A General Framework for the Benchmark pricing in a Fully Collateralized Market

TL;DR

This paper develops a comprehensive framework for benchmark pricing in fully collateralized markets, extending multi-currency interest rate models with a new currency funding spread formulation and a discretized HJM model for practical implementation.

Contribution

It introduces a generalized interest rate framework for collateralized markets, including a novel currency funding spread and a discretized HJM model for market applicability.

Findings

New formulation of currency funding spread for better dependence modeling

Discretized HJM framework suitable for traditional market models

Extension of multi-currency interest rate models in collateralized settings

Abstract

Collateralization with daily margining has become a new standard in the post-crisis market. Although there appeared vast literature on a so-called multi-curve framework, a complete picture of a multi-currency setup with cross-currency basis can be rarely found since our initial attempts. This work gives its extension regarding a general framework of interest rates in a fully collateralized market. It gives a new formulation of the currency funding spread which is better suited for the general dependence. In the last half, it develops a discretization of the HJM framework with a fixed tenor structure, which makes it implementable as a traditional Market Model.