1. Introduction

The purpose of this article is to help clarify double barrier binary options values and exotic options.

One-touch double barrier binary options are path-dependent options in which the existence and payment of the options depend on the movement of the underlying price through their option life. We discuss two types of one-touch double barrier binary options here: (1) up-and-down out binary option, and (2) American binary knock-out option. For the first type, the option vanishes if the underlying price hits the upper barrier or the lower barrier once in the option life. Otherwise, the option buyer receives a fixed payment at maturity. This option combines the characteristics of a European binary option and knock-out barrier options together. For the second type, the option vanishes if the underlying price hits a knock-out barrier, while it gives a fixed payment if another payment barrier is touched. This option can be considered as an American binary option with a knock-out barrier (Hui, 1996, p 343).

2. Exotic Options

Exotic options are those options that are more complex in the way they are traded; these options are not very common types of options in the stock market. Exotic options are traded in the Over the Counter (OTC) platform. The option enables the trader to choose the trade method, for instance an investor can trade them in put or call options ( Kuznetsov, 2009, p 452).

Exotic options owe their existence largely to the limitations and shortcoming of plain vanilla options. Exotics allow particular types of investors to achieve investment goals unattainable with plain vanilla option strategies. Investors can generally be classified as either speculators or hedgers. Speculators want to gear up their capital, namely to seek investment opportunities with higher leverage than plain vanilla options. This can be achieved through barrier (or partial barrier) plain vanilla options (Bermin, 2008, p 387).

Commoditized products have standard agreements in place, eliminate most surprises, and typically trade between dealers where constant matching of risks takes place. The existence of an interbank market is the test of standardization. They rank from the very simple cash products to some lower forms of exotic options. Nonstandardized products, like structures, have payoffs that are peculiar to the instrument itself and require special pricing capabilities, such as an on-staff mathematician. In contrast, the commoditized products can be priced and managed with the aid of commercially available software products (generally faulty). It can become necessary to design programs for every trade, with a higher incidence of pricing “bugs.” An option with a payoff attached to several assets, with a barrier that is reset six times and an uncertain expiration date (it can be extended) will not be easily booked in a commercial risk management system (Taleb, 1997, p 50).

Here we see the connection between commoditized products, exotic options and barrier options.

3. Double Barrier Options

Barrier options are a widely used class of path-dependent derivative securities. These options “knock in” or “knock out” when the price of the underlying asset crosses a certain barrier level. For example, an up-and-in call option gives the option holder the payoff of a call if the price of the underlying asset reaches a higher barrier level during the option’s life, and it pays off zero unless the asset price reaches that level. (Ku, 2012, p 968)

In single barrier options, it is easy to show that barrier options with a knock-in feature can be priced by buying an option without any knock-out feature and selling a knockout option. The same approach can be used in one-touch double barrier binary options. For example, an American binary option with a knock-in barrier H, the option premium is equal to buying an American binary option and selling an American binary knock-out option with a barrier at H. All the options have the same payment barrier (Hui, 1996, p 347).

Price is monitored with respect to a single constant barrier for the entire life of the option. Due to their popularity in a market, more complicated structures of barrier options have been studied by a number of authors. Kunitomo and Ikeda [5] derived a pricing formula for double barrier options with curved boundaries as the sum of an infinite series. Geman and Yor [1] followed a probabilistic approach to derive the Laplace transform of the double barrier option price. Heynan and Kat [3] studied so-called partial barrier options where the underlying price is monitored for a part of the option’s lifetime. For theses options, either the barrier disappears at a specified date strictly before the maturity (i.e., early ending option) or the barrier appears at a fixed date strictly after the start of the option (i.e., forward starting option). In the paper, the authors gave valuation formulas for partial barrier options in terms of bivariate normal distribution functions. As a natural variation on the partial barrier structure, window barrier options have become popular wit h investors, particularly in foreign exchange markets (Ku, 2012, p 968).

Since the payment of the one-touch double barrier binary option is binary, they are not ideal hedging instruments. However, they are suitable for investment. Recently structured accrual range notes are popular in financial market. The notes are linked to either foreign exchanges, equities or commodities (Hui, 1996, p 347).

4. Conclusions

The role of double barrier binary options is undervalued in the measurement of instruments and investments. It is significant that traders in binary examine exotic options and the role double barrier options plays in the consideration of investments. This is important in the discussion of returns and which option opportunities yield the best results. While double barrier options can provide more opportunity because they they are not as simple as plain binary options they come with an exceeded level of risk.

5. References

Bermin, H., Buchen, P., & Konstandatos, O. (n.d.). Two Exotic Lookback Options. *Applied Mathematical Finance,* 387-402.

Hui, C. (n.d.). One-touch double barrier binary option values. *Applied Financial Economics,*343-347.

Jun, D., & Ku, H. (n.d.). Cross a barrier to reach barrier options. *Journal of Mathematical Analysis and Applications,* 968-978.

Kuznetsov, A. 2009. *The Complete Guide to Capital Markets for Quantitative Professionals.*New York: McGraw-Hill. ISBN 0-07-146829-3.

Taleb, N. (1997). *Dynamic hedging: Managing vanilla and exotic options*. New York: Wiley.