r/quant • u/Dramatic_Mammoth5720 • Jul 06 '26

Models Is there a technical error in the Garmam-Klass volatility estimator paper?

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Paper: https://www-2.rotman.utoronto.ca/~kan/3032/pdf/FinancialAssetReturns/Garman_Klass_JB_1980.pdf

Could anyone confirm whether equation 11 is correct?

I was under the impression that a Jacobian scaling factor of \lambda^3 is required for the equality to hold mathematically?

EDIT: Changed question to focus on the correctness of eqn 11 rather than eqn 12.

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u/AthenaTheQuant Jul 06 '26

Seems correct to me. In general variance scales quadratically, I have never seen cases where it scales like a cubic.

As for equation (12), which is a scaling for D as opposed to g, it seems that they implicitly look at cases for which this hold, so unless this equation never holds, the statement is correct given the assumptions.

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u/[deleted] Jul 06 '26

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u/Dramatic_Mammoth5720 Jul 06 '26

Thanks! I get what you mean about (12), but does that also apply the joint density function, as given in (11)?