# Implied volatility

Implied volatility is the annualized volatility of an underlying asset that makes an option-pricing model match an option's observed market price, given the model's other inputs.

## What it means

An option's price contains information about how much uncertainty market participants are pricing into the underlying asset. Implied volatility (IV) expresses that uncertainty as an annualized percentage. It is extracted from an option price using a pricing model; it is not calculated directly from past stock returns.

IV applies to a particular option and model. Options on the same stock can have different IVs at different strike prices and expiration dates. A quoted IV is not a prediction that the stock will move by exactly that percentage, and it says nothing by itself about whether the stock will rise or fall.

## How it is calculated

A common approach for a European-style option is to solve a pricing model backward:

`Find σ_IV such that ModelPrice(S, K, T, r, q, σ_IV, type) = observed option price`

- `σ_IV` is implied volatility, quoted as an annualized standard deviation; 20% means `0.20` in the model.
- `S` is the current underlying stock price, in US$ per share.
- `K` is the option's strike price, in US$ per share.
- `T` is time to expiration, in years.
- `r` is the annualized risk-free interest-rate input, and `q` is the annualized dividend-yield input.
- `type` specifies whether the contract is a call or a put; the observed option price is in US$ per share.

There is generally no simple formula that isolates IV from the option price. Software tries volatility values until the model price matches the observed price. The result depends on the model and inputs, including how dividends and contract features are handled. A bid price and an ask price can also produce different IV estimates.

## Worked example

These are hypothetical round numbers, not a live quote. Suppose a European-style call has a stock price `S = US$100`, strike `K = US$100`, and 30 calendar days until expiration. For simplicity, set both the interest-rate and dividend-yield inputs to `0%`. Its observed price is `US$2.29` per share.

1. Convert the time input: `T = 30/365 ≈ 0.0822` years.
2. Try `σ = 20%` per year in a Black-Scholes call-pricing model. With those inputs, the model price is approximately `US$2.29` per share.
3. Because the model price matches the observed price to rounding, the option's IV is approximately `20%` annualized.

The square-root-of-time calculation `20% × √(30/365) ≈ 5.7%` gives a model-based one-standard-deviation scale for a 30-day return under simplifying assumptions. It is not a promised range, a maximum move, or a directional forecast.

## Why it matters before you trade

For an option trade, IV is one input for understanding the option premium and its sensitivity to a change in expected volatility. An option's price can change when IV changes even if the stock price does not. Comparing IV across contracts requires attention to expiration and strike, rather than treating one quoted percentage as a property of the stock.

For a stock trade, options IV can provide context about uncertainty around events such as earnings. It does not determine the stock order's spread, market impact, or likely fill price. Historical volatility describes observed past price changes; IV reflects an option price interpreted through a model. Neither measure guarantees a future outcome.

## How PreTrAIde uses it

PreTrAIde's stated quantitative volatility measure is **daily volatility**, blended from Parkinson, close-to-close, Yang-Zhang, and simplified GARCH(1,1) estimators. Its product facts do not say that it calculates or uses options-implied volatility. Do not read an IV estimate into its volatility score or success probability.

In a PreTrAIde pre-trade analysis, the user enters a stock basket before placing an order. The analysis reports risk and execution assessments alongside a GO, NO-GO, or MODIFY verdict as decision support, not an investment recommendation. Its 1-day 95% value at risk concerns a one-day risk estimate, not an option's IV or a guarantee against larger losses.

## Common mistakes

- **Reading IV as direction:** A high IV does not specify whether a stock will move up or down.
- **Confusing annual and daily units:** An annualized 20% IV is not a statement that tomorrow's move will be 20%.
- **Treating IV as observed volatility:** It is backed out of an option price; historical volatility is estimated from past prices.
- **Ignoring the contract and quote:** Strike, expiration, model assumptions, and the price used to calculate IV all matter.

---
Source: https://pretraide.com/glossary/implied-volatility