### Barrier option rebate formula

Where the coval vapes discount option springs into existence upon the underlying asset's price reaching the barrier level, it may be called an up and in, knock-in, or down and in option.
Another approach is to study the law of the maximum (or minimum) of the underlying.
However, computing the Greeks (sensitivities) using this approach is numerically unstable.
Yet another method is the partial differential equation (PDE) approach.How big would that trade have to be?Once it is out, it's out for good.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: C C i n C o u t displaystyle CC_inC_out.Variations edit Barrier options are sometimes accompanied by a rebate, which is a payoff to the option holder in case of a barrier event.What if the underlying only trades at the level for a single trade?In the case of constant interest rate r and constant volatility sigma, both the density function varphi and the integral int_0T e-rt varphi(t) dt can be computed analytically.This method is therefore inappropriate when there is a volatility smile.

"Static Options Replication." The Journal of Derivatives, 2(4) (Summer 1995. .
"Out" options start their lives active and become null and void in the event that a certain knock-out barrier price is breached.
Note that the option does not reactivate if the spot price falls below 120 again.
Rebates can either be paid at the time of the event or at expiration.
The four main types of barrier options are: Up-and-out : how to win free gas for a year mcdonald's spot price starts below the barrier level and has to move up for the option to be knocked out.For example, a European call option may be written on an underlying with spot price of 100 and a knockout barrier of 120.Down-and-in : spot price starts above the barrier level and has to move down for the option to become activated.Valuation edit 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."In" options start their lives worthless and only become active in the event that a predetermined knock-in barrier price is breached.

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