Barrier Options Primer

Option barrire : - Loption barrire activante appele knock-in option une valeur lchance dpendant du fait que le sous-jacent atteigne ou non un certain niveau de cours dite barrire, pendant la dure de vie de loption. Loption nest active que si elle atteint la barrire, lchance sa valeur est la mme quune option standard, mais elle cote moins chre quune option plain vanilla puisque plus risque. - Loption barrire dsactivante appele knock-out option fonctionne de la mme manire que loption barrire activante sauf que loption barrire est dsactive lorsque lactif sous-jacent atteint un certain niveau.

Infinance, abarrier optionis anexoticderivativetypically anoptionon theunderlying assetwhose price reaching the pre-setbarrier leveleither springs the option into existence or extinguishes an already existing option.

Where the option springs into existence on the price of the underlying asset breaching a barrier, it may be known as an "up and in," "knock-in," or "down and in" option.

Where the option is extinguished on the price of the underlying asset breaching a barrier, it may be known as an "up and out," "knock-out," or "down and out" option.

Barrier options are always cheaper than a similar option without barrier. Thus, barrier options were created to provide the insurance value of an option without charging as much premium. For example, if you believe that IBM will go up this year, but are willing to bet that it won't go above $200, then you can buy the barrier and pay less premium than the vanilla option.

Barrier options are a modified form of standard options that include both puts and calls. They are characterized by a strike level and a barrier level, as well as by a cash rebate associated with crossing the barrier. As with standard options, the strike level determines the payoff at expiration. The barrier options contract specifies, however, that the payoff depends on whether the stock price ever crosses the barrier level during the life of the option. In addition, Barrier options are sometimes accompanied by arebate, which is a payoff to the optionholder in case of a barrier event. Rebates can either be paid at the time of the event or at expiration.

TypesBarrier options are path-dependentexoticsthat are similar in some ways to ordinaryoptions. You cancallorputinAmerican,Bermudan, orEuropeanexercise style. But they become activated (or extinguished) only if the underlying reaches a predetermined level (the barrier).

Barriers come in two types: Up and Down Barriers

Up barrier: the barrier is above the current stock level; if it is ever crossed, it will be from below. Down barrier: the barrier is below the current stock level; if it is ever crossed, it will be from above.Barrier options come in two types: In options and Out optionsIn options start their lives worthless and only become active in the event that a predetermined knock-in barrier price is breached.

Out options start their lives active and become null and void in the event that a certain knock-out barrier price is breached.

If the option expires inactive, then it may be worthless, or there may be a cash rebate paid out as a fraction of the premium.

The four main types of barrier options thus are:

Up-and-out: spot price starts below the barrier level and has to move up for the option to be knocked out.

Down-and-out: spot price starts above the barrier level and has to move down for the option to become null and void.

Up-and-in: spot price starts below the barrier level and has to move up for the option to become activated.

Down-and-in: spot price starts above the barrier level and has to move down for the option to become knocked-in.

For example, a European call option may be written on an underlying with spot price of $100 and a knockout barrier of $120. This option behaves in every way like a vanilla European call, except if the spot price ever moves above $120, the option "knocks out" and the contract is null and void. Note that the option does not reactivate if the spot price falls below $120 again.Once it is out, it's out for good. Also note that once it's in, it's in for good.

In-out parity is the barrier option's answer toput-call parity. 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:Barrier options can have eitherAmerican,BermudanorEuropeanexercise style.

Barrier eventsAbarrier eventoccurs when the underlying crosses the barrier level. 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 MonitoringThe Barrier can be monitored in two distinct manners. Unless specified, a Barrier is continuously monitored; meaning that if the barrier is touched any time during the life of the option, the Activation (In) or Deactivation (Out) is triggered.Adiscrete barrieris one for which the barrier event is considered at discrete times, rather than the normalcontinuous barriercase.It is usual to specify the monitoring times at the writing of the Option.Variations AParisian optionis 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.

Aturbo warrantis 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. Partial Barrier Options: For these options, the barrier is active only during an initial period. In other words, the barrier disappears at a prescribed time. In general, the payoff at maturity may be a function of the spot price at the time the barrier disappears. Forward Starting Barrier Options: For these options, the barrier is active only over the latter period of the options life. The barrier level may be fixed initially, or alternatively, may be set at the forward start date to be a specified function of the contemporaneous spot price. The payoff may again be a function of the spot price at the time the barrier becomes active. Double Barrier Options: Options that knock in or out at the first hitting time of either a lower or upper barrier. Rolling Options: These options are issued with a sequence of barriers, either all below (for roll-down calls) or all above (for roll-up puts) the initial spot price. Upon reaching each barrier, the option strike is lowered (for calls) or raised (for puts). The option is knocked out at the last barrier. Ratchet Options: These options differ from rolling options in only two ways. First, the strike ratchets to the barrier each time a barrier is crossed. Second, the option is not knocked out at the last barrier. Instead, the strike is ratcheted for the last time. Lookback Options: The payoff of these options depends upon the maximum or the minimum of the realized price over the lookback period. The lookback period may start before or after the valuation date but must end at or before the options maturity.