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The collateral choice option allows a collateral-posting party theopportunity to change the type of security in which the collateral isdeposited. Due to non-zero collateral basis spreads, this optionalitysignificantly impacts asset valuation. Because of the complexity of valuing theoption, many practitioners resort to deterministic assumptions on thecollateral rates. In this article, we focus on a valuation model of thecollateral choice option based on stochastic dynamics. Intrinsic differences inthe resulting collateral choice option valuation and its implications forcollateral management are presented. We obtain sensitivities of the collateralchoice option price under both the deterministic and the stochastic model, andwe show that the stochastic model attributes risks to all involved collateralcurrencies. Besides an inability to capture volatility effects, thedeterministic model exhibits a digital structure in which only thecheapest-to-deliver currency influences the valuation at a given time. Wefurther consider hedging an asset with the collateral choice option by aportfolio of domestic and foreign zero-coupon bonds that do not carry thecollateral choice option. We propose static hedging strategies based on thecrossing times of the deterministic model and based on variance-minimizationunder the stochastic model. We show how the weights of this model can beexplicitly determined with the semi-analytical common factor approach and weshow in numerical experiments that this strategy offers good hedgingperformance under minimized variance.

Sensitivities and Hedging of the Collateral Choice Option