Concept
Delta
Delta measures how much a theoretical option price changes for a one-unit move in the underlying. A call with a Delta of 0.45 gains roughly 0.45 in value if the underlying rises by 1, holding everything else constant.
Delta across spot price (19800 – 24200)
| Theoretical price | 512.69 |
| Deltachange in option value per 1 unit move in the underlying | 0.5515 |
| Gammachange in delta per 1 unit move in the underlying | 0.00035 |
| Thetachange in value per calendar day, all else equal | -9.555 |
| Vegachange in value per 1 percentage point of implied volatility | 24.953 |
| Rhochange in value per 1 percentage point of interest rate | 9.550 |
Computed with the same Black-Scholes implementation CernoQuant uses for real trades, at a 6.5% risk-free rate and calendar-day theta. Values are theoretical: traded option prices differ from model prices, and every input above is hypothetical.
How to read it
- Calls have Delta between 0 and 1; puts between −1 and 0. Deep in-the-money options approach the extremes, far out-of-the-money options approach zero.
- An at-the-money option has a Delta near 0.5 for calls and −0.5 for puts, because a small move either way is roughly equally likely to end in or out of the money.
- Delta is not constant. It moves as the underlying moves, as time passes and as volatility changes — the sensitivity of Delta itself is Gamma.
What it does not tell you
- Delta is often described as the probability of finishing in the money. That is an approximation and not the definition — the two differ, particularly as volatility rises.
- It holds everything else constant, which never happens. A move in the underlying is usually accompanied by a change in volatility, and the two effects combine.
- It is a first-order estimate. For large moves it becomes progressively less accurate, because Delta itself has shifted during the move.
Frequently asked questions
What does delta 0.5 mean?
That the theoretical option price changes by about 0.5 for each one-unit move in the underlying, holding all else constant. It typically occurs near the money.
Is delta the probability of expiring in the money?
It is close to that under certain assumptions and is widely used as shorthand, but it is an approximation rather than the definition, and the gap widens at higher volatility.
Why does delta change?
Because the likelihood of the option finishing in the money changes as the underlying moves, as time passes and as volatility shifts. The rate of that change is Gamma.
What is delta for a put option?
Negative, between −1 and 0, because a put gains value as the underlying falls.
Related
- Options Greeks: An Overview — Concept
- Vega and Gamma — Concept
- Theta (Time Decay) — Concept
Educational use only
This page is educational material about how a technical tool is calculated and read. It is not investment advice, not a recommendation to buy or sell anything, and not a signal service. No indicator predicts future prices. CernoQuant is a trading journal and analytics platform, not a SEBI-registered investment adviser. Trading decisions and their outcomes are yours alone.
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