LIBOR Reform: Option Pricing for Compounded Rates
32 Pages Posted: 1 Mar 2021 Last revised: 21 Jun 2022
Date Written: June 21, 2022
I present new analytical pricing formulae for derivatives of compounded rates. Since the 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.
Keywords: Benchmark Rate Reform, Interest Rate Derivative, Asian Option, Central Limit Theorem, Zero Lower Bound
JEL Classification: E43, G13, C46
Suggested Citation: Suggested Citation