--- title: "25-Delta Butterfly: Formula, Meaning" description: "The 25-delta butterfly measures smile curvature: the average implied volatility of the 25-delta call and 25-delta put minus the at-the-money implied..." canonical: https://www.getswoopr.com/indicators/options/25-delta-butterfly/ source: "Swoopr Investment: https://www.getswoopr.com" --- ## Direct Answer > The 25-delta butterfly measures smile curvature: the average implied volatility of the 25-delta call and 25-delta put minus the at-the-money implied volatility, for one expiry. It is commonly quoted in volatility points. A larger positive value means the wings are priced richer than the center, so the smile is more curved and out-of-the-money options carry more of a premium for large moves. # 25-Delta Butterfly: Formula, Meaning, Signals, Examples and How to Use It ## How Is 25-Delta Butterfly Calculated? The 25-delta butterfly measures smile curvature: the average implied volatility of the 25-delta call and 25-delta put minus the at-the-money implied volatility, for one expiry. It is commonly quoted in volatility points. **Formula:** `BF25 = (IV_25dCall + IV_25dPut) / 2 - IV_ATM` **Inputs:** - Implied volatility of the 25-delta call - Implied volatility of the 25-delta put - At-the-money implied volatility - A single expiry **Worked example.** With a 25-delta call at 22%, a 25-delta put at 26% and an at-the-money level of 20%, the butterfly is 4.0% in volatility points. The inputs are illustrative numbers, not market data. **Reading it.** A larger positive value means the wings are priced richer than the center, so the smile is more curved and out-of-the-money options carry more of a premium for large moves. A value near zero means a flatter smile. Compare it with the same expiry's own history. **Limits.** Quoting conventions differ: some desks use a market-strangle version, and the delta grid and expiry matter. It also says nothing about direction, which is what the risk reversal captures. Thin or stale wing quotes can distort it. ## What is 25-Delta Butterfly? The 25-delta butterfly measures smile curvature: the average implied volatility of the 25-delta call and 25-delta put minus the at-the-money implied volatility, for one expiry. It is commonly quoted in volatility points. ## How to use 25-Delta Butterfly A larger positive value means the wings are priced richer than the center, so the smile is more curved and out-of-the-money options carry more of a premium for large moves. A value near zero means a flatter smile. Compare it with the same expiry's own history. A reading alone is never a buy or sell signal; it needs context from price structure, volume, volatility and the broader market regime. ## Strengths - Averaging the two wing volatilities and subtracting the at-the-money level isolates curvature, leaving out the tilt that the risk reversal reports. - Fixing delta means the butterfly tracks the same relative strike distance through time rather than a fixed price strike. - Reproducible when the formula and data convention are fixed. ## Weaknesses and limitations - Delta-based wings sit at different strikes as volatility changes, so the strike distance behind the number moves with the level of volatility itself. - Two wing points and one at-the-money point give only three samples of the smile, so its shape beyond those points is not described. - Correlated indicators can create false confidence by repeating the same underlying information. ## Editorial and risk note This page is educational content, not individualized investment advice. It should not imply guaranteed prediction, accuracy or outperformance. ## Frequently Asked Questions Is 25-Delta Butterfly a buy or sell signal? No. A larger positive value means the wings are priced richer than the center, so the smile is more curved and out-of-the-money options carry more of a premium for large moves. Quoting conventions differ: some desks use a market-strangle version, and the delta grid and expiry matter. A trade built on it still needs a trigger, an invalidation rule, a position size and realistic execution assumptions. What is the best setting for 25-Delta Butterfly? 25-Delta Butterfly is computed from implied volatility of the 25-delta call; implied volatility of the 25-delta put; at-the-money implied volatility, so the choices that matter are the data convention and the window it is read over. Test those across instruments, regimes and out-of-sample periods instead of fitting one historical winner. Can 25-Delta Butterfly be used by itself? Quoting conventions differ: some desks use a market-strangle version, and the delta grid and expiry matter. It also says nothing about direction, which is what the risk reversal captures. Thin or stale wing quotes can distort it. For that reason it is read next to measures of direction, participation, valuation, liquidity and risk, not alone. Does 25-Delta Butterfly work on every timeframe? The calculation (BF25 = (IV_25dCall + IV_25dPut) / 2 - IV_ATM) can be run on any bar size, but behavior is not portable: a reading on a five-minute chart describes a very different market window from the same reading on a daily chart. Validate the exact timeframe before relying on it. Why does 25-Delta Butterfly give false signals? Delta-based wings sit at different strikes as volatility changes, so the strike distance behind the number moves with the level of volatility itself. Two wing points and one at-the-money point give only three samples of the smile, so its shape beyond those points is not described. Lag, noise and regime changes add to this, because market participants react to new information after the reading is calculated. How should 25-Delta Butterfly be backtested? Rebuild 25-Delta Butterfly from implied volatility of the 25-delta call using point-in-time data, write the rules before testing, include delisted securities where relevant, model realistic fills and costs, reserve a validation sample and compare with a simpler baseline. S Swoopr Editorial Team The Swoopr Editorial Team produces independent investment education, research, and tools for understanding markets, evaluating opportunities, and managing risk. All content is educational only and does not constitute personalized investment advice. See our [editorial policy](https://www.getswoopr.com/legal/editorial-policy/) and [corrections policy](https://www.getswoopr.com/legal/corrections-policy/).