Delta

Quick definition Delta measures how much an option price changes when the underlying asset price changes by one unit. Delta ranges from 0 to 1 for calls, -1 to 0 for puts. What it is A call option with delta 0.6 means if the stock rises 1 dollar, the call rises 0.6 dollars. A put with delta -0.4 means if the stock rises 1 dollar, the put falls 0.4 dollars. Delta is the slope of the option price curve. It changes as the underlying price and time to expiration change. Deep in-the-money options approach delta 1 (move one-for-one with stock). Deep out-of-the-money options approach delta 0 (barely move when stock moves). Why it matters Delta is the hedge ratio. If you own 100 shares and sell 2 calls (each delta 0.5), you are delta-neutral: the 100 shares move one-for-one with the market, but the 2 calls move 0.5 each (net 1), so the combined position doesn't move. Market makers use delta to hedge inventory. If a market maker buys a call (long delta 0.6), they short 0.6 of the underlying to stay delta-neutral. Delta and Probability Delta approximates the probability that an option finishes in-the-money. A call with delta 0.7 has roughly 70 percent probability of being in-the-money at expiration (under the risk-neutral measure, not real-world probability). Practical example You buy 1 call with strike 100, underlying at 100. The call costs 2 dollars and has delta 0.5. The stock rises to 101. The call is now worth approximately 2.50 dollars (original 2 dollars plus 0.5 dollar gain from delta). Your 100-dollar call position gained 50 dollars. If the stock falls to 99, the call is worth approximately 1.50 dollars. Your position lost 50 dollars. Dynamic delta Delta is not constant. As the stock price rises, delta increases (the option becomes more in-the-money and more responsive). As time passes, at-the-money options' deltas decay slightly. See also - Gamma - Vega - Theta - Options Greeks