Put option

A contract defined by four terms: the underlying it references, the strike price at which the underlying may be sold, the expiry date, and the style, which decides whether the right may be used at any time up to expiry or only at it. The buyer pays a premium and holds the right. The seller, called the writer, receives that premium and carries the obligation to buy at the strike if the right is used. Many contracts settle the difference in cash rather than delivering anything.

The premium divides into two parts. Intrinsic value is the strike less the price of the underlying where that difference is positive, and nothing where it is not. Everything above intrinsic value is time value, which reflects how long is left and how much movement is expected over that time, and which decays to nothing by expiry however the underlying behaves. Sensitivities to each input are named with Greek letters, among them delta for the underlying's price and vega for expected movement, and the volatility figure quoted against a contract is implied by its traded price rather than observed in the market.

The asymmetry is the point and the trap at once. A buyer's loss is limited to the premium, but the premium is lost in full whenever the contract expires without intrinsic value, which is the ordinary outcome for a contract that finishes out of the money, and time decay works against the holder every day it is held. A writer's position is the mirror: a bounded premium received against a loss bounded only by the underlying falling towards nothing. The description of a put as insurance holds for the shape of the payoff and fails on cost, since the premium is paid whether or not the protection is used and is repriced each time the cover is renewed. A contract for difference is a different instrument entirely: it carries no strike, no premium and no expiry, and its loss is not limited to an amount paid at the outset.