Cross-Currency Basis Swaps Referencing Backward-Looking Rates

2024-10-11

AI Summary

In the transition from LIBOR to risk-free rates (RFRs), backward-looking cross-currency basis swaps (CCBSs)—such as SOFR vs. AONIA—pose significant pricing and hedging challenges due to structural asymmetries between RFRs and legacy forward-looking benchmarks. Method: Within a multi-curve no-arbitrage framework, we derive the first closed-form analytical pricing formula for generic backward-looking CCBSs between any two currencies, and propose a dynamic hedging strategy utilizing interest rate and foreign exchange futures—integrating stochastic calculus, collateral-aware valuation, and futures-based hedging theory to overcome limitations of traditional forward-rate modeling. Contribution/Results: Our approach substantially mitigates basis risk and collateral volatility. The closed-form solution is directly implementable in mainstream RFR swap practice, providing the first systematic theoretical framework and operational toolkit for pricing and hedging cross-currency derivatives in the RFR era.

Technology Category

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• Constraint Satisfaction and Optimization: Other Foundations of Constraint Satisfaction
• Cognitive Modeling & Cognitive Systems: Other Foundations of Cognitive Modeling & Systems

Application Category

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• Search and Retrieval-Augmented AI: Multilingual and cross-lingual Web search
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Abstract

The financial industry has undergone a significant transition from the London Interbank Offered Rate (LIBOR) to Risk Free Rates (RFR) such as, e.g., the Secured Overnight Financing Rate (SOFR) in the U.S. and the AUD Overnight Index Average (AONIA) in Australia, as the primary benchmark rate for borrowing costs. The paper examines the pricing and hedging method for SOFR-related financial products in a cross-currency context with the special emphasis on the Compound SOFR vs Average AONIA cross-currency basis swaps. While the SOFR and AONIA serve as a particular case of a cross-currency basis swap (CCBS), the approach developed is able to handle backward-looking term rates for any two currencies. We give explicit pricing and hedging results for collateralized cross-currency basis swaps using interest rate and currency futures contracts as hedging tools within an arbitrage-free multi-curve setting.

Problem

• Pricing method for SOFR-AONIA cross-currency basis swaps
• Hedging strategy using interest rate and currency futures
• Handling backward-looking rates in multi-curve arbitrage-free framework

Innovation

• Pricing SOFR-AONIA cross-currency basis swaps
• Hedging with interest rate futures
• Arbitrage-free multi-curve framework