Bessel’s Correction When Estimating GBM Drift and Volatility

Summary

The document asks whether sample variance and standard deviation should use Bessel’s correction when fitting the drift and volatility of a geometric Brownian motion to historical security returns. It frames the issue as a distinction between treating observed returns as a sample and choosing estimators consistent with the model and estimation objective.

No answer, derivation, data, or comparison of estimators is included. The question is relevant to quantitative finance because parameter estimates feed simulations and risk calculations, but the post alone does not explain when a degrees-of-freedom adjustment is appropriate. In particular, it does not distinguish unbiased estimation of a population variance from maximum-likelihood estimation under a specified return model, nor discuss sampling intervals, dependence, or uncertainty in the fitted parameters.

Key ideas

• The post asks how Bessel’s correction applies to variance estimates from historical returns.
• The parameters of interest are drift and volatility in a geometric Brownian motion model.
• The document presents the question without a derivation or empirical comparison.
• The appropriate variance estimator depends on the estimation objective and model assumptions.

Tags

# Bessel Correction and Geometric Brownian Motion


# Bessel Correction and Geometric Brownian Motion












Does it make sense to use bessel's correction for standard deviation and variance when fitting the drift and volatility parameters of geometric brownian motion to historical return data for a security. I've seen implementations without it but fail to see how that's defensible when historical data is essentially a sample.

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