This approach gives explicit (closed form) prices to barrier options.

Specifically, it is a barrier option of the Down and Out type.

Thus, barrier options were created to provide the insurance value of an option without charging as much premium.

Barrier options are always cheaper than a similar option without barrier.

The four main types of barrier options are:

Barrier options can have either American, Bermudan or European exercise style.

There are other barrier options.

In case of a single barrier option we use the same PDE with either or .

In-out parity is the barrier option's answer to put-call parity.

(For example, a knockout call can be "manufactured" out of standard options; see Barrier option.)

Barrier options are path-dependent exotics that are similar in some ways to ordinary options.

Barrier options are sometimes accompanied by a rebate, which is a payoff to the option holder in case of a barrier event.

When an exact formula is difficult to obtain, barrier options can be priced with the Monte Carlo option model.

Fiorani presents numerical solutions for European and American barrier options under variance gamma process.

He also provides computer programming code to price vanilla and barrier European and American barrier options under variance gamma process.

Barrier option - any option with the general characteristic that the underlying security's price must pass a certain level or "barrier" before it can be exercised.

Liquidity option: "Knock-in" barrier option, where the barrier is a liquidity metric.

If we combine one "in" option and one "out" barrier option with the same strikes and expirations, we get the price of a vanilla option: .

A turbo warrant is a barrier option namely a knock out call that is initially in the money and with the barrier at the same level as the strike.

A barrier option involves a mechanism where if a 'limit price' is crossed by the underlying, the option either can be exercised or can no longer be exercised.

When barrier options were first introduced to options markets, many banks had legal trouble resulting from a mismatched understanding with their counterparties regarding exactly what constituted a barrier event.

This approach was pioneered by Peter Carr and gives closed form prices and replication strategies for all types of barrier options, but usually only by assuming that the Black-Scholes model is correct.

A Parisian option is a barrier option where the barrier condition applies only once the price of the underlying instrument has spent at least a given period of time on the wrong side of the barrier.

In finance, a barrier option is an exotic derivative typically an option on the underlying asset whose price breaching the pre-set barrier level either springs the option into existence or extinguishes an already existing option.

A Commodore option is an exotic option consisting of a number of digital barrier options that pay a coupon if a pre-determined level of the Underlying or Basket of Underlyings is reached.