*The Business Professor*, updated March 1, 2019, last accessed August 5, 2020, https://thebusinessprofessor.com/lesson/binary-option-definition/.

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**Binary Option Definition**

This is a financial derivative which has a fixed payout if an option expires in the money and the risk of losing all the money invested in the option if it expires out of the money. Since it is called a binary option, its success depends on a yes or no proposition. The binary options have an expiry date, and when it arrives, the price of the underlying asset must be on the right side of the strike price for it to make a profit.

When the option expires, the loss or gain is automatically credited or debited in the trader’s account.

**A Little More on Binary Options**

Binary options are simple. For example, Will the share price of ABC Company be above $25 on March 1st at 2:40 pm? What the trader has to do is to select yes to mean it will be higher or no to suggest it will be lower and then stake the amount he willing to bet on the answer.

Suppose the trader chooses yes and stakes $100 and the payout established is 70%. If on that date and time the shares go above $25, a profit of $70 is credited to the trader’s account. If the price falls below $25 at that date and time, the trader loses the total investment of $100.

The holder of the option may be given the right of buying or selling an underlying asset at a certain price before the expiration date of the option by a vanilla American option. A European option is similar, but the right can only be exercised on the expiration date. Buyers are provided by vanilla options the potential ownership of the underlying asset. During the purchase of these options, the risk is capped although the profits shift depending on how further away the price of the underlying asset is.

Binary options are fixed since they don’t provide the possibility of taking a position in the underlying asset. They have a fixed payout and fixed maximum risk that is limited to the amount invested in the binary option. The movement of the underlying asset does not affect these payouts or losses.

The only factor affecting the profit or loss is whether the price of the underlying asset is on the right side of the strike price. However, some binary options can be closed before expiration, but this action reduces the payout received.

In the US, binary options are usually traded on platforms which are regulated by the SEC and other regulatory agencies. Most of the binary options trades that occur outside the US are not typically regulated. Investors are advised to be wary of the binary options brokers who are not held to a particular standard since they operate unregulated.

**Examples of Binary Options**

Nadex, which is a regulated binary options exchange in the US, has options based on the yes/no proposition and which allow traders to exit before expiry. A potential profit or loss is indicated by the price at which the binary option is entered. All the options expiring are worth either $100 or $0.

For example, the stock of NYZ is currently trading at $64.75. A binary option expiring tomorrow at noon has a strike price of $65, and a trader can purchase it at $40. If the price of XYZ finishes above $65, the option will expire in the money and be worth $100. As a result, the trader will make a profit of $60.

If the price of the stock is below 65 when the option expires, the trader loses the $40 used to purchase the option. With a Nadex binary option, the combination of the potential profit or loss always equals $100.

A trader can change the number of options being traded if he wishes to make a more substantial investment. He may, for example, select three contracts that would raise the risk to $120 and increase the potential profit to $180.

Non-nadex binary options are also the same except that they are not regulated in the US. They can be exited before they expire and also have fixed percentages payout for wins. These options may not trade in increments of $100.

**References for Binary Option**

- http://www.businessdictionary.com/definition/binary-option.html
- https://www.investopedia.com/terms/b/binary-option.asp
- https://en.wikipedia.org/wiki/Binary_option

**Academic Research on Binary Option**

- Rethinking risk management,
**Stulz, R. M. (1996).***Journal of* *applied corporate finance***,***9***(3), 8-25.**This paper puts forth a theory of corporate risk management which tries to advance beyond the variance-minimization model which dominates a majority of academic discussions on the subject.- Bivariate
**option**pricing with copulas,**Cherubini, U., & Luciano, E. (2002).***Applied Mathematical Finance***,***9***(2), 69-85.**For pricing bivariate contingent claims, this study suggests the adoption of copula functions which enable the marginal distractions gotten from vertical spreads to be embedded in a multivariate pricing kernel. - Pricing credit default swaps under Lévy models,
**Cariboni, J., & Schoutens, W. (2007).***Journal of Computational Finance***,***10***(4), 71.**This paper presents an assumption that a pure-jump Levy process drives the asset price process and that what triggers a default is the crossing of a preset barrier. - Dynamic hedging portfolios for derivative securities in the presence of large transaction costs,
**Marco, A., & Antonio, P. (1994).***Applied Mathematical Finance***,***1***(2), 165-194.**This article introduces a new cluster of strategies for hedging derivative securities in the presence of transaction costs while assuming lognormal continuous-time prices for the underlying asset. - Convergence remedies for non-smooth payoffs in
**option**pricing,**Pooley, D. M., Vetzal, K. R., & Forsyth, P. A. (2003).***Journal of Computational Finance***,***6***(4), 25-40.**This paper presents three methods for dealing with discontinuities which are averaging the initial data, shifting the grid and finally projection method. - Robust hedging of barrier options,
**Brown, H., Hobson, D., & Rogers, L. C. (2001).***Mathematical Finance***,***11***(3), 285-314.** **Binary**particle swarm optimization for black-Scholes**option**pricing,**Lee, S., Lee, J., Shim, D., & Jeon, M. (2007, September). In***International Conference on Knowledge-Based and Intelligent Information and Engineering Systems***(pp. 85-92). Springer, Berlin, Heidelberg.**In this paper, a new model of particle swarm optimization which finds more precise values of options with estimates of the implied volatility than genetic algorithms is proposed.- A Study on the
**Binary Option**Model and its Pricing,**Peng, B., & Han, Y. (2004).***Academy of Accounting and Financial Studies. Proceedings***(Vol. 9, No. 1, p. 71). Jordan Whitney Enterprises, Inc.**This paper explains how the binary option model works and how the binary options are priced. - A simple approach for pricing barrier options with time-dependent parameters,
**Lo, C. F., Lee, H. C., & Hui, C. H. (2003).***Quantitative Finance***,***3***(2), 98-107.**This is a presentation of a simple and easy-to-use method used in the calculation of accurate estimates of Black-Scholes barrier option prices that possess time-dependent parameters. - A framework for valuing corporate securities,
**Ericsson, J., & Reneby, J. (1998).***Applied Mathematical Finance***,***5***(3-4), 143-163.**This study proposes a method of valuing corporate securities that provide for the straightforward derivation of closed-form solutions for complex scenarios. - A new method of pricing lookback options,
**Buchen, P., & Konstandatos, O. (2005).***Mathematical Finance: An International Journal of Mathematics, Statistics and Financial Economics***,***15***(2), 245-259.**In this paper, a new method of pricing lookback options is proposed. This method simplifies the derivation of analytical formulas for this class of exotics in the Black-Scholes framework. - How close are the
**option**pricing formulas of Bachelier and Black–Merton–Scholes?,**Schachermayer, W., & Teichmann, J. (2008).***Mathematical Finance: An International Journal of Mathematics, Statistics and Financial Economics***,***18***(1), 155-170.**This paper presents a comparison of the option pricing formulas of Louis Bachelier and Black-Scholes and then observes that the prices are coinciding perfectly.