  The general problem of asset pricing when the discount rate differs from the
rate at which an asset's cash flows accrue is considered. A pricing kernel
framework is used to model an economy that is segmented into distinct markets,
each identified by a yield curve having its own market, credit and liquidity
risk characteristics. The proposed framework precludes arbitrage within each
market, while the definition of a curve-conversion factor process links all
markets in a consistent arbitrage-free manner. A pricing formula is then
derived, referred to as the across-curve pricing formula, which enables
consistent valuation and hedging of financial instruments across curves (and
markets). As a natural application, a consistent multi-curve framework is
formulated for emerging and developed inter-bank swap markets, which highlights
an important dual feature of the curve-conversion factor process. Given this
multi-curve framework, existing multi-curve approaches based on HJM and
rational pricing kernel models are recovered, reviewed and generalised, and
single-curve models extended. In another application, inflation-linked,
currency-based, and fixed-income hybrid securities are shown to be consistently
valued using the across-curve valuation method.
