Discounting in The New World

The only truly credit-risk-free assets available in post-crisis economy are those that are fully collateralized on a continuous basis. They differ significantly from the assets traditionally used in Asset Pricing Theory and are a special kind of the so-called zero-price dividend-paying (ZPDP) assets. We prove a variant of the Fundamental Theorem of Asset Pricing in an economy where all assets are ZPDP and no natural numeraire exists. In particular we show that absence of arbitrage implies existence of a measure in which each asset is discounted at its own collateral rate. We then consider multi-currency extensions.