LIBOR Reform: Option Pricing for Compounded Rates

I present a new statistical solution for pricing derivatives of compounded rates. Since the replacement of LIBOR, the compounded overnight rate has become the new standard for floating-rate loans. Many contracts contain a zero-based floor. The compounded rate is a time average of a sequence of benchmark rates. Floors and caps on compounded rates are thus Asian options. Under very weak and quite general assumptions, without explicit probability distributions, I prove that even if the benchmark rate process is non-Gaussian, the simple Gaussian model is asymptotically correct for pricing due to Lyapunov's central limit theorem. The approximation's maximum mispricing is bounded by the Berry-Esseen inequality.