Interpreting Implied Volatility and Stock Price Distributions
Summary
This exchange examines whether implied volatility can be used to estimate the range of future stock prices. The question raises three concerns: log returns may be modeled as normal while prices are lognormal, the expected return affects longer-horizon outcomes, and return variance grows with time. These points motivate a distinction between describing price uncertainty and predicting a realized future range.
The answer notes that a normal-price approximation can approximate the Black–Scholes distribution over short horizons, when drift may have less influence than volatility. Over longer horizons, drift matters more. It also emphasizes that an option-implied distribution is risk-neutral: it is constructed for pricing and can differ substantially from the real-world distribution investors experience. Consequently, interpreting implied volatility depends on the intended measure and horizon. The response is conceptual and does not give a numerical conversion method, forecast test, or guarantee that market-implied distributions predict realized returns.
Key ideas
- A normal model for returns implies a lognormal distribution for prices under the stated assumptions.
- A normal-price approximation can be reasonable for short horizons.
- Drift becomes more relevant as the forecast horizon lengthens.
- Option-implied distributions are risk-neutral and may differ from real-world price distributions.
- Choose the probability measure according to whether the goal is pricing or forecasting.
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# Interpretation of IV and its use in stock movement prediction
# Interpretation of IV and its use in stock movement prediction
I found this interpretation has three pitfalls: 1. what the model says is ROR follows a normal disrtibution with $E={\mu}t$ and $Var={\sigma^2}t$, so the price itself is a log-normal distribution which has a different Variance (and confidence interval) 2. the interpretation does not take into account the drift compoent which increases as time increases. 3. the ROR Variance also increases with time and not a constant. Hence it will be very difficult to correctly use IV as a tool to predict the range of stock price movements. If you see my understanding incorrect, please kindly give your comments. Thanks in advance.
I found this interpretation has three pitfalls: 1. what the model says is ROR follows a normal disrtibution with $E={\mu}t$ and $Var={\sigma^2}t$, so the price itself is a log-normal distribution which has a different Variance (and confidence interval) 2. the interpretation does not take into account the drift compoent which increases as time increases. 3. the ROR Variance also increases with time and not a constant. Hence it will be very difficult to correctly use IV as a tool to predict the range of stock price movements. If you see my understanding incorrect, please kindly give your comments. Thanks in advance.
1. what the model says is ROR follows a normal disrtibution with $E={\mu}t$ and $Var={\sigma^2}t$, so the price itself is a log-normal distribution which has a different Variance (and confidence interval) 2. the interpretation does not take into account the drift compoent which increases as time increases. 3. the ROR Variance also increases with time and not a constant. Hence it will be very difficult to correctly use IV as a tool to predict the range of stock price movements. If you see my understanding incorrect, please kindly give your comments. Thanks in advance.
Hence it will be very difficult to correctly use IV as a tool to predict the range of stock price movements. If you see my understanding incorrect, please kindly give your comments. Thanks in advance.
## Answer by Ezy (score 1, accepted)
https://quant.stackexchange.com/a/42184
- The Bachelier model which assumes that price follows a normal distribution is a correct approximation for the Black-Scholes one for short times t. When time is short it's fine to ignore drift because the movements will be more driven by volatility
- For longer time intervals you cannot ignore drift any more. But the actual distribution of the stock price at horizon T may be very different from the one implied by the options market because the latter one describes the stock in a very specific measure called the "risk neutral" measure.
So overall I would answer that if your goal is to get insight about the distribution of the stock at a certain date T you first need to express whether you are interested by this distribution in the real world measure or the risk neutral measure.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.