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Why Implied Volatility Varies Across Option Strikes

Article Quant Q&A · Author: Kap
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Summary

Implied volatility is the volatility input that makes an option pricing model, such as Black–Scholes, match an option’s market price. Because each strike, maturity, and option type is a distinct contract, each can trade at a different price and therefore imply a different volatility.

The discussion links price differences to supply and demand and to how difficult a contract may be to hedge. Its example describes a far out-of-the-money call that could trade below a model-based fair value if buyers show little interest, producing a lower implied volatility. This is an informal illustration, not evidence that demand alone determines prices or that the quoted example is a reliable valuation. The answers point readers toward volatility skew as a related concept, but do not explain its causes or provide a method for measuring it.

Key ideas

  • Implied volatility is the model input that reconciles a theoretical option price with its market price.
  • Options with different strikes, maturities, or call and put types are separate contracts and can have different market prices.
  • Different market prices for otherwise comparable options produce different implied volatility readings.
  • Supply, demand, and hedging difficulty may contribute to price differences across strikes.
  • Volatility skew describes variation in implied volatility across strikes, but the document does not explain it in detail.

Tags

OptionsVolatilityDerivatives pricing
Full text
# What does implied volatility means for different call and put strike prices?


# What does implied volatility means for different call and put strike prices?












Why there different implied volatility for different strike prices?, Can plz someone explain to me? I am pretty new to options. Thanks in advance

## Answer by FX_NINJA (score 2)

https://quant.stackexchange.com/a/30109

Implied volatility will depend on the price the option is trading at. If more people buy a certain strike than another, or the given option is more difficult to hedge then the implied volatility will not be the same due to a different price. A simple example would be a stock trading at 10000 USD, and a call option expiring in 30 days with a strike of 12000 USD. Lets also say there is a 20% expected volatility at that time. While there is is a very small chance of the strike being hit, no one in there right mind would expect the strike to be hit and thus no one would buy it. So the fair value would be about 0.1 USD, but because pretty much no one would buy this option it is likely to trade at a lower price maybe even 0 USD and thus implied vol woul be lower or even 0%. The opposite is possible as well, the price of a specific contract could rise due to more investors buying that specific strike than others. As some people mentioned volatility skew is something you may want to read more about.

## Answer by Juan Ignacio Gil (score 1)

https://quant.stackexchange.com/a/30137

Every line in the market in your example defines a different option (with a strike, maturity and call/put flag). Everyone of this function has a different price given by the market.

What we call implied volatility is just the number you have to input as $\sigma$ in the Black Scholes equation to get the price which is traded in the market.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.