Downbet

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 ‘inthe-
money’ below the strike.
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.
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.

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.