Posted on August 12, 2016

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## Regulation and compliance

The Cypriot regulator also temporarily suspended the license of the Cedar Finance on December 19, 2013. The decision was taken by CySEC because the potential violations referenced appeared to seriously endanger the interests of the company’s customers and the proper functioning of capital markets, as described in the official issued press release. CySEC also issued a warning against binary option broker PlanetOption at the end of the year and another warning against binary option broker LBinary on January 10, 2014, pointing out that it was not regulated by the Commission and the Commission had not received any notification by any of its counterparts in other European countries to the effect of this firm being a regulated provider.

## Example of a binary options trade

At 2:00 p.m. the EUR/USD 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 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 x 10 = 0, or receive 0 x 10 = ,000. If the EUR/USD price will close at or above 1.2500 at 3:00 p.m. the trader's profit will be the payoff at expiry minus the cost of the option: ,000 – 0 = 0.

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 ,000. The trader's net profit is 0.

## Black–Scholes valuation

σ {\displaystyle \sigma }Φ {\displaystyle \Phi }

### Cash-or-nothing call

This pays out one unit of cash if the spot is above the strike at maturity. Its value now is given by

### Cash-or-nothing put

This pays out one unit of cash if the spot is below the strike at maturity. Its value now is given by

### Asset-or-nothing call

This pays out one unit of asset if the spot is above the strike at maturity. Its value now is given by

### Asset-or-nothing put

This pays out one unit of asset if the spot is below the strike at maturity. Its value now is given by

### American style

T {\displaystyle T}K {\displaystyle K}K ≥ S {\displaystyle K\geq S}K ≤ S {\displaystyle K\leq S}

K < S {\displaystyle K<S}K > S {\displaystyle K>S}T {\displaystyle T}

erf {\displaystyle \operatorname {erf} }sgn {\displaystyle \operatorname {sgn} }

### Foreign exchange

r F O R {\displaystyle r_{FOR}}r D O M {\displaystyle r_{DOM}}

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,

### Skew

σ {\displaystyle \sigma }σ ( K ) {\displaystyle \sigma (K)}

C v {\displaystyle C_{v}}

σ {\displaystyle \sigma }K {\displaystyle K}

The first term is equal to the premium of the binary option ignoring skew:

∂ C v ∂ σ {\displaystyle {\frac {\partial C_{v}}{\partial \sigma }}}∂ σ ∂ K {\displaystyle {\frac {\partial \sigma }{\partial K}}}

## Relationship to vanilla options' Greeks

Since a binary call is a mathematical derivative of a vanilla call with respect to strike, the price of a binary call has the same shape as the delta of a vanilla call, and the delta of a binary call has the same shape as the gamma of a vanilla call.

• Options strategies
• Options arbitrage
• Synthetic position
• Prediction Market

## References

Source: https://en.wikipedia.org/wiki/Binary_option