(the Greeks): Delta
Among the Greeks, Delta is the best known and most
commonly used options indicator. Delta represents the rate of change of
an option's fair value with respect to changes in the price of its
underlying. It indicates the sensitivity of an option's value to small
changes in the underlying asset price. Delta is simply a number that
measures how much the theoretical value of an option will change if the
underlying stock goes up or down by $1. A call option will rise in value
if the underlying stock price rises, and drop in value if the stock
price falls – this is described by means of a positive Delta. A put
option will rise in value if the underlying stock price falls - this is
described by means of a negative Delta.
Example 1: If the price of an underlying asset
goes up by $1 and the price of an associated call option on that asset
goes up by $.50, then that option's Delta is 50% or .50. This means that
the option moves half as fast as its underlying asset - at current
Example 2: If an option moves identical with
its underlying, i.e., on a one-to-one basis, the Delta of the position
is 100%, or 1.
Deltas are positive: They range from 0% to 100% (0 to 1). Long
calls, short puts, and long stock all have positive Deltas;
- Put Deltas
are negative: They range from – 100% to 0% (-1 to 0). Long puts,
short calls, and short stock all have negative Deltas;
- Deltas will
approach 100% (1) if an option is in-the-money at expiration. If an
option is out-of-money, delta will approach 0% (0);
- Delta is
close to 0.5 for at-the-money options;
approaches 1 (for calls) or -1 (for puts) the further an option is
approaches 0 the further an option is out-of-the-money.
At-the-money options have Deltas that are relatively
immune to changes in time and volatility. This means that an
at-the-money option with 100 days left to expiration and the same
at-the-money option with 10 days to expiration will both have Deltas
close to 0.5. Deltas are more sensitive to changes in volatility or time
to expiration, the more in-the-money or out-of-the money an option
becomes. When fewer days remain to expiration, or when volatility
decreases, the Deltas of in-the-money calls are pushed closer to 1 (- 1
for puts) whereas the Deltas of out-of-the-money options move closer to
0. We may see a Delta grow to 0.99 with only a few days left to
expiration - without a stock moving at all. On the other hand, the same
in-the-money option might have a Delta of only 0.8 when about 100 days
remain to expiration.
The Delta of an option is
largely a function of the price of its underlying relative to its strike
price. Deltas change when the stock price of the underlying changes
(that is why Gamma is important).
Deltas are of
key importance when traders use options as tools to hedge positions –
that is why Delta is also known as the “hedge ratio”. The hedge ratio
allows a trader to correctly determine a portfolio's mix of assets,
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