LIBOR Reform: Option Pricing for Compounded Rates
33 Pages Posted: 1 Mar 2021 Last revised: 10 Feb 2024
Date Written: February 9, 2024
Abstract
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 series of benchmark rates. Floors and caps on compounded rates are thus Asian options. Under 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.
Keywords: Benchmark Rate Reform, Interest Rate Derivative, Asian Option, Central Limit Theorem, Zero Lower Bound
JEL Classification: E43, G13, C46
Suggested Citation: Suggested Citation