Theta is a ratio that measures how much the bet price will change due
to the passing of time.
Theta is probably the easiest ‘greek’ to conceptually grasp and is possibly
the most easily forecast since the passage of time itself moves in a
reasonably uniform manner.
Bets on many financial instruments are now always ‘in-running’, i.e. there
is always a market open on which to trade. These days there is a 24-hour
market in foreign exchange trading so any bet on the future level of the
$/£ rate is always ‘in-running’ with the theta constantly impacting on the
price of bets. On other markets which operate in discrete time periods,
where the market is open for a limited period of five days a week, marketmakers
will often use Monday’s theoretical prices on a Friday afternoon
in order not to get too exposed to the weekend’s three-day time decay.
An understanding of time decay and theta is thus critical to the trading
and risk management of binary options. The remainder of this section on
theta will analyse the effect of time decay on upbets and downbets, and
how this impact on the price of a bet is measured.
Upbets v the Underlying over Time
This section discusses time decay and its effect on the price of upbets as
time to expiry decreases, ultimately resulting in the profile of Fig 1.2.1.
Fig 2.1.1 shows the profile of upbets with a strike price of $100 and a
legend indicating the time to expiry. A unique characteristic of the binary
is that, irrespective of whether upbet or downbet or time to expiry, each
profile travels through the price 50 when the underlying is at-the-money,
i.e. the underlying is exactly the price of the strike. This is because a
symmetrical bell-shaped normal probability distribution is assumed so
that when the underlying is at-the-money there is a 50:50 chance of the
underlying going up or down. This feature of the binary immediately
distinguishes it from the conventional option where the at-the-money can
take any value.
Upbet Theta
Table 2.3.1 provides 1 and 5 day thetas for underlying prices ranging from
$99.50 to $99.90 and assumes a strike price of $100 and therefore
applies to Fig 2.2.1. The theta for the $99.70 profile with 5 days left to
expiry is –6.5057. This value of theta defines how much the upbet will
decline in value over one year at the current rate of decay. To gauge
how much the upbet will lose in time decay over 1-day divide the theta
by 365 so the rough estimate of one-day decay at 5 days would be –
6.5057 / 365 = –0.017824. But remember, by convention binary prices
are multiplied by 100 to establish trading prices within a range of 0 –
100, so likewise we need to multiply the theta by 100 to get comparable
decay. In effect the time decay over 1 day of an upbet with 5 days to
expiry is –0.017824 × 100 = –1.7824 points. In fact the upbet with 5.5
and 4.5 days to expiry is worth 28.2877 and 26.2938 respectively, a
decay of –1.9939, so it can be argued that a 5-day theta of –1.7824 is a
reasonably accurate measure.