Upbets and Downbets
An upbet can only win or lose at the moment the bet expires and not at
any time leading up to the expiry of the bet.
Examples of upbets are:
1. Will the price of the CBOT US Sep 10 year Notes future be above
$114 at 1600hrs on the last trading day of August?
2. Will the Dow Jones Index be above 12,000 at 1600hrs on the last
trading day of the year?
3. Will the LIFFE Euribor Dec/Sep spread be above 10 ticks at settlement
on the last day of November?
4. Will a non-farm payroll number be above +150,000?
Examples 1, 2 & 3 enable the bettor to make a minute by minute
assessment of the probability of the bet winning. Example 4 is a number
(supposedly) cloaked in secrecy until the number is announced at 13.30
hrs on a Friday.
In all the above examples the bet always has a chance of winning or
losing right up to the expiry of the bet although the probability may be
less than 1% or greater than 99%. The Notes could be trading two full
points below the strike the day before expiry but it is possible, although
highly improbable, for them to rise enough during the final day to settle
above the strike. Conversely the Notes could be trading a full two points
higher than the strike the day prior to expiry and still lose although the
probability of losing may be considered negligible.
Ultimately the upbet is not concluded until the bet has officially expired
and until then no winners or losers can be determined.
Downbets too can only win or lose at expiry. Although in many circumstances
the downbet is simply the reverse of the upbet, the downbet has
been treated with the same methodology as the upbet in order that other
bets, e.g. the eachwaybet, can be analysed within a uniform structure.
Also a separate treatment of downbets will provide a firmer base on
which to analyse the sensitivity of downbets.
Upbet Specification
Fig 1.1.1 presents three different random walks that have been generated
in order to illustrate winning and losing bets. All the upbets start with an
underlying price of $100, have twenty-five days to expiry and a strike
price of $101.
1. RandomWalk 1 (RW1) flirts with the $101 level after five days, retreats
back to the $100 level, rises and passes through the $101 strike after
eighteen days and then drifts to settle at a price around $100. The
buyer of the upbet loses.
2. RW2 travels up to the $101 level after the eighth day where it moves
sideways until, with nine days to expiry, 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.
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.