VOLUME 1, NUMBER 20/July 24, 1995
*****************************************************************
DERIVATIVES 'R US is a weekly non-profit publication on the
Internet user group misc.invest.futures that provides a simple
non-technical treatment of various topics in derivatives. DRU
is written by Don M. Chance, Professor of Finance at the Center
for the Study of Futures and Options Markets at Virginia Tech.
He can be contacted at dmc @ vt.edu or by phone at 540-231-5061
or fax at 540-231-4487. DRU is for educational purposes only
and does not provide trading advice.
Back issues of DRU are available by anonymous ftp from
fbox.vt.edu/filebox/business/finance/dmc/DRU or can be accessed
using a Web browser at
http://fbox.vt.edu:10021/business/finance/dmc/DRU. The file
contents.txt can be viewed to see a list of old filenames and
topics available for reading or downloading.
*****************************************************************
Barrier Options
This week's issue of DRU addresses a group of exotic derivatives called barrier options. These options are becoming increasingly popular, particularly in currency markets. Barrier options are options that contain a special provision that causes them to either expire prematurely or fail to come into existence even though the premium has been paid.
There are two general classes of barrier options: in-options and out-options. With an in-option the buyer pays a premium up front and receives an option that will not start until the price of the underlying asset hits a certain level, which is called the barrier. If the asset price never touches the barrier, the option never comes into existence and would then expire with no value at expiration, even though it might ostensibly end up in-the-money. For example, consider one form of this type of option called a down-and-in option. Let it be a call. This call grants the right to buy the stock at $40 (the strike). The current stock price is $50. We set the barrier at $45. The buyer pays the premium up front but the option will never actually start unless the stock price falls to $45. Once it hits $45, the option comes into existence and is, in effect, an ordinary call option. This type of in-option is called a kick-in option. When the barrier is hit and the option comes into existence, it is in-the-money. If the barrier is set below the strike, the option will be out-of-the-money when it comes into existence. This type of option is called a kick-out option. So kick-in options are barrier options that are in-the-money when they start and kick-out options are barrier options that are out-of-the-money when they start. Using that definition, barrier put options can be easily constructed accordingly.
In-options are also known as knock-in options. In addition to down-and-in options, there are up-and-in options, which are barrier options that come into existence if the underlying asset price rises and hits the barrier.
Out-options, sometimes called knock-out options, are barrier options that terminate before expiration if the underlying asset price reaches the barrier. For example, consider the down-and-out call. Let the stock price be $50 and the exercise price be $40. Set the barrier at $35. If the stock price ever falls to $35, the option expires immediately with no value, even though it is in-the-money at the time. Out- or knock-out options can be either down-and-out, meaning that the barrier is below the current asset price or up-and-out, meaning that the barrier is above the current asset price.
You can combine a down-and-out call with a down-and-in call and obtain an interesting result. If the barriers and strikes are the same on the two options, the down-and-out call terminates when the barrier is hit but the down-and-in call starts when the barrier is hit. Thus, the combination of these two options creates an ordinary European option. Naturally the sum of the formulas for pricing these two options equals the Black-Scholes formula.
In addition to knock-in and knock-out options, there are knock-out forwards and kick-in forwards. The former are forward contracts that terminate with no value if the underlying asset price hits the barrier. Kick-in forwards are options that turn into forward contracts if the barrier is hit.
Some barrier options have an additional feature called a "rebate." If the asset price on an out-option hits the barrier and the option, thus, terminates, the holder is paid a sum of money as a form of a rebate. On an in-option the rebate is paid if the asset price never reaches the barrier.
Pricing formulas for barrier options are generally well-known. However, the formulas require the condition that breaching the barrier is defined as occurring whenever the asset price touches the barrier. Many barrier options recognize the touching of a barrier only at the close of a trading day. For options that recognize touching the barrier at any time, statistical theory has provided known formulas that evaluate the probability distribution of the condition of the stock price either touching or not touching the barrier. The formulas are just slightly more complex than the Black-Scholes formula. For barrier options that recognize only the touching of a barrier at the close, methods such as the binomial model, with some very careful calibration, are used.
In the real world, barrier options trade in the OTC market. There have been some experiments with barrier options on the exchange-listed market. The CBOE's S&P Caps were option contracts that were effectively bull and bear spreads that expired when they reached their maximum value at the close of any trading day.
But of course the most important question is why would anyone want one of these exotic animals. The most obvious reason is that the options are cheaper. The condition that the option can terminate early or never come into existence creates outcomes that provide no payoff (except maybe a rebate) that are not present in ordinary options. This means that the cost of barrier option is cheaper (note that a sufficiently large rebate can negate this statement). Consequently some users find them more attractive.
For example, suppose you held a portfolio that is roughly equivalent to the S&P Mid-Cap index. You would like to buy an ordinary put on this portfolio to protect an accumulated profit. An options dealer will gladly sell you this over-the-counter option. However, you feel that it is more costly than you are willing to pay. The dealer suggests an up-and-out put. This option will terminate if the value of the Mid-Cap Index rises to a certain level. You find that condition acceptable because if the index rises to that level, you will feel more confident that you do not need the protection; thus, you get a lower premium. The risk you run is that the index hits the barrier and then falls down below the strike by the expiration.