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Delta

In short

How much an option's price changes per $1 move in the underlying stock

If a call has delta of 0.5, it gains $0.50 for every $1 the stock rises. Delta 1.0 means the option moves dollar-for-dollar with the stock. At-the-money options typically have delta near 0.5.

Delta ranges from 0 to 1 for calls (-1 to 0 for puts). It approximates the probability the option expires in-the-money. Delta-neutral positions (overall delta near zero) are hedged against small price moves. Delta changes as the stock price moves (captured by gamma).

Formula

Delta = ∂Option Price ÷ ∂Underlying Price

Thresholds

0-0.25
Deep OTM — low probability
0.25-0.45
OTM — cheaper premium
0.45-0.55
ATM — balanced
0.55-1
ITM — high probability

Related concepts

  • Gamma — Gamma measures how fast delta changes. High gamma means your option becomes more or less sensitive quickly as the stock moves. Near expiration, gamma is highest — small stock moves cause big swings in option value.
  • Theta — Options are like ice cubes that melt over time. Theta measures how fast value evaporates daily. An option with theta of -$0.05 loses $5 per day per contract, all else equal. Time is your enemy as an option buyer.
  • Vega — Vega measures how much an option's price changes when market expectations of volatility change. If you expect a big announcement (earnings, FDA), buy before the event — vega will boost your option's value as uncertainty rises.
  • Implied Volatility — Implied volatility is the market's guess about how much a stock will move. High IV means expensive options (the market expects big moves). Low IV means cheap options. Buy options when IV is low, sell when IV is high.