Sensitivities and Hedging of the Collateral Choice Option

Abstract

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 has significant impact on 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 upon 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 zerocoupon bonds that do not carry the collateral choice option. We propose hedging strategies based on the deterministic and stochastic models and introduce a novel, variance-minimizing hedging strategy, which uses the semi-analytical common factor approach of Wolf et al. [13] and analytical results to obtain the hedging weights. We show that this strategy offers good hedging performance under minimized variance, and that it can be entered at no cost in a setting cleared from domestic risk factors.