# Difference between binary and barrier options

While it seems straightforward to define a barrier event as "underlying trades at or above a given level," in reality it's not so simple. What if the underlying only trades at the level for a single trade?

How big would that trade have to be? Would it have to be on an exchange or could it be between private parties?

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.

Barrier options are sometimes accompanied by a rebate , which is a payoff to the option holder in case of a barrier event. Rebates can either be paid at the time of the event or at expiration. Barrier options can have either American , Bermudan or European exercise style. The valuation of barrier options can be tricky, because unlike other simpler options they are path-dependent — that is, the value of the option at any time depends not just on the underlying at that point, but also on the path taken by the underlying since, if it has crossed the barrier, a barrier event has occurred.

Although the classical Black—Scholes approach does not directly apply, several more complex methods can be used:. From Wikipedia, the free encyclopedia. A barrier option is an option whose existence depends upon the underlying asset's price reaching a preset barrier level Contents. Energy derivative Freight derivative Inflation derivative Property derivative Weather derivative. Retrieved from " https: There are other types of digital options available within the FINCAD library, including various flavors of double barrier binary options.

Introduction A Binary Barrier Option is a type of digital option for which an option's payout depends on whether or not the asset touched a barrier level at some time during the life of the option.

Technical Details There are two classes of binary barrier options. Calculate the fair value, risk statistics and probability of hitting the barrier for a binary barrier option with a payoff equal to the asset value if the barrier is touched, or nothing if the barrier is never touched. Calculate the fair value, risk statistics and probability of hitting the barrier for a binary barrier option with a payoff of a fixed amount of cash if the barrier is touched, or nothing if the barrier is never touched.

Calculate the fair value, risk statistics and probability of hitting the barrier for a knock-in binary barrier call or put option with a payoff equal to the value of the asset if the barrier is touched and the option is in the money. Calculate the fair value, risk statistics and probability of hitting the barrier for a knock-in binary barrier call or put option with a payoff of a fixed amount of cash if the barrier is touched and the option is in-the-money.

Calculate the fair value, risk statistics and probability of hitting the barrier for a binary barrier option with a payoff equal to the value of the asset if the barrier is not touched, or nothing if the barrier is touched. Calculate the fair value, risk statistics and probability of hitting the barrier for a binary barrier option with a payoff of a fixed amount of cash if the barrier is not touched, or nothing if the barrier is touched.

Calculate the fair value, risk statistics and probability of hitting the barrier for a knock-out binary barrier call or put option with a payoff equal to the value of the asset if the barrier is not touched and the option is in the money at expiry, or nothing if the barrier is touched. Calculate the fair value, risk statistics and probability of hitting the barrier for a knock-out binary barrier call or put option with a payoff of a fixed amount of cash if the barrier is not touched and the option is in the money at expiry, or nothing if the barrier is touched.

Calculate the fair value, delta, and probability of hitting the barrier for a path dependent digital option where the payoff is on the expiration date. Calculate the fair value, delta, and probability of hitting the barrier for a path dependent digital option where the payoff is made at the time the barrier is touched. The next generation of powerful valuation and risk solutions is here. Portfolio valuation and risk analytics for multi-asset derivatives and fixed income.