Delta
The five figures commonly used by option traders are represented by Greek
letters: delta, gamma, theta, vega, rho. The figures are referred to as option
greeks. Vega, of course, is not an actual letter of the greek alphabet, but in
the options vernacular, it is considered one of the greeks.
The greeks are a derivation of an option-pricing model, and each Greek
letter represents a specific sensitivity to influences on the option’s value. To
understand concepts represented by these five figures, we’ll start with delta,
which is defined in four ways:
1. The rate of change of an option value relative to a change in the
underlying stock price.
2. The derivative of the graph of an option value in relation to the stock
price.
3. The equivalent of underlying shares represented by an option
position.
4. The estimate of the likelihood of an option expiring in-the-money. 1
Definition 1 : Delta (Δ) is the rate of change of an option’s value relative
to a change in the price of the underlying security. A trader who is bullish
on a particular stock may choose to buy a call instead of buying the
underlying security. If the price of the stock rises by $1, the trader would
expect to profit on the call—but by how much? To answer that question, the
trader must consider the delta of the option.
Delta is stated as a percentage. If an option has a 50 delta, its price will
change by 50 percent of the change of the underlying stock price. Delta is
generally written as either a whole number, without the percent sign, or as a
decimal. So if an option has a 50 percent delta, this will be indicated as
0.50, or 50. For the most part, we’ll use the former convention in our
discussion.
Call values increase when the underlying stock price increases and vice
versa. Because calls have this positive correlation with the underlying, they
have positive deltas. Here is a simplified example of the effect of delta on
an option: