$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 $1 per point. Clearly the upbet’s profit potential is limited to $75 with the ‘draw’ generating a profit of $25.
For the conventional call there is no limited upside, with the 45° profit line travelling upwards from –25 through breakeven, through 75, through 100 and upwards out of sight. But this increased potential profit comes at a cost, of course, because at any underlying price between A and B the conventional call performs less profitably than the upbet. At A, the upbet makes a 100% profit and turns a $25 bet into a $25 profit whereas the conventional option loses the full premium of $25.
Figure 1.7.1
Where the conventional call breaks even at an underlying price 25¢ higher than A, the upbet is worth 100 generating a profit of 300%. The difference between the conventional and binary’s profits subsequently diminishes until the underlying reaches B, where both conventional and upbet make a profit of $75. Above B the conventional call gains in value point for point with the underlying while the upbet is stuck on 100.
Figure 1.7.2
Fig 1.7.2 illustrates P&L profiles of the seller of the upbet and the writer of the conventional call. Here the profile of Fig 1.7.1 is reflected through the horizontal axis with the writer of the conventional losing less than the seller of the binary between A and B, but subsequently facing an unlimited loss scenario above B.
Downbets v Puts
Figs 1.7.3 and 1.7.4 illustrate the comparisons of long and short downbet/put expiry P&Ls.
Figure 1.7.3
Assuming the price of the downbet and put options are both 25 and the strike at A is $99, then the trader who bought the conventional put has a breakeven at C where the underlying is equal to $99 – 25¢ = $98.75.
The breakeven for the downbet buyer is at A, the strike, where the downbet is worth 50 and the buyer doubles his money. At B, an underlying of $98, both conventional put and downbet make a profit of 300%, but lower than $98 the conventional is now behaving like a short future.
The scale of Fig 1.7.4 might suggest that a short conventional put has a limited downside. It does, at the point where the stock is worth zero. If the downbet and put options are worth $10/pt, then with the underlying at zero, the maximum loss for the downbet would be limited to:
$10 ¥ ( 25 – 100 ) = – $750;
whereas the maximum loss for the conventional put would be:
$10 ¥ (0.00 – ( $99 – 25¢ ) = – $98,750.
Figure 1.7.4
The above comparisons between conventional calls, puts, upbets and downbets enable the user to further tailor the instrument to his market view. Furthermore, the combination of conventionals and binaries provides a highly sophisticated method of creating bespoke strategies for the imaginative and creative speculator.
1.8 Formulae
1.9 Summary
The probability of an event happening plus the probability of that same event not happening is 100%. Therefore, the probability that the share price at expiry ends up above $101, on $101, or below $101 must aggregate to 100%.
On comparing Fig 1.3.1 with Fig 1.6.2 and then Fig 1.3.2 with Fig 1.6.1 enables us to draw some interesting conclusions:
1. Selling an upbet for 40 is identical to buying a same strike, same expiry downbet for 60.
2. Buying an upbet for 40 is identical to selling a same strike, same expiry downbet for 60.
As a rule:
1. For the same strike and same expiry, BUYING an upbet for price X is the same as SELLING a downbet for 100 – X.
2. For the same strike and same expiry, SELLING an upbet for price Y is the same as BUYING a downbet for 100 – Y.
3. For the same strike and the same expiry the value of the upbet plus the value of the downbet must sum to 100. This rule may appear obvious and trivial but it absolutely differentiates binaries from conventional options as the section on vega demonstrates.
This chapter has covered the two most basic of binary instruments, the upbet and the downbet. The upbet and the downbet are the basic foundation
