Sensitivities and Hedging of the Collateral Choice Option

TL;DR

This paper develops a stochastic valuation model for the collateral choice option, analyzing its sensitivities and proposing effective static hedging strategies, highlighting differences from deterministic models and implications for collateral management.

Contribution

It introduces a stochastic model for valuing the collateral choice option, compares it with deterministic models, and proposes explicit static hedging strategies with demonstrated effectiveness.

Findings

Stochastic model captures risks across all collateral currencies.

Deterministic model shows digital valuation structure influenced only by cheapest currency.

Hedging strategies based on variance minimization perform well in numerical tests.

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 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.