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.
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.
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;
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 blocks to which all financial instruments can be reduced.