Annualizing Variance from a Local Volatility Formula

Summary

The document asks how to interpret the time scale of a variance quantity computed from a local volatility formula, using the relationship between variance, volatility, and elapsed time. It wonders whether a value associated with a six-month horizon should be converted to an annual figure by dividing by the time fraction.

No answer or derivation is included, so the document does not establish the correct annualization procedure. The distinction to resolve is whether the formula produces total variance over the selected horizon or an instantaneous variance rate; only a horizon-integrated variance would ordinarily be scaled by the inverse of the time fraction to express an annual rate. The source is a question rather than a complete explanation and gives no market example or evidence.

Key ideas

• The question concerns the time units of variance obtained from a local volatility formula.
• It distinguishes a horizon-dependent variance from an annualized variance rate.
• The document provides no answer or derivation to confirm the proposed scaling.

Tags

# Local Vol - Time Scale


# Local Vol - Time Scale












I am a beginner in derivatives and I am studying the Local Vol formula. My question is related to the time-scale of the volatility found after applying the formula below:

Since W = Sigma^2 * T, I believe the result is related to T (0.50 for 6 months, for example).

In annual terms, do we just multiply the final variance by 1/T?

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