Delta as a metric for moneyness

The moneyness of an option was defined earlier in terms of the difference between
the underlying asset price and the exercise price. Dealers in the currency option
markets often rely on a different metric for moneyness, the option delta, which we
encountered earlier as an option sensitivity and risk management tool.
As shown in Figure 1.23, the call delta declines monotonically as exercise price
rises – and the option goes further out-of-the-money – so dealers can readily find the
unique exercise price corresponding to a given delta, and vice versa. The same holds
for puts.
Recall that the delta of a put is equal to the delta of a call with the same exercise
price, minus the present value of one currency unit (slightly less than one). Often,
exercise prices are set to an exchange rate such that delta is equal to a round number
like 25% or 75%. A useful consequence of put–call parity (discussed above) is that
puts and calls with the same exercise price must have identical implied volatilities.
The volatility of a 25-delta put is thus equal to the volatility of a 75-delta call.
Because delta varies as market conditions, including implied volatility, the exercise
price corresponding to a given delta and the difference between that exercise price
and the current forward rate vary over time. For example, at an implied volatility of
15%, the exercise prices of one-month 25-delta calls and puts are about 3% above
and below the current forward price, while at an implied volatility of 5%, they are
about 1% above and below.

The motivation for this convention is similar to that for using implied volatility: it
obviates the need to revise price quotes in response to transitory fluctuations in the
underlying asset price. In addition, delta can be taken as an approximation to the
market’s assessment of the probability that the option will be exercised. In some
trading or hedging techniques involving options, the probability of exercise is more
relevant than the percent difference between the cash and exercise prices. For
example, a trader taking the view that large moves in the asset price are more likely
than the market is assessing might go long a 10-delta strangle. He is likely to care
only about the market view that there is a 20% chance one of the component options
will expire in-the-money, and not about how large a move that is.