Cooking with collateral

In the wake of the crisis, the traditional assumption of a risk-free counterparty and rate has been shown to be false, yet it still underpins finance theory. Vladimir Piterbarg develops theoretical foundations for a model of an economy without a risk-free rate and with all assets traded on a collateralised basis. A cross-currency extension is considered, with a view to develop a model of multi-currency collateral choice

An economy without a risk-free rate has been considered in the past (see Black, 1972) but traditional derivatives pricing theory (see, for example, Duffie, 2001) assumed the existence of such a rate as a matter of course. Until the crisis, this assumption worked well, but now even government bonds cannot be considered credit risk-free. Hence, using a risk-free money-market account or a zero-coupon