LITMIR.BIZ

      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 downbet expires with the underlying below the $99 strike, the downbet is in-the-money, has won and is worth 100.

      1.6 Downbet Profit & Loss Profiles

      Trader A and Trader B now decide to trade a downbet with each other. Trader A is no longer feeling bullish and wishes to buy a downbet (Fig 1.6.1) and since Trader B has conveniently turned bullish, he sells it to him. This is not an aggressive trade that Trader A is putting on; since the strike price is $101 and the underlying is $100 therefore the downbet is already $1 in-the-money and has a better than an ‘evens money’ chance of winning. The price of his downbet has to reflect this probability and the price is agreed at 60, where they trade for $1/pt.

      Figure 1.6.1

      Trader A’s maximum loss since he bought the downbet is 60 ¥ $1 = $60, and this he will have to bear if the share price rises by over $1 from its current level of $100. His maximum potential winnings have been reduced to $40, which he will receive if the underlying either falls, stays where it is at $100, or rises less then $1. In other words Trader A has backed an ‘odds-on’ bet.

      Fig 1.6.2 shows Trader B’s profile having sold the in-the-money downbet to Trader A for 60. Trader B needs the share price to rise $1 in order to win. If the underlying rises exactly $1 to $101, then the downbet will be worth 50 and Trader B wins $10. A rise over $1 and the downbet expires with the underlying above $101 and Trader B collects the full $60.

      Figure 1.6.2

      1.7 Up/Downbets v Conventional Calls/Puts

      Some readers of this book will have an understanding of conventional options and may well find a comparison between binaries and conventionals of interest.

      Upbets v Calls

      In Fig 1.7.1 the price of the upbet and call are both 25 and both are worth

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