Pricing Caps and Floors using the SOFR and ESTR

Oct 13, 2025 by wbrum.org 99 views

Introduction

The London Interbank Offered Rate (LIBOR) has been a cornerstone of the global financial system for decades, serving as a benchmark for short-term interest rates. However, in 2021, the ICE Benchmark Administration (IBA) announced the cessation of LIBOR, marking the end of an era. As a result, financial institutions and market participants are facing a significant challenge in pricing and managing interest rate derivatives, including caps and floors. In this article, we will delve into the post-LIBOR pricing of caps and floors, exploring the implications of the LIBOR cessation and the new frameworks that have emerged to replace it.

The LIBOR Cessation: A New Era for Interest Rate Derivatives

The LIBOR cessation has sent shockwaves throughout the financial industry, with many market participants struggling to adapt to the new reality. The LIBOR benchmark was based on a survey of banks' borrowing costs, which were then used to calculate the forward LIBOR rates. However, the LIBOR rate was not a true market rate, as it was subject to manipulation and was not a reflection of the actual borrowing costs of banks. The LIBOR cessation has led to the development of new frameworks for pricing interest rate derivatives, including the use of alternative benchmarks such as the SOFR (Secured Overnight Financing Rate) and the ESTR (Euro Short-Term Rate).

Post-LIBOR Pricing of Caps and Floors: A New Paradigm

Caps and floors are a type of interest rate derivative that provide protection against changes in interest rates. A cap is a contract that limits the maximum interest rate that can be paid, while a floor is a contract that limits the minimum interest rate that can be paid. In the pre-LIBOR era, caps and floors were priced using the LIBOR benchmark, which was used to calculate the forward LIBOR rates. However, with the LIBOR cessation, market participants are now required to use alternative benchmarks to price these derivatives.

The SOFR and ESTR: Alternative Benchmarks for Post-LIBOR Pricing

The SOFR and ESTR are two alternative benchmarks that have emerged as replacements for LIBOR. The SOFR is a daily secured overnight rate, calculated based on transactions in the U.S. Treasury market. The ESTR, on the other hand, is a daily euro short-term rate, calculated based on transactions in the euro overnight market. Both benchmarks are designed to be more robust and less susceptible to manipulation than LIBOR.

Pricing Caps and Floors using the SOFR and ESTR

Pricing caps and floors using the SOFR and ESTR requires a different approach than pricing them using LIBOR. The SOFR and ESTR are not martingales, unlike LIBOR, which means that they do not have the same properties as LIBOR. As a result, market participants must use different models and techniques to price these derivatives.

The Bachelier Model: A New Approach to Pricing Caps and Floors

The Bachelier model is a new approach to pricing caps and floors that takes into account the properties of the SOFR and ESTR. The model is based on the idea that the forward rates are lognormal, rather than normal, which is a key difference from the LIBOR-based models. The Bachelier model has been shown to provide more accurate prices for caps and floors than the traditional LIBOR-based models.

The Hull-White Model: A Hybrid Approach to Pricing Caps and Floors

The Hull-White model is a hybrid approach to pricing caps and floors that combines elements of the Bachelier model with traditional LIBOR-based models. The model uses a combination of lognormal and normal distributions to price the forward rates, which provides a more accurate representation of the market data.

Conclusion

The LIBOR cessation has sent shockwaves throughout the financial industry, with many market participants struggling to adapt to the new reality. However, with the emergence of new benchmarks such as the SOFR and ESTR, market participants are now required to use alternative models and techniques to price interest rate derivatives, including caps and floors. The Bachelier model and the Hull-White model are two new approaches to pricing caps and floors that take into account the properties of the SOFR and ESTR. As the financial industry continues to evolve, it is likely that new models and techniques will emerge to replace the traditional LIBOR-based models.

Recommendations for Market Participants

Market participants who are pricing caps and floors using the SOFR and ESTR should consider the following recommendations:

Use the Bachelier model or the Hull-White model: These models have been shown to provide more accurate prices for caps and floors than traditional LIBOR-based models.
Use a combination of lognormal and normal distributions: This approach provides a more accurate representation of the market data.
Monitor market data closely: The SOFR and ESTR are subject to changes in market conditions, which can impact the prices of caps and floors.
Consider using a hybrid approach: Combining elements of the Bachelier model with traditional LIBOR-based models can provide a more accurate representation of the market data.

Future Developments

The LIBOR cessation is a significant event that has sent shockwaves throughout the financial industry. As the industry continues to evolve, it is likely that new models and techniques will emerge to replace the traditional LIBOR-based models. Market participants should stay informed about the latest developments and adapt their pricing models accordingly.

References

Bachelier, L. (1900): "Theorie de la Speculation". Gauthier-Villars.
Hull, J. C. (2005): "Options, Futures, and Other Derivatives". Prentice Hall.
International Swaps and Derivatives Association (ISDA): "ISDA LIBOR Fallbacks Protocol".
Securities and Exchange Commission (SEC): "SEC Approves ISDA LIBOR Fallbacks Protocol".