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Introduction

Barrier options are vanilla options with path-dependent payoffs. The payoff is not only a function of stock level relative to strike but also dependent upon whether or not the stock reaches certain prespecified barrier level before maturity. 

 

There are many types of barrier options but 2 common ones: knock-out and knock-in barrier options. 

For knock-out barrier options, the option will be knocked out and become worthless if the underlying asset crosses a prespecified barrier level. 

For knock-in barrier options, the option will be knocked in and become a vanilla option only if the underlying crosses the prespecified level before maturity. 

 

Depending upon the barrier level relative to the initial underlying asset level, we can have an "up" barrier or a "down" barrier. 

If barrier > initial underlying level --> up barrier. 

If barrier < initial underlying level --> down barrier. 

 

 

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