Interest-Rate Modelling in Collateralized Markets: Multiple curves, credit-liquidity effects, CCPs

by Andrea Pallavicini of Banca IMI, Milan, and
Damiano Brigo of Imperial College, London

April 5, 2013

Abstract: The market practice of extrapolating different term structures from different instruments lacks a rigorous justification in terms of cash flows structure and market observables. In this paper, we integrate our previous consistent theory for pricing under credit, collateral and funding risks into term structure modelling, integrating the origination of different term structures with such effects. Under a number of assumptions on collateralization, wrong-way risk, gap risk, credit valuation adjustments and funding effects, including the treasury operational model, and via an immersion hypothesis, we are able to derive a synthetic master equation for the multiple term structure dynamics that integrates multiple curves with credit/funding adjustments.

JEL Classification: G13.

AMS Classification: 60J75, 91B70.

Keywords: Yield Curve Dynamics, Multiple Curve Framework, HJM Framework, Interest Rate Derivatives, Basis Swaps, Counterparty Credit Risk, Liquidity Risk, Funding Costs, Central Clearing Counterparties.

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