Options for collateral options

When collateral can be posted in multiple currencies, pricing even the simplest derivatives involves optionality, which is often tackled numerically. But by conditioning on a risk factor to make variables independent, this can be simplified. Alexandre Antonov and Vladimir Piterbarg show this is both quicker and more accurate than more obvious methods

Credit support annexes specify rules for posting collateral. If multiple currencies are allowed, then the party posting collateral has, now and at each future point in time, a choice of which currency to post. This choice leads to optionality that needs to be accounted for when valuing even the most basic of derivatives, such as forwards or swaps (see Piterbarg, 2012).

Options for collateral