Choice of Collateral Currency in Differential Swaps

2026-03-09

AI Summary

This study investigates the additional risks arising from a mismatch between the collateral currency and the cash flow currency in basis swaps, and its implications for pricing and hedging. Focusing on overnight risk-free rate–based basis swaps (e.g., those referencing SOFR), the work departs from the conventional assumption of same-currency collateralization by developing a multi-currency no-arbitrage framework. Integrating futures-based replication strategies with stochastic interest rate models, the paper proposes an explicit pricing and hedging methodology. Numerical simulations demonstrate that foreign-currency collateralization induces significant valuation adjustments even when cash flows are denominated in the domestic currency, thereby underscoring the critical role of collateral currency choice in modern derivatives risk management.

Technology Category

• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty
• Cognitive Modeling & Cognitive Systems: Other Foundations of Cognitive Modeling & Systems
• Game Theory and Economic Paradigms: Other Foundations of Game Theory & Economic Paradigms

Application Category

• Economics, Online Markets and Human Computation: Economic aspects of blockchain and cryptocurrencies
• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Multilingual and cross-lingual Web search

Abstract

The role of collateral in derivative pricing has evolved beyond credit risk mitigation, particularly following the global financial crisis, when funding costs and basis spreads became central to valuation practices. This development coincided with the transition from the London Interbank Offered Rate (LIBOR) to risk-free rates (RFRs) and the increasing standardization of collateralised trading. We study the valuation and hedging of a class of differential swaps referencing backward-looking averages of overnight rates, with SOFR swaps appearing as a particular instance. The focus is on the impact of the collateral currency. Extending earlier results Ding et al. [Math. Finance 36 (2026), pp.~180--202], we allow the collateral account to be denominated in a currency different from that of the contractual cash flows and derive explicit pricing and hedging strategies using a futures-based replication approach. We show that the choice of collateral currency can have a non-trivial effect on both valuation and risk management. In particular, foreign-currency collateral can introduce additional risk exposures even when contractual cash flows are entirely denominated in the domestic currency. Numerical study demonstrates that collateral effects can lead to significant valuation adjustments and therefore need to be properly incorporated in modern multi-currency modelling frameworks.

Problem

• collateral currency
• differential swaps
• valuation adjustment
• multi-currency modelling
• risk management

Innovation

• differential swaps
• collateral currency
• futures-based replication
• multi-currency modeling
• valuation adjustment