A Note on Building Proxy Volatility Cubes

Abstract

In this note, we introduce a simple approach for building volatility cubes of an interest-rate index based on the existing volatility cube of another index. Our approach can be formulated as a specific linear factor model, but it is dynamical in nature, and has the advantage of simple, explicit formulas for the ATM implied volatility and skew. As an example, we will construct SOFR volatility smiles from LIBOR-based ones.