Black-Scholes Formula: Objective or Risk-Neutral?

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SUMMARY

The Black-Scholes formula utilizes the normal distribution to model stock returns, specifically employing the risk-neutral probability distribution. This approach assumes continuous pricing and the ability to short-sell the underlying asset without limits. The discussion highlights a common misconception regarding implied volatility, which is often interpreted as an estimate of the variance of the subjective probability of asset returns, rather than distinguishing between subjective and risk-neutral probabilities. Academic sources are sought to clarify these distinctions further.

PREREQUISITES
  • Understanding of the Black-Scholes formula
  • Knowledge of probability distributions, specifically normal distribution
  • Familiarity with concepts of risk-neutral valuation
  • Basic grasp of implied volatility in financial markets
NEXT STEPS
  • Research the mathematical derivation of the Black-Scholes formula
  • Study the differences between subjective and risk-neutral probability distributions
  • Explore academic literature on implied volatility and its interpretations
  • Learn about continuous pricing models in financial mathematics
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Finance students, quantitative analysts, and anyone involved in options pricing or financial modeling will benefit from this discussion.

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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