# European Binary Options

### Exercise Rules

European binary options, European digital options, can only be exercised at expiry.

Options are described as ‘American’ or ‘European’. The former means that the option can be exercised at any time prior to and including expiry. This contrasts with European options that can’t be exercised until expiry.

Both European options and American options can be traded anywhere. The geographical connotations to the names are irrelevant.

### European Binary Options Table

Each of the above can only be exercised after expiry.

The top two rows of instruments are directional. These instruments enable speculators to bet that the underlying price is heading either up or down.

The tunnel, eachway tunnel and tunnel accumulator primarily enable the speculator to bet that the underlying is, or is not, going to move.

### Settlement Prices Policy

If the underlying at expiry is exactly on the strike settlement can be treated in numerous ways:

1. the two obvious candidates are that the option is treated as in-the-money or out-of-the-money. This means the bets are settled at 100 or 0 respectively.
2. another possible approach would be to treat the settlement as a ‘dead heat’. The bet would then be settled at 50.
3. another approach sometimes used with the underlying settling on the strike is to simply void all bets.

#### Approach #1

• Many, if not most, traders will consider the price of the binary, or digital option, to represent probability. If a price is ’31 bid, at 32′ and a trader reckons the bet has a 40% chance of winning then they might buy it at 32. Say the strike price is 100.00 and at expiry the asset price is now 99.99 bid, at 100.00. So what would the settlement prices look like?
• If it was taken off the bid then it settles at 0
• If it is taken off the average of the bid and offer, i.e. 99.995, then it settles at 0.
• If the settlement is based on the offer, i.e. 100.00, then the binary call settles at 100.
##### 200% Chance of Winning?

So if the winning call can settle at 100.00 and above what should the same strike put settle at? Here is the problem since if the put strike is deemed as a winner, like the call, then the call and put together are now worth 200. Or there is a 200% chance of winning! Yet what if the put settles at 0? Then there is a call/put disparity where the put holder is clearly being disadvantaged. Being short a binary call is not the same as being long the same strike binary put.

• If the asset price is 99.99 bid, at 100.00 what would be a sensible price for the market maker to make? 25 bid, at 75? Based on expected returns that would be the market makers ‘toss a coin’ price. Realistically a market maker would make 20 bid, at 80.

#### Approach #2

This approach has a particular advantage if digital call and put options are being offered with the same strike. This is because the call and put settlements would sum to 100. Market makers can still make competitive markets with the opportunities arising whereby both call buyer and put buyers are bidding in aggregate over 100.

##### A Digital Options Conversion/Reversal

For example: a broker is holding an order to pay 54 for the 100.00 binary calls but the future is trading at 100.10. The broker’s binary call order is in-the-money so is likely to win and settle at 100. A panic merchant broker gets a market order to buy the 100.00 put at market. “53 Bid!” All of a sudden the broker holding the 54 call bid gets hit. Why? Because the quickest market maker has immediately hit the put broker’s 53 bid who then hits the call bid at 54. In aggregate these tow trades have made the market maker 7 risk-free ticks. Unlike the conventional market maker, she doesn’t even need to buy or sell any futures to lock that 7 ticks in. The maximum those two trades can settle at is 100. Work it out……….

Binaries offer a wide and flexible manner to take a view on the markets. Their limited and known risk profile ensure that binary options are an ideal speculating tool for the retail client. The limited risk feature also makes them an ideal instrument for brokers to offer via the internet.

#### Approach 3#

Utterly impractical!

### Other European Binary Options Structures

In the table above are 9 different European binaries. Yet there are many, many more variations of those 9 structures that could be adopted. For example, there are no structures that take the form of a condor, a butterfly or even just 1x2s. Other variables will be covered in due course. American binaries, Knock-In and Knock-Out binaries plus two-asset binaries need to be dealt with first.

by: Hamish Raw

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