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Example of a binary options trade
A trader who thinks that the EUR/USD strike price will close at or above 1.2500 at 3:00 p.m. can buy a call option on that outcome. A trader who thinks that the EUR/USD strike price will close at or below 1.2500 at 3:00 p.m. can buy a put option or sell the contract.
At 2:00 p.m. the EUR/USD spot price is 1.2490. the trader believes this will increase, so he buys 10 call options for EUR/USD at or above 1.2500 at 3:00 p.m. at a cost of $40 each.
The risk involved in this trade is known. The trader’s gross profit/loss follows the ‘all or nothing’ principle. He can lose all the money he invested, which in this case is $40 x 10 = $400, or make a gross profit of $100 x 10 = $1000. If the EUR/USD strike price will close at or above 1.2500 at 3:00 p.m. the trader's net profit will be the payoff at expiry minus the cost of the option: $1000 – $400 = $600.
The trader can also choose to liquidate (buy or sell to close) his position prior to expiration, at which point the option value is not guaranteed to be $100. The larger the gap between the spot price and the strike price, the value of the option decreases, as the option is less likely to expire in the money.
In this example, at 3:00 p.m. the spot has risen to 1.2505. The option has expired in the money and the gross payoff is $1000. The trader's net profit is $600.
[edit]Black-Scholes Valuation
In the Black-Scholes model, the price of the option can be found by the formulas below.[12] In these, S is the initial stock price, K denotes the strike price, T is the time to maturity, q is the dividend rate, r is the risk-free interest rate and is the volatility. denotes the cumulative distribution function of the normal distribution,
