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Graphical Representation of Option Price and Sensitivities

Barrier Options are options where the payoff depends on whether the underlying asset's price reaches a certain level during a certain period of time.
A particular type of Barrier Options is known as Knockout Option
the regular options will cease to exist if the underlying's asset's price reaches a certain barrier.
It holds the similar reason for Knockin Option where the options come to exist when the underlying's asset's price reaches a certain barrier.

Four types of barrier:

1. Call Knockout, the barrier is generally below the strike price (H < X). It is also known as down-and-out option.
2. Put Knockout, the barrier is generally above the strike price (H > X). It is also known as up-and-out option.
3. Call Knockin, the barrier is generally below the stike price (H < X). It is also known as down-and-in option.
4. Put Knockin, the barrier is generally above the strike price (H > X). It is also known as up-and-in option.

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