Stuck with collateral

Values of derivatives contracts for which there is a choice of asset to post as collateral have been shown to depend on the instantaneous interest rates these assets return. However, the models developed so far assumed perfect substitution. In reality, such agreements are hard to enforce. Vladimir Piterbarg shows that in that case, the optimal posting strategy is actually determined by a suitable term collateral rate

Collateral agreements have features that can provide more economic value than just counterparty credit risk mitigation. In particular, credit support annexes (CSAs) that allow for more than one type of asset to be posted as collateral introduce an optionality into the pricing of even the most vanilla instruments (see Piterbarg, 2012, and Fujii & Takahashi, 2011). However, the models studying this have assumed the full collateral balance can be switched from one asset to another on a whim for