# How Is Implied Volatility Calculated from the Black-Scholes Model? ⎊ Path

**Published:** 2025-12-04
**Author:** Greeks.live
**Categories:** Path

---

## How Is Implied Volatility Calculated from the Black-Scholes Model?

Implied volatility is not calculated directly from the Black-Scholes formula; rather, it is found by reversing the process. The model's formula is used to solve for the volatility that would make the theoretical option price equal to the current market price of that option.

Since there is no simple algebraic solution for volatility in the formula, this requires an iterative numerical method, such as the Newton-Raphson method. Traders input the known variables (stock price, strike price, time to expiration, risk-free rate) and the option's market price, and the algorithm finds the volatility value that fits.

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## Glossar

### [Implied Volatility](https://learn.greeks.live/area/implied-volatility/?utm_source=crypto.greeks.live&utm_medium=referral&utm_campaign=satellite)

Expectation ⎊ This value represents the market's consensus forecast of future asset price fluctuation, derived by reversing option pricing models using current market premiums.

### [Theoretical Option Price](https://learn.greeks.live/area/theoretical-option-price/?utm_source=crypto.greeks.live&utm_medium=referral&utm_campaign=satellite)

Valuation ⎊ A theoretical option price, within cryptocurrency markets, represents a calculated estimate of an option’s fair value, derived from a mathematical model incorporating factors like the underlying asset’s price, strike price, time to expiration, volatility, and risk-free interest rate.

### [Black-Scholes Formula](https://learn.greeks.live/area/black-scholes-formula/?utm_source=crypto.greeks.live&utm_medium=referral&utm_campaign=satellite)

Derivation ⎊ The Black-Scholes Formula, initially proposed in 1973, provides a theoretical estimate of the price of European-style options, fundamentally altering quantitative finance and risk management practices.

## Discover More

### [Does the Black-Scholes Model Work Well for Options on Bitcoin?](https://learn.greeks.live/path/does-the-black-scholes-model-work-well-for-options-on-bitcoin/?utm_source=crypto.greeks.live&utm_medium=referral&utm_campaign=satellite)
![Does the Black-Scholes Model Work Well for Options on Bitcoin?](https://learn.greeks.live/wp-content/uploads/2025/10/Asymmetric-Volatility-Surface-Contraction-Sculpting-Cryptographic-Digital-Asset-Hedging-Mechanisms.webp)

It is used as a starting point, but modifications are needed due to Bitcoin's non-constant volatility and non-normal price movements.

### [What Is the Difference between "Historical Volatility" and "Implied Volatility"?](https://learn.greeks.live/path/what-is-the-difference-between-historical-volatility-and-implied-volatility-2/?utm_source=crypto.greeks.live&utm_medium=referral&utm_campaign=satellite)
![What Is the Difference between "Historical Volatility" and "Implied Volatility"?](https://learn.greeks.live/wp-content/uploads/2025/10/Bifurcated-Digital-Asset-Volatility-Surface-Modeling-Implied-Skew-Distribution-Dynamics.webp)

Historical volatility is a factual, backward-looking measure of past price movement; implied volatility is a forward-looking, market-derived forecast of future volatility.

### [What Is the Difference between Implied Volatility and Historical Volatility?](https://learn.greeks.live/path/what-is-the-difference-between-implied-volatility-and-historical-volatility/?utm_source=crypto.greeks.live&utm_medium=referral&utm_campaign=satellite)
![What Is the Difference between Implied Volatility and Historical Volatility?](https://learn.greeks.live/wp-content/uploads/2025/10/Quantum-Leveraged-Token-Mechanics-Revealing-Hidden-Volatility-Surface-Parameters-in-Digital-Asset-Swaps.webp)

Historical volatility is a backward-looking measure of past price movement; implied volatility is the market's forward-looking expectation derived from option price.

### [What Is the Black-Scholes Model and What Are Its Core Inputs?](https://learn.greeks.live/path/what-is-the-black-scholes-model-and-what-are-its-core-inputs/?utm_source=crypto.greeks.live&utm_medium=referral&utm_campaign=satellite)
![What Is the Black-Scholes Model and What Are Its Core Inputs?](https://learn.greeks.live/wp-content/uploads/2025/10/Quantum-Entanglement-Parity-Violation-in-High-Frequency-Crypto-Derivatives-Settlement-Mechanisms.webp)

Black-Scholes prices European options using underlying price, strike, time, risk-free rate, and implied volatility as inputs.

### [How Does 'Implied Volatility' Differ from 'Realized Volatility' and How Can This Spread Be Arbitraged?](https://learn.greeks.live/path/how-does-implied-volatility-differ-from-realized-volatility-and-how-can-this-spread-be-arbitraged/?utm_source=crypto.greeks.live&utm_medium=referral&utm_campaign=satellite)
![How Does 'Implied Volatility' Differ from 'Realized Volatility' and How Can This Spread Be Arbitraged?](https://learn.greeks.live/wp-content/uploads/2025/10/Precision-Engineering-Mechanics-Interfacing-Cryptocurrency-Derivatives-Settlement-Infrastructure-Physicalization.webp)

Implied volatility is the market's guess on future swings; realized volatility is what actually happens. Bet on the gap.

### [What Is "Implied Volatility" and How Is It Derived from the Black-Scholes Model?](https://learn.greeks.live/path/what-is-implied-volatility-and-how-is-it-derived-from-the-black-scholes-model/?utm_source=crypto.greeks.live&utm_medium=referral&utm_campaign=satellite)
![What Is "Implied Volatility" and How Is It Derived from the Black-Scholes Model?](https://learn.greeks.live/wp-content/uploads/2025/10/Crystalline-Pyramidal-Volatility-Proxy-Mounted-on-Decentralized-Ledger-Hardware-Interface-Analysis.webp)

IV is the market's expected future volatility, derived by solving the Black-Scholes model for the volatility input.

### [How Does an Increase in the Risk-Free Rate Affect the Price of a Call Option According to Black-Scholes?](https://learn.greeks.live/path/how-does-an-increase-in-the-risk-free-rate-affect-the-price-of-a-call-option-according-to-black-scholes/?utm_source=crypto.greeks.live&utm_medium=referral&utm_campaign=satellite)
![How Does an Increase in the Risk-Free Rate Affect the Price of a Call Option According to Black-Scholes?](https://learn.greeks.live/wp-content/uploads/2025/10/Angular-Bifurcation-Of-A-Digital-Asset-Hinge-Mechanism-Displaying-Polarization-Filters.webp)

An increase in the risk-free rate increases the Call option's price because it raises the present value of the strike price.

### [What Is the Black-Scholes Model and What Are Its Main Inputs?](https://learn.greeks.live/path/what-is-the-black-scholes-model-and-what-are-its-main-inputs/?utm_source=crypto.greeks.live&utm_medium=referral&utm_campaign=satellite)
![What Is the Black-Scholes Model and What Are Its Main Inputs?](https://learn.greeks.live/wp-content/uploads/2025/10/Exploded-View-High-Fidelity-Visualization-of-Decentralized-Finance-Protocol-Core-Mechanism-and-Volatility-Metric-Translucence.webp)

Black-Scholes prices European options. Key inputs are asset price, strike price, time, interest rate, and implied volatility.

### [What Role Does the Risk-Free Rate Play in Options Pricing Models like Black-Scholes for Long-Dated Contracts?](https://learn.greeks.live/path/what-role-does-the-risk-free-rate-play-in-options-pricing-models-like-black-scholes-for-long-dated-contracts/?utm_source=crypto.greeks.live&utm_medium=referral&utm_campaign=satellite)
![What Role Does the Risk-Free Rate Play in Options Pricing Models like Black-Scholes for Long-Dated Contracts?](https://learn.greeks.live/wp-content/uploads/2025/10/Stratified-Spherical-Volatility-Surface-Decomposition-Modeling-Deriving-Intrinsic-Option-Value.webp)

The risk-free rate discounts future payoffs; a higher rate increases call prices and decreases put prices, especially for long-dated options.

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