Why Black–Scholes Implied Volatility Varies Across Option Strikes

Summary

The document asks why options on the same underlying with the same maturity can show different implied volatilities. Implied volatility is the volatility input that makes a chosen pricing model reproduce an option’s quoted price; it is not necessarily a direct forecast of one constant future volatility. The examples concern quotes across options, which typically differ by strike.

The answers explain that Black–Scholes assumes a simplified return distribution and market setup, including lognormal prices, while actual markets can exhibit skewness and heavier tails. Consequently, prices across strikes may not fit a single Black–Scholes volatility, producing a volatility smile or skew when each price is translated back into the model. The discussion also notes that demand for protection against rare but costly outcomes can affect option prices. It offers a qualitative explanation, not an analysis of the cited quotes or proof of a particular market mechanism. Implied volatility remains model-dependent, and the excerpt does not examine other pricing models, liquidity, or bid-ask effects.

Key ideas

• Implied volatility is the volatility input that reproduces an option price under a specified model.
• Options with the same underlying and expiry can have different implied volatilities across strikes.
• A single Black–Scholes volatility may not capture skewness or heavy tails in real return distributions.
• Demand for protection against low-probability, high-cost events can influence option prices.
• The explanation is qualitative and does not isolate the causes of any particular quote pattern.

Tags

# Why does the implied volatility on options (with the same underlying and maturity) vary?


# Why does the implied volatility on options (with the same underlying and maturity) vary?












Having studied the basic premises behind option pricing, I thought it would be interesting to look at some real-world options data. I found the following quotes for options on APPL:

https://finance.yahoo.com/quote/AAPL/options?date=1610668800

However, I was surprised to see that the implied volatility for these options varies quite signigicantly, despite having the same underlying and maturity.

Why is this?

## Answer by Bikenfly (score 1)

https://quant.stackexchange.com/a/58578

Bear in mind that the IV you see quoted is Black Scholes IV. The only takeaway can be that the BS model is not the correct model to ACCURATELY price options. Differing IVs are the "fudge" to get better pricing and that option quoting (at the market maker level) really occurs through IV and is just expressed as price. When you look at the assumptions in the BS model, they are AT LEAST the shortcoming of the model (no commissions, continuous price movements, returns are gaussian...) and are return even gaussian? Some research points to that some asset returns are, some returns are more fractal.

## Answer by AlRacoon (score 1)

https://quant.stackexchange.com/a/58579

In short, because 1) the assumption of lognormal returns does not hold in real life--the markets have more skewness and kurtosis and 2) writers of protection want to be compensated more for writing insurance on low probability but high cost events.

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.