Cheapest-to-deliver collateral: a common factor approach

Abstract

The collateral choice option gives the collateral posting party the opportunity to switch between different collateral currencies which is well-known to impact the asset price. Quantification of the option's value is of practical importance but remains challenging under the assumption of stochastic rates, as it is determined by an intractable distribution that requires involved approximations. Indeed, many practitioners still rely on deterministic spreads between the rates for valuation. We develop a scalable and stable stochastic model of the collateral spreads under the assumption of conditional independence. This allows for a common factor approximation that admits analytical results from which further estimators are obtained. We show that in modelling the spreads between collateral rates, a second-order model yields accurate results for the value of the collateral choice option. The model remains precise for a wide range of model parameters and is numerically efficient even for a large number of collateral currencies.

Keywords:

• Collateral choice option
• Currency spreads
• Conditional independence
• Factor model
• CSA

JEL Classifications:

• C63
• G13

Acknowledgments

The authors thank two anonymous referees for their valuable comments, which helped improve this article. The authors are grateful to the participants of ABC–EU–XVA for their helpful feedback on the content of this article.

Disclosure statement

The views expressed in this paper are the personal views of the authors and do not necessarily reflect the views or policies of their current or past employers.

Additional information

Funding

This research is part of the ABC–EU–XVA project and has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Skłodowska–Curie grant agreement No. 813261.