LIBOR reform: option pricing for compounded rates

Abstract

I present new analytical pricing formulae for derivatives of compounded rates. Since the announced replacement of LIBOR, the compounded overnight rate has become the new market standard for floating-rate loans and notes. Many contracts contain a zero-based floor. The compounded rate is a time average of a series of benchmark rates. Floors and caps on compounded rates are thus Asian types of options. I prove that even if the rate process is non-Gaussian, the Gaussian process is asymptotically the correct model for pricing derivatives due to Lyapunov's central limit theorem. The approximation's maximum mispricing is bounded by the Berry-Esseen inequality.