Interest Rate Modeling: Post-Crisis Challenges and Approaches

verfasst von: Zorana Grbac, Wolfgang J. Runggaldier

Verlag: Springer International Publishing

Buchreihe : SpringerBriefs in Quantitative Finance

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Wirtschaft"

Einloggen, um Zugang zu erhalten

Über dieses Buch

Filling a gap in the literature caused by the recent financial crisis, this book provides a treatment of the techniques needed to model and evaluate interest rate derivatives according to the new paradigm for fixed income markets. Concerning this new development, there presently exist only research articles and two books, one of them an edited volume, both being written by researchers working mainly in practice. The aim of this book is to concentrate primarily on the methodological side, thereby providing an overview of the state-of-the-art and also clarifying the link between the new models and the classical literature. The book is intended to serve as a guide for graduate students and researchers as well as practitioners interested in the paradigm change for fixed income markets. A basic knowledge of fixed income markets and related stochastic methodology is assumed as a prerequisite.

Inhaltsverzeichnis

Frontmatter

Chapter 1. Post-Crisis Fixed-Income Markets

Abstract

The fixed income market is a sector of the global financial market in which various interest rate-sensitive instruments are traded, such as bonds, forward rate agreements, various forms of swaps, swaptions, caps and floors. It makes up a large portion of the global financial market. The recent financial crisis, of which the key features are counterparty and liquidity/funding risk, has heavily impacted the entire financial market and the fixed income market in particular. Inspection of quoted interest rates and derivative prices reveals that some classical relationships have broken down, which has induced the actors on the fixed income market to model as separate objects rates that correspond to different maturities (multi-curve models). In this chapter we review the basic notions and concepts in use before the crisis and describe how they have found an extension to the multi-curve setup.

Zorana Grbac, Wolfgang J. Runggaldier

Chapter 2. Short-Rate and Rational Pricing Kernel Models for Multiple Curves

Abstract

In this chapter we consider mainly strict-sense short-rate models in view of constructing multiple curves. Because the pre-crisis rational pricing kernel models can be seen as short-rate models in a wider sense, we shall furthermore present some recent multi-curve extensions of these models as well. For the strict-sense short rate models we consider a basic OIS short rate and various spreads to be added on top of it, one for each of the multiple curves. The setup is mainly that of exponentially affine, but also exponentially quadratic models driven by several stochastic factors. This allows us to obtain explicit formulas for various linear and optional interest rate derivatives also in the multi-curve setting.

Zorana Grbac, Wolfgang J. Runggaldier

Chapter 3. Multiple Curve Heath–Jarrow–Morton (HJM) Framework

Abstract

This chapter concerns the HJM framework for forward rate models in a multi-curve setup. As in Chap. 2, also in this chapter we shall model a basic OIS forward rate and the various risky multi-curve rates are obtained by adding a spread over the OIS rate. Since the ultimate goal is the pricing of interest rate derivatives, where the main underlying quantity are the Libor rates, one of the first objectives is to derive models for the dynamics of the Libor rates that are arbitrage-free. To this effect we shall first obtain models for OIS bond prices under a martingale measure and then choose suitable quantities connected to the FRA contracts, modeling them in the spirit of the HJM framework so that the complete model is arbitrage-free. Finally, we consider pricing of linear and optional interest rate derivatives in this HJM context.

Zorana Grbac, Wolfgang J. Runggaldier

Chapter 4. Multiple Curve Extensions of Libor Market Models (LMM)

Abstract

The subject of this chapter are multi-curve models in the spirit of the Libor market model (LMM). The modeling is here done on a discrete tenor structure and the interest rates are discretely compounded, reflecting thus the market practice. We consider the discretely compounded forward OIS rates as reference rates, together with the forward Libor rates or, equivalently, the Libor-OIS spreads. The rates and the spreads are modeled directly under the forward martingale measures used for derivative pricing. First we describe a general framework that extends the classical BGM Libor market model to multiple curves. Then we present a multiple-curve affine Libor model based on families of exponentially affine martingales representing the forward OIS and Libor rates. Finally we also indicate modeling based on multiplicative Libor-OIS spreads. For each modeling approach, we mention corresponding methods for derivative pricing.

Zorana Grbac, Wolfgang J. Runggaldier

Backmatter

Titel: Interest Rate Modeling: Post-Crisis Challenges and Approaches
verfasst von: Zorana Grbac
Wolfgang J. Runggaldier
Verlag: Springer International Publishing
Electronic ISBN: 978-3-319-25385-5
Print ISBN: 978-3-319-25383-1
DOI: https://doi.org/10.1007/978-3-319-25385-5

Springer Professional

Über dieses Buch

Inhaltsverzeichnis

Frontmatter

Chapter 1. Post-Crisis Fixed-Income Markets

Chapter 2. Short-Rate and Rational Pricing Kernel Models for Multiple Curves

Chapter 3. Multiple Curve Heath–Jarrow–Morton (HJM) Framework

Chapter 4. Multiple Curve Extensions of Libor Market Models (LMM)

Backmatter

Premium Partner