Interpreting Black–Scholes Implied Volatility from Normal-Model Prices

Summary

The document raises a question about interpreting implied volatility when prices are generated under a model with normally distributed returns and then inverted through the Black–Scholes formula. It asks whether the resulting Black–Scholes implied volatility corresponds to the volatility of a lognormal model.

This distinction matters because implied volatility is defined relative to a pricing model: applying Black–Scholes inversion to a price from a different distribution produces a model-dependent equivalent volatility, not automatically the generating model’s volatility. The source contains only the question and provides no answer, derivation, numerical example, or assumptions about the underlying, strike, or maturity. It therefore identifies a useful conceptual issue in option pricing but does not resolve how the implied volatility relates quantitatively to normal-model parameters. Any interpretation would require additional context and analysis beyond what is supplied here.

Key ideas

• Implied volatility depends on the pricing model used to invert an option price.
• A Black–Scholes inversion of a price from a normal-return model yields a model-dependent equivalent volatility.
• The document asks whether this value corresponds to lognormal volatility but does not provide an answer.
• A quantitative relationship would require assumptions and analysis absent from the source.

Tags

# BS Implied Volatility under Normal returns


# BS Implied Volatility under Normal returns












If I use theoretical prices under a normal valuation model, and I estimate their implied volatility using BLACK SCHOLES implied volatility, do I'll get corresponding log normal volatility?

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