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text courtesy Wikipedia
Example of a Binary Options TradeA 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.
Cash-or-nothing callThis pays out one unit of cash if the spot is above the strike at maturity. Its value now is given by,
[edit] Cash-or-nothing putThis pays out one unit of cash if the spot is below the strike at maturity. Its value now is given by,
[edit] Asset-or-nothing callThis pays out one unit of asset if the spot is above the strike at maturity. Its value now is given by,
[edit] Asset-or-nothing putThis pays out one unit of asset if the spot is below the strike at maturity. Its value now is given by,
[edit] Foreign exchangeFurther information: Foreign exchange derivative
If we denote by S the FOR/DOM exchange rate (i.e. 1 unit of foreign currency is worth S units of domestic currency) we can observe that paying out 1 unit of the domestic currency if the spot at maturity is above or below the strike is exactly like a cash-or nothing call and put respectively. Similarly, paying out 1 unit of the foreign currency if the spot at maturity is above or below the strike is exactly like an asset-or nothing call and put respectively. Hence if we now take , the foreign interest rate, , the domestic interest rate, and the rest as above, we get the following results.
In case of a digital call (this is a call FOR/put DOM) paying out one unit of the domestic currency we get as present value,
In case of a digital put (this is a put FOR/call DOM) paying out one unit of the domestic currency we get as present value,
While in case of a digital call (this is a call FOR/put DOM) paying out one unit of the foreign currency we get as present value,
and in case of a digital put (this is a put FOR/call DOM) paying out one unit of the foreign currency we get as present value,
