the underlying resumes its upwards momentum. The underlying continues to rise and is around the $102.75 level at expiry, well above the strike of $101, so is consequently a winning bet with the seller ending the loser.
Figure 1.1.1
3. RW3 drifts sideways from day one and never looks like reaching the strike. RW3 is a losing bet for the backer with the underlying settling around $100.50 at expiry.
1.2 Upbet Pricing
Fig 1.2.1 illustrates the expiry price profile of an upbet. One of the features of binaries is that at expiry, bets have a discontinuous distribution, i.e. there is a gap between the winning and losing bet price. Bets don’t ‘almost’ win and settle at, say 99, but are ‘black and white’; they’ve either (except in the case of a ‘dead heat’) won or lost and settle at either 100 or zero respectively.
1. If the upbet is in-the-money, i.e. in the above example of Fig 1.1.1 the underlying is higher than $101, then the upbet has won and has a value of 100.
2. Alternatively if the upbet is out-of-the-money, i.e. the underlying is lower than $101, then the upbet has lost and therefore has a value of zero.
3. In the case of the underlying finishing exactly on the strike price of $101, i.e. the upbet is at-the-money, then the bet may settle at 0, 50 or 100 depending on the rules or contract specification.
Figure 1.2.1
One issuer of binaries may stipulate that there are only two alternatives, a winning bet whereby the underlying has to finish above $101, or a losing bet whereby the underlying finishes below or exactly on $101. A second company might issue exactly the same binary but with the contract specification that if the underlying finishes exactly on the strike then the bet wins. A third company may consider that the underlying finishing exactly on the strike is a special case and call it a ‘draw’, ‘tie’ or ‘dead heat’, whereby the upbet will settle at 50. This company’s rules therefore allow three possible upbet settlement prices at the expiry of the bet.
N.B. Throughout the examples in this book the latter approach will be adopted whereby in the event that a bet is a ‘dead heat’, or in other words, where the underlying is exactly on the strike price at expiry, then it is settled at 50.
1.3 Upbet Profit & Loss Profiles
The purchaser of a binary option, just like a conventional option, can only lose the amount spent on the premium. If Trader A paid 40 for an upbet at $1 per point then Trader A can lose a maximum of just 40 ¥ $1 = $40. But with a binary not only the loss has a maximum limit but the potential profit has a maximum limit also. So although Trader A’s loss is limited to $40, his profit is limited to (100 – 40) ¥ $1 = $60. As a general rule the profit and loss of the buyer and seller of any binary must sum to 100 ¥ $ per point.
In Figs 1.3.1 and 1.3.2 respectively Trader A’s and Trader B’s P&L profiles are illustrated. Both traders are taking opposite views on whether a share price will be above $101 at the expiry of the upbet.
In Fig 1.3.1 Trader A has bought the upbet at a price of 40 for $1 per point ($1/pt) so his three possible outcomes are:
1. Trader A loses $40 at any level of the underlying below $101.
2. At $101 the rules of this particular upbet determine a ‘dead heat’ has taken place and the upbet settles at 50 with Trader A making a profit of $10.
3. Above $101 Trader A wins outright and the upbet is settled at 100 to generate a profit of $60.
Figure 1.3.1
Trader B has sold this upbet at 40 for $1/pt so conversely Trader B’s P&L profile is, as one would expect, the mirror image of Trader A’s reflected through the horizontal axis.
Figure 1.3.2
Trader B’s three possible outcomes are:
1. Trader B has sold 40s and therefore wants to see the underlying below $101 where the upbet is worth zero at expiry and Trader B collects the premium of 40 ¥ $1 = $40.
2. If the upbet settles at-the-money the upbet is worth 50 and Trader B loses $10 having gone ‘short’ $1/pt at 40.
3. The underlying is above $101 at the upbet’s expiry so Trader B loses outright to the tune of $60.
1.4 Downbet Specification
The random walk model in Fig 1.4.1 describes when downbets win and lose. The starting point is yet again $100 with twenty-five days to expiry, except here the strike is $1 below at $99. In this instance the downbet is ‘out-of-the-money’ when the underlying is above the strike of $99 and ‘in-the-money’ below the strike.
Figure 1.4.1
1. After day three RW1 falls to $99.01 and bounces up. This is the closest RW1 gets to the strike and is trading at around $99.75 at the downbet expiry. Consequently RW1 closes out-of-the-money and is a losing bet.
2. RW2 initially falls to the $99 level in tandem with RW1 but breaches the strike. After ten days the underlying travels back up through the strike to trade alongside RW1 at expiry. Therefore this too is a losing bet.
3. RW3 trades down to the $99 level with seven days left. With three days to go RW3 trades back up to $99 from below the strike before making a final downward move on the last day to trade around $98.25 at expiry. This downbet closes in-the-money, and is a winning bet settling at 100.
1.5 Downbet Pricing
The expiry price profile of a downbet is illustrated in Fig 1.5.1. It is Fig 1.2.1 reflected through the vertical axis but with a strike of $99 as opposed to $101.
Figure 1.5.1
1. In this case if the underlying is above the strike of $99 at expiry, the downbet is out-of-the-money, has lost and is worth zero.
2. At $99 the downbet is at-the-money, is deemed a draw and worth 50.
3. While if the
