delta 20 and hedging it means selling twenty shares. An at-the-money call sits around delta 50; deep in the money tends to 100, deep out of the money to 0.
Gamma: The change in delta per one point move in the underlying, the second derivative with respect to the underlying. Calls and puts of the same strike share it. Largest at the money, where the outcome is closest to a coin flip.
Theta: The change in option value per day that passes. Always negative for a long option: you pay it for the chance the option gives you.
Vega: The change in option value per one point change in implied volatility. The Greek a volatility trader lives by.
Rho: The change in option value per move in the interest rate. The smallest of the five Greeks for short-dated options.
Theta scales with the square root of time: Four times the time to expiry is roughly half the daily theta, so decay accelerates as expiry approaches. The same at-the-money position pays about twice the daily theta with one day left as it does with four.
Gamma P&L is quadratic: The profit from gamma goes with the square of the move: a two percent move makes four times what a one percent move makes.
Gamma scalping: Hedging long gamma on the moves: sell into a rise, buy into a fall. It makes money on movement and pays theta to do it.
Short gamma: The mirror image of gamma scalping: buy into a rise, sell into a fall, so buy high and sell low. Loses on movement, collects theta.

Part 2

Option pricing

The six inputs

Underlying price: Where the asset trades now. The first input to any option price.
Strike price: The exercise level of the option: the price at which a call buys or a put sells the underlying.
Time to expiry: How long is left until the option expires, measured in years for the formulas: days divided by about 252 trading days.
Interest rate: Pushes the forward above spot: holding the underlying costs money, and the option is priced off the forward, not off spot.
Dividends: Leave the stock on the pay date and pull the forward down by the same amount. A dividend of a given size takes exactly that out of the stock.
Implied volatility: The annualised volatility the market expects until expiry, expressed as a standard deviation of the yearly return. It is not the expected move. The input with the most uncertainty, and the one you can hold a real opinion on.

Formulas

Forward price: Where the underlying is priced for a future date: spot plus the interest to carry it, minus the dividends paid in the meantime.
Cost of carry: Interest rate and dividends together: what it costs to hold the underlying, and so where the forward sits against spot.
Expected move: The average absolute move the market is pricing, which is smaller than the standard deviation. Twenty percent implied volatility is an expected move of about sixteen percent over the year.
Expected daily move: The yearly expected move divided by the square root of the number of trading days. At twenty percent implied volatility that is about one percent a day.
The straddle approximation: The price of an at-the-money straddle from the underlying, the implied volatility and the time, close enough to do in your head. The 0.8 is the same 0.8 that turns a standard deviation into an expected move. Straddles scale with the square root of time: two days is not twice one day, it is about 1.4 times.
Straddle: A call plus a put on the same strike. A bet on movement in either direction, and the cleanest way to trade volatility.

The model

Black-Scholes: Prices an option from a distribution of outcomes and their probability-weighted payoff. Given a volatility it returns a price; given a price it returns an implied volatility. The first term is the present value of the underlying multiplied by the chance it ends in the money.
Black-Scholes limitations: It assumes continuous trading, which the closing bell rules out. It assumes one volatility, one distribution shape and no jumps. It is still used as a common language and a starting point: firms begin with it and build over the top, correcting the assumptions that hurt them most.
Skew: The volatility curve across strikes. Downside puts trade above upside calls in equities, because markets grind up and fall hard, and black swans occur more often than a normal distribution allows.
Volatility surface: Implied volatility across every strike and every expiry, the full map of what the market is pricing.

Part 3

Market making

Quoting

Market maker: A firm quoting two-sided prices continuously, earning the spread and managing what it accumulates.
Theoretical value (theo): Your own fair value for the option. Everything you show to the market is derived from it.
Credit: The amount either side of theo that your quote sits at: it is what you earn for taking the other side.
Automated quoting (AQ): The system publishing your bid and offer continuously from the theo, so a desk can quote thousands of options at once.
Retreating: After a trade, moving your theo to the last traded price. Leaving theo where it was while trading through it books paper profits that are not real.
Quote width: Set by the market, not by you. If everyone shows a one-point market, a six-point quote is a joke quote that never trades.
Screen and broker markets: The exchange order book, and prices shown to a broker by phone or chat. Broker trades earn more credit and bring information, and are still crossed on screen afterwards.

Hedging and risk

Delta hedge: Trading the underlying against an option position so the combined delta is flat. Buy a call with delta 25 and sell twenty-five shares against it.
Hedge frequency: How often a desk re-hedges its delta, set by choosing a move size rather than a clock: to hedge n times a day, take the expected move over one nth of a day and hedge every time the underlying moves that far. Higher volatility does not mean more hedges, you just wait for a bigger move first.
Vega P&L: What a position makes or loses when implied volatility moves.
Theta limit: A cap on how much daily decay a book may carry, so a desk cannot quietly bleed more than it has agreed to.
Vega limit: The maximum volatility exposure a book may run. In practice a desk runs near the top of it only when the conviction is strong.
Left-over position: What you cannot trade out of by the close, because crossing the book everywhere is too expensive. You decide whether to carry it, against your limits.
Correlated hedging: Offsetting risk in a related product rather than doubling up in the same one, for instance buying Eurostoxx options against a short S&P position.
Position stacking: Short volatility and short puts is the same bet twice, since short volatility usually goes wrong on a downtick. Sell calls instead.

Analysis

Strike P&L: Profit and loss by strike: where the position actually is. One of the two reports that matter most on a desk.
Short-term trade metrics: How the quoting systems perform trade by trade. The other report that matters most.
Broker trade quality: Which brokers bring good flow. Good flow is a hedger who wants the puts and is not fighting you on volatility.
Base volatility: At-the-money implied volatility with the event premium stripped out.
Realised volatility: What the underlying actually did, against which implied volatility is judged.

Part 4

Positional volatility trading

The trade

Positional trading: Taking a view on volatility and holding it rather than quoting back and forth. Days to weeks.
Within and between products: Relative value across strikes or expiries of one underlying, or across two underlyings.
Volatility spread: Long volatility in one product against short volatility in another, sized so the vega on each side matches. Executed by lifting the market makers across the strikes that matter, so small moves do not force a rebalance.
Correlation requirement: The two legs of a spread must move together enough that the pair actually spreads risk. Two bond markets under two central banks are correlated, but not perfectly, because the ECB and the FOMC are not the same.

Sizing and analysis

Volatility ratio: One implied volatility divided by another, tracked over its history. Implied over realised for the same product is another way of reading the same thing.
Z-score and percentile: How far the spread sits from its own history. The ninetieth or ninety-fifth percentile is a signal, not a certainty.
Edge and realisable profit: The edge on paper is the mispricing times the size. You never capture all of it, because the position has to survive first.
Leg sizing: Making one side of the spread larger on a view. If overall volatility is low, size the long leg bigger.
Regime analysis: How the same event behaved under different conditions, high inflation or a wild tape, rather than on average.

What goes wrong

Correlation breakdown: A tech crash hits the S&P far harder than a European index weighted to old industry. The relationship fails exactly when the position is largest.
The re-entry test: If you held nothing right now, would you put this position on? If not, cut it, unless cutting costs too much.
Opportunity cost: The real cost of a losing position is the risk it consumes, which stops you taking anything else.
Illiquid legs: Little volume means long holding periods, and the holding period determines when profits are realised.
Trading too much: Positional trading means waiting, sometimes for days. Most traders trade too much.

Part 5

Going for the trading job

The process

CV selection: Ten to thirty seconds of attention. Study programme, plus anything that shows you commit to something and get good at it: trading projects, algorithms, workshops, results in sport.
Online assessment: Timed numerical and logical tests, usually the first filter.
HR interview: Motivation and cultural fit: whether they have confidence you will deliver.
Technical interview: Market making exercises, mental arithmetic, probability and brain teasers, deliberately under time pressure. The bottleneck of the process.
Final assessment day: On site with the desk. Genuine interest in markets, and whether you fit the team.

What firms select on

Numerical ability under pressure: Not just the answer, but the answer while being pushed.
Decision making with incomplete information: Committing to a price and revising it as new information arrives.
Cultural fit: Work ethic, and whether the desk wants you next to them for a decade.
Genuine interest: Following markets because you want to, not because the interview is next week.