  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 which
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 which
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.
