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central limit theorem 1financial derivatives 1limiting distribution 1strong law of large numbers 1vega conversion 1volatility target index 1

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math.PR2026

A central limit theorem and its application to the limiting distribution of volatility target index

Xuan Liu, Michel Gauthier

The paper proves a strong law of large numbers and a central limit theorem for a volatility‑target index as the discretisation step goes to zero, derives the exact limiting distrib…