# How Does the Black-Scholes Model Use Implied Volatility? ⎊ Path

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

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## How Does the Black-Scholes Model Use Implied Volatility?

The Black-Scholes model is a theoretical framework used to estimate the fair price or premium of a European-style option. It requires five inputs: the underlying asset's price, the option's strike price, the time to expiration, the risk-free interest rate, and the volatility.

In practice, traders use the known option price and solve the formula backward for the volatility, which is the implied volatility. Therefore, IV is an output when pricing options in the market, but it's an input when using the model to calculate a theoretical price.

- [What Does ‘European-Style’ Mean in the Context of an Option Contract?](https://learn.greeks.live/path/what-does-european-style-mean-in-the-context-of-an-option-contract/)

- [How Does the Concept of ‘Implied Volatility’ Arise from the Black-Scholes Model?](https://learn.greeks.live/path/how-does-the-concept-of-implied-volatility-arise-from-the-black-scholes-model/)

- [Which Volatility Measure Is Used as an Input in the Black-Scholes Model and Which Is the Output?](https://learn.greeks.live/path/which-volatility-measure-is-used-as-an-input-in-the-black-scholes-model-and-which-is-the-output/)

- [Which ‘Greek’ Is Directly Influenced by the Risk-Free Interest Rate Assumption in Black-Scholes?](https://learn.greeks.live/path/which-greek-is-directly-influenced-by-the-risk-free-interest-rate-assumption-in-black-scholes/)

- [What Are the Key Limitations of the Black-Scholes Model in Cryptocurrency Options?](https://learn.greeks.live/path/what-are-the-key-limitations-of-the-black-scholes-model-in-cryptocurrency-options/)

- [How Is Implied Volatility Calculated from the Black-Scholes Model?](https://learn.greeks.live/path/how-is-implied-volatility-calculated-from-the-black-scholes-model/)

- [Why Is the Risk-Free Rate Often Adjusted for Crypto Option Pricing?](https://learn.greeks.live/path/why-is-the-risk-free-rate-often-adjusted-for-crypto-option-pricing/)

- [How Is Implied Volatility Derived from the Black-Scholes Model?](https://learn.greeks.live/path/how-is-implied-volatility-derived-from-the-black-scholes-model/)

## Glossar

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

Foundation ⎊ The Black-Scholes model serves as the cornerstone for modern options pricing theory, providing a continuous-time framework for calculating the fair value of derivatives.

## Discover More

### [How Is the Black-Scholes Model Adapted for Use in Cryptocurrency Options?](https://learn.greeks.live/path/how-is-the-black-scholes-model-adapted-for-use-in-cryptocurrency-options/?utm_source=crypto.greeks.live&utm_medium=referral&utm_campaign=satellite)
![How Is the Black-Scholes Model Adapted for Use in Cryptocurrency Options?](https://learn.greeks.live/wp-content/uploads/2025/10/Crystalline-Bifurcation-Modeling-Volatility-Surface-Geometry-in-Decentralized-Finance-Structures.webp)

It is adapted by replacing the risk-free rate with a crypto-specific cost of carry or funding rate for perpetual futures.

### [What Are the Limitations of Applying the Black-Scholes Model to American-Style Crypto Options?](https://learn.greeks.live/path/what-are-the-limitations-of-applying-the-black-scholes-model-to-american-style-crypto-options/?utm_source=crypto.greeks.live&utm_medium=referral&utm_campaign=satellite)
![What Are the Limitations of Applying the Black-Scholes Model to American-Style Crypto Options?](https://learn.greeks.live/wp-content/uploads/2025/10/Symmetrical-Bifurcation-Visualization-of-Decentralized-Finance-Collateralized-Derivatives-Execution.webp)

Black-Scholes assumes European-style exercise only at expiration, not the early exercise feature of American options.

### [How Does the Black-Scholes Model Relate to the Pricing of Tokenized Options?](https://learn.greeks.live/path/how-does-the-black-scholes-model-relate-to-the-pricing-of-tokenized-options/?utm_source=crypto.greeks.live&utm_medium=referral&utm_campaign=satellite)
![How Does the Black-Scholes Model Relate to the Pricing of Tokenized Options?](https://learn.greeks.live/wp-content/uploads/2025/10/Precision-Engineering-of-Digital-Asset-Volatility-Management-Through-Spherical-Interface-Mechanisms.webp)

Black-Scholes uses five inputs (including volatility) to calculate the theoretical fair price (premium) of a tokenized option.

### [How Does the UTXO Model Differ Fundamentally from the Account/Balance Model Used by Ethereum?](https://learn.greeks.live/path/how-does-the-utxo-model-differ-fundamentally-from-the-account-balance-model-used-by-ethereum/?utm_source=crypto.greeks.live&utm_medium=referral&utm_campaign=satellite)
![How Does the UTXO Model Differ Fundamentally from the Account/Balance Model Used by Ethereum?](https://learn.greeks.live/wp-content/uploads/2025/10/Teal-Blue-Granular-Texture-Encapsulating-a-Spherical-Quantum-Refraction-Mechanism-in-a-Precision-Bearing-Track.webp)

UTXO tracks discrete, spent/unspent transaction outputs; Account/Balance tracks a global state of user balances, like a bank ledger.

### [What Is the Risk of Using a Flat Volatility Assumption (Like in Black-Scholes) for Pricing Options?](https://learn.greeks.live/path/what-is-the-risk-of-using-a-flat-volatility-assumption-like-in-black-scholes-for-pricing-options/?utm_source=crypto.greeks.live&utm_medium=referral&utm_campaign=satellite)
![What Is the Risk of Using a Flat Volatility Assumption (Like in Black-Scholes) for Pricing Options?](https://learn.greeks.live/wp-content/uploads/2025/10/Precision-Engineered-Cryptocurrency-Asset-Apex-Representing-Volatility-Surface-Skew-Configuration.webp)

Flat volatility risks mispricing OTM and ITM options, underestimating the true cost of tail risk protection (skew).

### [Why Is IV a Key Input for the Black-Scholes Model?](https://learn.greeks.live/path/why-is-iv-a-key-input-for-the-black-scholes-model/?utm_source=crypto.greeks.live&utm_medium=referral&utm_campaign=satellite)
![Why Is IV a Key Input for the Black-Scholes Model?](https://learn.greeks.live/wp-content/uploads/2025/10/Microstructure-of-Precision-Executions-Balancing-Volatility-Through-Decentralized-Financial-Primitives.webp)

IV is the required measure of price fluctuation; it is the only unknown parameter that determines the option's time value.

### [Which Volatility Measure Is Used in the Black-Scholes Model?](https://learn.greeks.live/path/which-volatility-measure-is-used-in-the-black-scholes-model/?utm_source=crypto.greeks.live&utm_medium=referral&utm_campaign=satellite)
![Which Volatility Measure Is Used in the Black-Scholes Model?](https://learn.greeks.live/wp-content/uploads/2025/10/Beige-Monolithic-Haptic-Interface-Device-Representing-Decentralized-Autonomous-Organization-Governance-Mechanisms.webp)

The Black-Scholes model uses implied volatility (IV) as a key input.

### [What Modifications to the Black-Scholes Model Are Used to Price American Options?](https://learn.greeks.live/path/what-modifications-to-the-black-scholes-model-are-used-to-price-american-options/?utm_source=crypto.greeks.live&utm_medium=referral&utm_campaign=satellite)
![What Modifications to the Black-Scholes Model Are Used to Price American Options?](https://learn.greeks.live/wp-content/uploads/2025/10/Refined-Glass-Sphere-Equilibrium-on-Digital-Asset-Curve-Illustrating-Stochastic-Volatility-Modeling.webp)

Models like the Bjerksund-Stensland or binomial tree models are used, as they can account for the early exercise feature of American options.

### [How Does the Black-Scholes Model Account for the Early Exercise Feature of American Options?](https://learn.greeks.live/path/how-does-the-black-scholes-model-account-for-the-early-exercise-feature-of-american-options/?utm_source=crypto.greeks.live&utm_medium=referral&utm_campaign=satellite)
![How Does the Black-Scholes Model Account for the Early Exercise Feature of American Options?](https://learn.greeks.live/wp-content/uploads/2025/10/Optical-Medium-Delamination-Reflecting-Asymmetric-Futures-Curve-Volatility-Skew.webp)

Black-Scholes does not price American options; numerical methods like Binomial Trees are required to model early exercise.

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**Original URL:** https://learn.greeks.live/learn/how-does-the-black-scholes-model-use-implied-volatility/
