In options trading, standard deviation represents the expected price range of the underlying asset over a defined time frame, based on current implied volatility.
For example, if the implied volatility (IV) of NIFTY is 12%, it means the market is theoretically expecting NIFTY to move:
+12% or -12% over 1 year, with approximately 68% probability (1 standard deviation range)
Similarly:
2 standard deviations (~±24%) capture about 95–99% probability.
This gives traders a probabilistic range of where the price is likely to stay.
Standard deviation is derived from IV using time scaling. Since IV is annualised, it must be adjusted for the selected time period.
The formula is:
SD = (IV / 100) × √(t / 252) × Underlying Price
Where:
IV = Implied volatility
t = Number of days (e.g., 7 days, 30 days)
252 = Trading days in a year
Underlying Price = Current price of the index/stock
If:
NIFTY = 20,000
IV = 12
Time = 7 days
Then:
SD = (12 / 100) × √(7 / 252) × 20,000
This gives the expected price movement for the next 7 days.
This means the platform calculates standard deviation dynamically based on the selected time frame (e.g., 7 days, expiry-based, etc.).
Standard deviation corresponds to probability ranges:
±1 SD → ~68% probability
±2 SD → ~95% probability
±3 SD → ~99% probability
This means:
There is a ~68% probability that price stays within 1 SD
There is a small probability of extreme moves beyond 2 SD
Standard deviation helps traders estimate the probability of profit (POP) by comparing option strike prices to the expected range.
If a trader sells options outside the standard deviation range, the probability of profit increases.
Example:
Selling a call at +1 SD
→ ~68% probability the price stays below the strike
→ POP ≈ 68%
Sell Call at +1 SD
Sell Put at -1 SD
This creates a range where:
Price is expected to stay within the range ~68% of the time
POP ≈ 68%
1 SD → ~68% POP
1.5 SD → ~80–85% POP
2 SD → ~95% POP
Further strikes increase POP but reduce premium.
The number of days to expiry directly impacts standard deviation due to the square root of time factor.
As days increase:
- Standard deviation increases
- Expected move becomes larger
- Probability range widens
- POP decreases for the same strike
As days decrease:
- Standard deviation decreases
- Expected move becomes smaller
- Probability range contracts
- POP increases for the same strike
For example, a strike that lies near 1 SD in a 30-day setup may fall outside 1 SD in a 7-day setup. This increases the probability of profit without changing the strike.
As time passes (time decay), the expected move shrinks if price remains stable, which naturally improves POP for option sellers.
Option Chain:
Many trading platforms display expected move or SD-based ranges directly
These are derived using the same IV formula
Time-Based Selection:
Traders can select different time frames (e.g., 7 days, expiry)
The system recalculates SD accordingly using √(t/252)
ATM Straddle Approximation:
Expected Move ≈ ATM Call Premium + ATM Put Premium
This gives a quick estimate of 1 SD move
Markets do not follow a perfect normal distribution. Standard deviation-based probabilities are theoretical and may underestimate sharp or sudden price movements, especially during events or high volatility periods.
| Scenario | Outcome |
|---|---|
| If price moves beyond 1 SD | This occurs about 32% of the time |
| If IV increases | Standard deviation range expands |
| If IV decreases | Standard deviation range contracts |
| Selling inside SD | Higher premium but lower probability of profit |
| Selling outside SD | Lower premium but higher probability of profit |
| Changing time frame (e.g., 7 days vs expiry) | SD recalculates based on time |
| As days to expiry decrease | Standard deviation contracts and POP increases for the same strike (if price remains stable) |
Standard deviation represents the expected move of the underlying derived from implied volatility. Since IV is annualised, it is adjusted for time using the square root of time. The 1 SD range captures about 68% probability, and traders use this to estimate probability of profit by selecting strikes relative to this range. It is commonly used in strategies like short options, strangles, and iron condors.
Last updated: 21 Apr 2026