Barrier-Option

Barrier options are a special form of options and are among the exotic options. The main difference between the options is that barrier options can be enabled or disabled by the occurrence of certain events. One distinguishes the following main types of options:

Knock- out option

In knock-out options are ordinary ( call or put ) options that expire, however, if a certain, submitted barrier is reached.

Example: A Barrier call with start value, Strike, a term of years, and knock -out level has the following payoff profile:

  • The share price reaches some point in the mark of 120 or rises above this, then, regardless of the closing value, nothing is paid.
  • If the closing value below the strike price of 90, the option expires also ( regardless of whether or between the barrier has been reached).
  • Only if the closing price is above the strike ( approximately ), the mark of 120 was never reached, the difference between the closing price and Strike will be paid (in this example ).

Since in this example is the barrier above the initial value, it is also referred by an up-and -out call. The counterpart to this would be a down-and -out call, which is forfeited if a barrier that is lower than the opening price is below.

Knock-In Option

In the knock-in option is the other way round: it is only valid if the barrier is reached in the course of time at least once, otherwise it will be forfeited.

Example: A Barrier call with, strike price and knock -in level causes the following payment structure:

  • If the course during the entire term never reached the mark of 130, nothing will be paid, even then not, if the closing price is above the strike.
  • Likewise nothing is paid, if the closing price is below 110, regardless of whether the mark of 130 was ever achieved.
  • Exceeds the price in the course of time the mark of 130 and is located on the final day still have more than 110 ( approximately at 124 ), the difference of closing price and is paid Strike (here 124-110 = 14).

In this example, it is consistent enough, to an up -and -in call, its counterpart would be a down-and -in call. The latter would in fact be a bet on a "comeback" of the stock: in order not to fall, the underlying 'd have to fall below a barrier and then stand at the end again above the strike.

Digital barrier option

With digital barrier options, in contrast to the above derivatives not Strike is agreed that it applies to the end - on (call) or below (put). Here is just a predetermined nominal value paid if the barrier has been reached during the term.

For example, a digital barrier option with start value, face value, and barrier pays off on the final day 50 when the course has located some point below 80. The closing price is irrelevant. With such an option can an investor who wants to invest in precisely that underlying hedging against heavy losses.

Other variants

The above-mentioned types of options are the most common and most liquid far barrier options. However, there are still a number of other, more complex instruments based on the barrier concept:

  • Knock- out options with premium: This is the knock-out options in the above sense, but with an additional agreement: the option expires, because the barrier has been reached, a previously abgemachte premium is paid as compensation. This option is often considered not as a separate type of barrier options, as they can be represented as a linear combination of knock-out and digital barrier option.
  • Dynamic barriers: Here, the barrier condition is amended to specify the knock-out or knock-in level can change in the course of time. For example, it may be agreed that the underlying asset in the first year no less than 90, the second must not fall below 80, or that the price may fall at any time below the function. This is especially advantageous for long-term maturities, since the expected exponential increase in the price may be considered.
  • Tunnel options provide the broadest possible generalization of the barrier option is: here the option expires when the price falls below a ( possibly dynamic ) falls lower limit or rises above an upper limit. The Underlying therefore only allowed to move in a certain range ( within a tunnel just ). With this instrument, the investor can bet on the volatility of the underlying quasi: Strongly fluctuating shares break through one of the boundaries rather than the values.
  • Parisian options cams only when the barrier condition is met for a specified period of time, eg when at a down-and -in option, the price for a month is less than the Barrier Levels. Depending on whether the length of time must be at or below piece accumulates, we distinguish between the pure Parisian options and the cumulative Parisian options, also called Parasian options.

Evaluation of barrier options

The calculation of the fair option price is at barrier options, a general tendency for path-dependent derivatives ( ie the payout depends not only on the closing price, but the overall price development taken into account), often no easy task. Explicitly must be known here information about the probability distribution of the extreme values ​​of the course. In the Black- Scholes model, which is for example the case, just as in binomial models. In more sophisticated capital market models but often helps only a discretization (ie an approximation by a discrete-time model) or a Monte Carlo simulation.

  • Option trading
Put option
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