Heterogeneous Yield Curves and Basis Swaps

We present a framework of heterogeneous yield curves of agents based on the pricing kernel approach in order to model LIBOR and basis swap rates. Each yield curve may imply different prices of assets but is consistent with swap rates, basis swap rates and foreign exchange rates. We show three conditions that gurantee the no-arbitrage and the consistency with these rate processes. The introduction of contributors and the Market Representative Agent (gMRAh) leads to an explanation of a non-zero basis swap rate as a swap rate priced by one of the MRAs.