In the Black–Scholes model, the price of the option can be found by the formulas below. In fact, the Black–Scholes formula for the price of a vanilla call option (or put option) can be interpreted by decomposing a call option into an asset-or-nothing call option minus a cash-or-nothing call option, and similarly for a put – the binary options are easier to analyze, and correspond to the two terms in the Black–Scholes formula.
While binary options may be used in theoretical asset pricing, they are prone to fraud in their applications and hence banned by regulators in many jurisdictions as a form of gambling. Many binary option outlets have been exposed as fraudulent. The U.S. FBI is investigating binary option scams throughout the world, and the Israeli police have tied the industry to criminal syndicates. The European Union is publishing regulations that will ban binary options trading. ASIC considers binary options as a “high-risk” and “unpredictable” investment option.