Why Yang–Zhang Volatility Estimator Implementations Use Different k Formulas

Summary

The document raises a formula discrepancy in the Yang–Zhang drift-independent volatility estimator. It compares the expression for the weighting constant k in the original paper with a different expression shown in R documentation, and asks why the two versions differ.

The note identifies the estimator and the specific point requiring investigation: whether the formulas reflect a change in convention, a derivation, or an implementation error. It provides no answer, derivation, numerical example, or comparison of resulting volatility estimates. As a result, it is useful as a narrowly framed implementation question, but does not establish which expression is correct or when either should be used. Researchers applying the estimator would need to consult the original derivation and the relevant software documentation before choosing a formula.

Key ideas

• The document compares two published forms of the Yang–Zhang estimator’s weighting constant.
• It asks why the formula in the original paper differs from the one shown in R documentation.
• No derivation or resolution of the discrepancy is provided.
• Implementers should verify the formula against the estimator’s derivation and their software’s conventions.

Tags

# Why are some Yang Zhang constant k different from the original paper?


# Why are some Yang Zhang constant k different from the original paper?












I've seen this in the original paper (Yang, Zhang: Drift Independent Volatility Estimation ...) (see Equation 10, Page 483)

$$k = \frac{\alpha - 1 }{\alpha + \frac{ n + 1 }{ n - 1 }}$$

while there are some implementations with this (in R documentation)

$$k =\frac{\alpha}{1 + \frac{ n + 1}{n - 1 } }$$

Why the difference ?

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.