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

TL;DR

This paper develops a rigorous theoretical framework for modeling multiple interest rate curves in collateralized markets, incorporating credit, liquidity, and funding effects to unify different term structures.

Contribution

It introduces a synthetic master equation that integrates multiple curves with credit and funding adjustments based on a consistent theoretical approach.

Findings

Derivation of a master equation for multiple term structures

Integration of credit, collateral, and funding risks into interest rate models

Provides a theoretical justification for market practices of curve extrapolation

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.