# Which Options Pricing Model Incorporates Volatility? ⎊ Path

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

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## Which Options Pricing Model Incorporates Volatility?

The most widely recognized and foundational model is the Black-Scholes-Merton (BSM) model. Volatility is a critical input in this model, specifically the expected future volatility of the underlying asset.

This volatility input heavily influences the extrinsic value (time value) of the option premium.

- [How Does the Black-Scholes Model Mathematically Represent This Acceleration?](https://learn.greeks.live/path/how-does-the-black-scholes-model-mathematically-represent-this-acceleration/)

- [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/)

- [How Does the Black-Scholes Model Simplify the Valuation of European Options?](https://learn.greeks.live/path/how-does-the-black-scholes-model-simplify-the-valuation-of-european-options/)

- [How Does the Black-Scholes Model Relate to Calculating the Options Premium?](https://learn.greeks.live/path/how-does-the-black-scholes-model-relate-to-calculating-the-options-premium/)

- [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/)

- [How Does the Black-Scholes Model Use Volatility?](https://learn.greeks.live/path/how-does-the-black-scholes-model-use-volatility/)

- [How Does the Black-Scholes Model Use Implied Volatility to Calculate Option Price?](https://learn.greeks.live/path/how-does-the-black-scholes-model-use-implied-volatility-to-calculate-option-price/)

- [What Is the Black-Scholes Model’s Primary Use in Valuing Options?](https://learn.greeks.live/path/what-is-the-black-scholes-models-primary-use-in-valuing-options/)

## Glossar

### [Options Pricing Model](https://learn.greeks.live/area/options-pricing-model/?utm_source=crypto.greeks.live&utm_medium=referral&utm_campaign=satellite)

Valuation ⎊ Options pricing models, within cryptocurrency markets, extend established financial derivative theory to nascent digital asset classes, requiring adaptation due to unique market microstructure and volatility characteristics.

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

Expectation ⎊ Expected Future Volatility represents the market's collective anticipation of the underlying asset's price fluctuation over the remaining life of a derivative contract.

## Discover More

### [In Which Derivatives Markets (E.g. Futures, Swaps, Options) Is the Cost of Immediacy Generally Highest?](https://learn.greeks.live/path/in-which-derivatives-markets-e-g-futures-swaps-options-is-the-cost-of-immediacy-generally-highest/?utm_source=crypto.greeks.live&utm_medium=referral&utm_campaign=satellite)
![In Which Derivatives Markets (E.g. Futures, Swaps, Options) Is the Cost of Immediacy Generally Highest?](https://learn.greeks.live/wp-content/uploads/2025/10/Quantum-Lattice-Bifurcation-in-Decentralized-Finance-Option-Hedging-Mechanisms.webp)

The cost of immediacy is highest in less liquid, complex derivatives like long-dated or exotic options and bespoke OTC swaps.

### [Explain the Concept of 'Greeks' in Options Trading and Which One Is Most Critical for Delta-Hedging](https://learn.greeks.live/path/explain-the-concept-of-greeks-in-options-trading-and-which-one-is-most-critical-for-delta-hedging/?utm_source=crypto.greeks.live&utm_medium=referral&utm_campaign=satellite)
![Explain the Concept of 'Greeks' in Options Trading and Which One Is Most Critical for Delta-Hedging](https://learn.greeks.live/wp-content/uploads/2025/10/Hypergeometric-Probability-Distribution-Modeling-Decentralized-Autonomous-Organization-Governance-Mechanism-Symmetry.webp)

Greeks measure option sensitivity; Delta is the most critical Greek for delta-hedging to neutralize directional risk.

### [How Do Volatility Feeds, beyond Simple Price Feeds, Assist in Options Pricing Models?](https://learn.greeks.live/path/how-do-volatility-feeds-beyond-simple-price-feeds-assist-in-options-pricing-models/?utm_source=crypto.greeks.live&utm_medium=referral&utm_campaign=satellite)
![How Do Volatility Feeds, beyond Simple Price Feeds, Assist in Options Pricing Models?](https://learn.greeks.live/wp-content/uploads/2025/10/Precision-Engineering-of-Decentralized-Finance-Volatility-Skew-Measurement-Apparatus.webp)

Provide the rate of price change (volatility index) needed for accurate options pricing models, impacting the option premium.

### [Explain the Concept of "Volatility Smile" in Options Pricing and Its Financial Implication](https://learn.greeks.live/path/explain-the-concept-of-volatility-smile-in-options-pricing-and-its-financial-implication/?utm_source=crypto.greeks.live&utm_medium=referral&utm_campaign=satellite)
![Explain the Concept of "Volatility Smile" in Options Pricing and Its Financial Implication](https://learn.greeks.live/wp-content/uploads/2025/10/Crystalline-Volatility-Surface-Structure-Representing-Implied-Volatility-Skew-in-Decentralized-Derivatives-Markets.webp)

Volatility smile shows higher implied volatility for out-of-the-money options, implying the market expects larger, more extreme price movements.

### [What Role Does Volatility Play in Pricing Crypto Options Compared to Stock Options?](https://learn.greeks.live/path/what-role-does-volatility-play-in-pricing-crypto-options-compared-to-stock-options/?utm_source=crypto.greeks.live&utm_medium=referral&utm_campaign=satellite)
![What Role Does Volatility Play in Pricing Crypto Options Compared to Stock Options?](https://learn.greeks.live/wp-content/uploads/2025/10/Electrostatic-Potential-Measurement-Needle-Apex-and-Metallic-Ball-Centered-on-Darkened-Volatility-Surface-Instrument.webp)

Higher crypto volatility leads to higher options premiums due to increased probability of large price moves.

### [What Is the Primary Mathematical Model Used to Price American Options, and Why Is It More Complex than the Black-Scholes Model?](https://learn.greeks.live/path/what-is-the-primary-mathematical-model-used-to-price-american-options-and-why-is-it-more-complex-than-the-black-scholes-model/?utm_source=crypto.greeks.live&utm_medium=referral&utm_campaign=satellite)
![What Is the Primary Mathematical Model Used to Price American Options, and Why Is It More Complex than the Black-Scholes Model?](https://learn.greeks.live/wp-content/uploads/2025/10/Abstract-Deployment-Configuration-of-Decentralized-Exchange-Liquidity-Provision-Mechanisms-Versus-Options-Gamma-Exposure.webp)

The Binomial Model or numerical Black-Scholes methods are used; complexity comes from modeling the optimal early exercise decision.

### [How Does the Black-Scholes Model Use Implied Volatility to Calculate Option Price?](https://learn.greeks.live/path/how-does-the-black-scholes-model-use-implied-volatility-to-calculate-option-price/?utm_source=crypto.greeks.live&utm_medium=referral&utm_campaign=satellite)
![How Does the Black-Scholes Model Use Implied Volatility to Calculate Option Price?](https://learn.greeks.live/wp-content/uploads/2025/10/Quantum-State-Collapse-Mechanisms-Governing-Digital-Asset-Volatility-Hedging-Instruments.webp)

The Black-Scholes model uses implied volatility as a key input to determine the option's theoretical fair price.

### [How Does Volatility Skew Affect the Pricing of Out-of-the-Money Crypto Options?](https://learn.greeks.live/path/how-does-volatility-skew-affect-the-pricing-of-out-of-the-money-crypto-options/?utm_source=crypto.greeks.live&utm_medium=referral&utm_campaign=satellite)
![How Does Volatility Skew Affect the Pricing of Out-of-the-Money Crypto Options?](https://learn.greeks.live/wp-content/uploads/2025/10/Oscillating-Asset-States-Representing-Volatility-Skew-in-Decentralized-Finance-Derivative-Pricing.webp)

OTM options often have higher implied volatility than ATM options, reflecting market crash-risk perception.

### [Define "Implied Volatility" in Options Pricing](https://learn.greeks.live/path/define-implied-volatility-in-options-pricing/?utm_source=crypto.greeks.live&utm_medium=referral&utm_campaign=satellite)
![Define "Implied Volatility" in Options Pricing](https://learn.greeks.live/wp-content/uploads/2025/10/Tangible-Manifestation-of-Tokenized-Asset-Allocation-Within-High-Frequency-Trading-Architecture.webp)

The market's expectation of future price fluctuation, derived from the option's current price, reflecting supply and demand.

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