Options, strikes and open interest
An option is a contract. A standard stock or ETF call gives its owner the right to buy 100 shares at a fixed price, called the strike, until the option expires. A put gives the right to sell 100 shares at the strike. The buyer pays a price, the premium, to the seller.
Index options such as SPX, NDX and RUT work a little differently. There are no shares to deliver, so they settle in cash: at expiry the owner receives the in-the-money amount times a multiplier of $100 per index point.
Open interest is the number of contracts that are still open at a given strike and expiration: opened by a trade and not yet closed, exercised or expired. The clearinghouse, OCC, counts it once a day. Open interest tells you how much is outstanding. It does not tell you who holds the contracts or which way they are positioned.
An option is in the money when exercising it now would be worth something: a call with its strike below the current price, or a put with its strike above it. At the money means the strike is close to the current price. Out of the money means exercising now would be worth nothing, so the option's value is all time value.
Five sensitivities
Delta is how much the option's price changes when the stock moves $1. A call's delta runs from 0 to 1 and a put's from −1 to 0. Gamma is how much delta itself changes when the stock moves $1. Theta is the change in value from one day passing. Vega is the change in value when implied volatility moves one point, for example from 20% to 21%. Rho is the change when interest rates move.
Example: a call with a delta of 0.50 gains about $0.50 per share when the stock rises $1. One contract covers 100 shares, so that is about $50. If its gamma is 0.04, its delta becomes about 0.54 after that $1 rise, and the next $1 adds a little more.
Owning an option and selling one have opposite signs. A long call has positive delta and a long put negative delta. Long calls and long puts both have positive gamma and positive vega; the seller of either holds negative gamma and negative vega. That sign rule is what the rest of this library depends on.
Dealers and hedging
A dealer, or market maker, is a firm that quotes prices and takes the other side of customer trades. Dealers earn the spread between buying and selling. They do not want to bet on direction, so they hedge: they take an offsetting position, usually in the stock or its futures, so that small price moves leave them roughly flat. A position hedged this way is called delta-neutral.
As the price moves, the option's delta changes (that is gamma at work), so the hedge has to be adjusted. Those adjustments are trades in the underlying market, and they are the subject of most of this library.
One caveat: delta is sometimes read as the odds of finishing in the money. It is only a rough guide. Finishing in the money, touching the strike before expiry, and making a profit are three different events.