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The collateral choice option gives the collateral posting party theopportunity to switch between different collateral currencies which iswell-known to impact the asset price. Quantification of the option's value isof practical importance but remains challenging under the assumption ofstochastic rates, as it is determined by an intractable distribution whichrequires involved approximations. Indeed, many practitioners still rely ondeterministic spreads between the rates for valuation. We develop a scalableand stable stochastic model of the collateral spreads under the assumption ofconditional independence. This allows for a common factor approximation whichadmits analytical results from which further estimators are obtained. We showthat in modelling the spreads between collateral rates, a second order modelyields accurate results for the value of the collateral choice option. Themodel remains precise for a wide range of model parameters and is numericallyefficient even for a large number of collateral currencies.

Cheapest-to-Deliver Collateral: A Common Factor Approach