Estimating a One-Sigma Price Range from Volatility
Summary
The document answers a question about how far an asset price might move over a three-month horizon given its annualized volatility. The response treats the estimate as a static one-standard-deviation range, scaling volatility by the square root of time and applying the resulting percentage move above and below the current price. Its example uses a spot price of 100, annualized volatility of 15.7%, and 90 days to expiry, producing an approximate range from 92.20 to 107.80.
The surrounding question discusses an option and financing costs, but the answer addresses only the likely price range, not the option’s value or the economic comparison between positions. The result is a simple volatility-based estimate, not a forecast of direction or a guarantee that prices will remain within the range. It does not discuss distribution assumptions, volatility changes, jumps, or how to adjust the estimate for other market conditions.
Key ideas
- A simple one-standard-deviation price range scales annualized volatility by the square root of the time horizon.
- The example applies the resulting percentage move symmetrically above and below the current spot price.
- The estimate describes a range of possible movement, not a directional forecast.
- The calculation is a static snapshot and does not address changing volatility or other distribution features.
- The response does not resolve the option financing comparison raised in the question.
Tags
Full text
# How far the spot price is likely to go from the current level in three months if its volatility is 15.7% # How far the spot price is likely to go from the current level in three months if its volatility is 15.7% On Page 24 of N. Taleb's "Dynamic Hedging" the author gives the following example > Example: Assume that an asset trades at \$100, with interest rates at 6% (annualized) and volatility at 15.7%. Assume also that the 3-month 80 call is worth \$20, at least if it is American. Forgoing early exercise would create an opportunity cost of 20 x 90/360 x .06 = .30 cents, the financing of \$20 premium for 3 months. The time value of the equivalent put is close to zero (by put-call parity), so the intelligent operator can swap the call into the underlying asset and buy the put to replicate the same initial structure at a better cost. He would end up long the put and long the underlying asset. The possible position of the operator before swap: - 1 call worth of \$20 a - \$80 in cash. The position after the swap: - 1 asset worth of $100 at the current spot price - 1 put worth of almost zero If I could earn 6% both on \$80 in cash and on 1 asset (i.e. if the asset is another currency for example) and the spot price would remain the same \$100 then I would agree with the calculations of the author: 1 asset x 90/360 x .06 - \$80 x 90/360 x .06 = (100 - 80) x 90/360 x .06 = 30 cents But if the price of the asset will go down to say \$75, then I'd better stay with the call because: 1 asset x 90/360 x .06 - \$80 x 90/360 x .06 = (75 - 80) x 90/360 x .06 = -7.5 cents So,how far the spot price is likely to go from the current level in three months if its volatility is 15.7%? ## Answer by amdopt (score 2, accepted) https://quant.stackexchange.com/a/33025 Keep in mind that there is nothing dynamic about this at all...it is only a snapshot and it is only a 1 sigma range. High side: ``` ([Price] * (1 + ([Vol] * SQRT[days to expiry]/365))) (100 * (1 + (.157 * sqrt(90/365))) 107.7960 ``` Low side: ``` ([Price] * (1 - ([Vol] * SQRT[days to expiry]/365))) (100 * (1 - (.157 * sqrt(90/365))) 92.2040 ```
Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.