  The collateral choice option allows a collateral-posting party the
opportunity to change the type of security in which the collateral is
deposited. Due to non-zero collateral basis spreads, this optionality
significantly impacts asset valuation. Because of the complexity of valuing the
option, many practitioners resort to deterministic assumptions on the
collateral rates. In this article, we focus on a valuation model of the
collateral choice option based on stochastic dynamics. Intrinsic differences in
the resulting collateral choice option valuation and its implications for
collateral management are presented. We obtain sensitivities of the collateral
choice option price under both the deterministic and the stochastic model, and
we show that the stochastic model attributes risks to all involved collateral
currencies. Besides an inability to capture volatility effects, the
deterministic model exhibits a digital structure in which only the
cheapest-to-deliver currency influences the valuation at a given time. We
further consider hedging an asset with the collateral choice option by a
portfolio of domestic and foreign zero-coupon bonds that do not carry the
collateral choice option. We propose static hedging strategies based on the
crossing times of the deterministic model and based on variance-minimization
under the stochastic model. We show how the weights of this model can be
explicitly determined with the semi-analytical common factor approach and we
show in numerical experiments that this strategy offers good hedging
performance under minimized variance.
