Black-Scholes Formula: Objective or Risk-Neutral?

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The discussion centers on the use of normal distribution in the Black-Scholes formula for modeling stock returns. It clarifies that the distribution referenced is the risk-neutral probability distribution, which assumes continuous prices and the ability to short-sell without limits. The conversation also touches on implied volatility, suggesting that it serves as an estimate of the variance of the subjective probability of asset returns. This raises questions about whether the distinction between subjective and risk-neutral probabilities is often overlooked in academic discussions. The request for academic sources indicates a desire for deeper understanding and validation of these concepts.
pkxt
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Hello,

I understand that the normal distribution is used to model stock returns in the Black-Scholes formula.

Can someone please tell me whether this is meant to be the subjective probability distribution or the risk-neutral probability distribution?

Thank you!
 
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risk neutral (assuming prices are continuous & the underlying can be sold short without limit)
 
Thank you for your response! Can you perhaps point me to some academic sources?

I read something that claims the implied volatility is an estimate of the variance of the subjective probability of asset return -- is that just because they are not drawing the distinction between subjective and risk-neutral?
 

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