Interest-Rate Modeling with Multiple Yield Curves

TL;DR

This paper introduces a multi-curve interest rate modeling framework that reflects recent market realities, enabling more accurate pricing of various interest rate derivatives by fitting multiple yield curves to market data.

Contribution

It develops a Heath-Jarrow-Morton (HJM) multi-curve framework and a bootstrapping algorithm for fitting multiple yield curves, enhancing interest rate modeling post-financial crisis.

Findings

The multi-curve approach fits market prices of plain-vanilla contracts.

The framework can be used to price complex exotic options.

Numerical examples demonstrate the model's practical application.

Abstract

The crisis that affected financial markets in the last years leaded market practitioners to revise well known basic concepts like the ones of discount factors and forward rates. A single yield curve is not sufficient any longer to describe the market of interest rate products. On the other hand, using different yield curves at the same time requires a reformulation of most of the basic assumptions made in interest rate models. In this paper we discuss market evidences that led to the introduction of a series of different yield curves. We then define a HJM framework based on a multi-curve approach, presenting also a bootstrapping algorithm used to fit these different yield curves to market prices of plain-vanilla contracts such as basic Interest Rate Swaps (IRS) and Forward Rate Agreements (FRA). We then show how our approach can be used in practice when pricing other interest rate products, such as forward starting IRS, plain-vanilla European Swaptions, Constant Maturity Swaps (CMS) and CMS spread options, with the final goal to investigate whether the market is actually using a multi-curve approach or not. We finally present some numerical examples for a simple formulation of the framework which embeds by construction the multi-curve structure; once the model is calibrated to market prices of plain-vanilla options, it can be used via a Monte Carlo simulation to price more complicated exotic options.