A barrier option is a path dependent option that has one of two features: 1) A knockout feature causes the option to immediately terminate if the underlier reaches a specified barrier level, or 2) A knock-in feature causes the option to become effective only if the underlier first reaches a specified barrier level. Premiums are paid in advance. Due to the contingent nature of the option, they tend to be lower than for a corresponding vanilla option.">
Barrier Option
Explained:
barrier option
knock-in option
knockout option
reverse barrier option
A
barrier option is a
path dependent option that has one of two features:
A
knockout feature causes the option to immediately terminate if
the underlier reaches a specified barrier level, or
A
knock-in
feature causes the option to become effective only if the underlier first
reaches a specified barrier level.
Premiums are paid in advance. Due to the contingent nature of
the option, premiums tend to be lower than for a corresponding
vanilla option.
Consider a knock-in
call option
with a strike price of EUR 100 and a
knock-in barrier at EUR 110. Suppose the option was purchased when the
underlier was at
EUR 90.
If the option expired with the underlier at EUR 103, but the underlier never
reached the barrier level of EUR 110 during the life of the option, the option
would expire worthless. On the other hand, if the underlier first rose to the
EUR 110 barrier, this would cause the option to knock-in. It would
then be worth EUR 3 when it expired with the underlier at EUR103. This is
illustrated in Exhibit 1:
Example:
Up-And-In Barrier Call Option
Exhibit 1
An up-and-in barrier call option expires
worthless unless the underlier value hits the barrier at some time
during the life of the option.
The particular option in this
example is known as an "up-and-in" option because the underlier must first go
"up" to the barrier before the option knocks "in."
In all, there are eight flavors of barrier options
comprising European puts or calls having barriers that are:
up-and-in,
down-and-in,
up-and-out, or
down-and-out.
Of the eight, four either knock-in or knockout when they
are in-the-money. These are called
reverse barrier options. They can pose significant hedging
challenges for the issuer.
Alternative structures include multiple barriers or
barriers incorporated into other types of derivatives. For example,
binary
options can be structured with barriers.
Merton priced a down-and-out call option in his seminal (1973)
paper. The classic paper providing analytic pricing formulas for barriers
is Reiner and Rubinstein (1991). See Haug (1997)
for an alternative treatment of the same formulas. A shortcoming of
analytic formulas is their use of a single implied volatility. Because
barrier options are path-dependent, it is desirable to model a term
structure of implied volatilities. See Taleb (1996).
up-and-in,