Pricing on Trees Using New Risk-Free Rates

This article presents a novel tree approach to pricing derivatives linked to new Risk-Free Rate benchmarks. The methodology is versatile and can be applied to both backward–and forward-looking caplets. It draws upon the analogy with the pricing of Asian options, allowing for effective pricing in the context of these new benchmark rates. This article demonstrates the efficacy of this approach by applying it to model the overnight rate using numerical examples. The focus is on established interest rate tree models, which are widely utilized in the financial industry for valuing bonds with options linked to legacy benchmarks like LIBOR. The numerical examples presented in this article validate the reliability and accuracy of the proposed tree-based approach, showcasing its superiority over traditional Monte Carlo simulation methods.