The SABR/LIBOR Market Model: Pricing, Calibration and Hedging for Complex Interest-Rate Derivatives

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9780470740057: The SABR/LIBOR Market Model: Pricing, Calibration and Hedging for Complex Interest-Rate Derivatives
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This book presents a major innovation in the interest rate space.It explains a financially motivated extension of the LIBOR Marketmodel which accurately reproduces the prices for plain vanillahedging instruments (swaptions and caplets) of all strikes andmaturities produced by the SABR model. The authors show how toaccurately recover the whole of the SABR smile surface using theirextension of the LIBOR market model. This is not just a new model,this is a new way of option pricing that takes into account theneed to calibrate as accurately as possible to the plain vanillareference hedging instruments and the need to obtain prices andhedges in reasonable time whilst reproducing a realistic futureevolution of the smile surface. It removes the hard choice betweenaccuracy and time because the framework that the authors providereproduces today's market prices of plain vanilla options almostexactly and simultaneously gives a reasonable future evolution forthe smile surface.

The authors take the SABR model as the starting point for theirextension of the LMM because it is a good model for Europeanoptions. The problem, however with SABR is that it treats eachEuropean option in isolation and the processes for the variousunderlyings (forward and swap rates) do not talk to each other soit isn't obvious how to relate these processes into the dynamics ofthe whole yield curve. With this new model, the authors bring thedynamics of the various forward rates and stochastic volatilitiesunder a single umbrella. To ensure the absence of arbitrage theyderive drift adjustments to be applied to both the forward ratesand their volatilities. When this is completed, complex derivativesthat depend on the joint realisation of all relevant forward ratescan now be priced.

Contents
THE THEORETICAL SET-UP
The Libor Market model
The SABR Model
The LMM-SABR Model

IMPLEMENTATION AND CALIBRATION
Calibrating the LMM-SABR model to Market Caplet prices
Calibrating the LMM/SABR model to Market Swaption Prices
Calibrating the Correlation Structure

EMPIRICAL EVIDENCE
The Empirical problem
Estimating the volatility of the forward rates
Estimating the correlation structure
Estimating the volatility of the volatility

HEDGING
Hedging the Volatility Structure
Hedging the Correlation Structure
Hedging in conditions of market stress

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From the Back Cover:

The authors take two market standards, the SABR and the LIBORMarket Model (LMM) and produce a coherent synthesis for the pricingof complex interest rate derivatives. The SABR model has become themarket standard to recover the price of European options. Its mainstrengths are its financial justifiability, and its ability torecover the dynamics of the smile evolution when the underlyingchanges. However, the SABR model treats each European option inisolation. The processes for forward rates and swap rates cannoteasily be combined to create coherent dynamics for the entire yieldcurve.

With their new model, the authors bring the dynamics of thevarious forward rates and stochastic volatilities under a singlemeasure, and derive ‘drift adjustments’ to ensure theabsence of arbitrage and to allow for the pricing of complexderivatives. The credible evolution of future smiles generated bythe model is essential to complex derivatives pricing as itdetermines future prices for caplets and swaptions and thereforeplausible re-hedging costs.

The authors calibrate their model to hedging instruments in away that is both accurate and extremely simple. They also propose apragmatic hedging approach, inspired by work done with thetwo-state Markov-chain approach which relies on the empiricalregularities of the dynamics of the smile surface and therobustness of the fits proposed. The final chapter considers‘survival’ hedging in times of market turmoil. It doesso by providing a set of transactions that can protect the value ofa complex derivatives book in a stressed market.

The extension of the LMM model provides a valid description ofthe financial reality while retaining tractability, computationalspeed and ease of calibration. The goal for the new model is tooffer the ability to reduce uncertainty in market prices to anacceptable minimum by making as judicious a use as possible of theeconometric information available. The grounding in empiricalinformation of the modelling approach utilised by the authorsdifferentiates this title from the stochastic-calculus-heavy, butempirically light, work of others.

The title will be of interest to quantitative analysts,quantitative developers, risk managers and traders in complexderivatives.

From the Inside Flap:

This is the best of Rebonato’s books. Theconversational spirit of the previous manuscripts is herepleasantly retained. But, the value added is the mathematical rigorthat permeates the description of the proposed model. Definitely amust.”

Fabio Mercurio, Senior Quantitative Analyst, Bloomberg NewYork

A book that has all the hallmarks of RiccardoRebonato: rigorous theory, up-to-date market knowledge, practicalapplication, and empirical testing to destruction. This time, withco-authors, he applies himself to the most central banking market:LIBOR-related contracts.”

Ian Cooper, Professor of Finance, London BusinessSchool

In this concise book Riccardo Rebonato and hisco-authors introduce a new financially motivated model combiningthe best features of the Libor Market and SABR models. The authorsprovide a useful roadmap to pricing, calibrating, and hedginginterest rate derivatives in the new framework. The book will be ofinterest to practitioners and academics alike.”

Alexander Lipton, Managing Director, Merrill Lynch andVisiting Professor, Imperial College

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Book Description John Wiley and Sons Ltd, United Kingdom, 2009. Hardback. Condition: New. 1. Auflage. Language: English. Brand new Book. This book presents a major innovation in the interest rate space. It explains a financially motivated extension of the LIBOR Market model which accurately reproduces the prices for plain vanilla hedging instruments (swaptions and caplets) of all strikes and maturities produced by the SABR model. The authors show how to accurately recover the whole of the SABR smile surface using their extension of the LIBOR market model. This is not just a new model, this is a new way of option pricing that takes into account the need to calibrate as accurately as possible to the plain vanilla reference hedging instruments and the need to obtain prices and hedges in reasonable time whilst reproducing a realistic future evolution of the smile surface. It removes the hard choice between accuracy and time because the framework that the authors provide reproduces today's market prices of plain vanilla options almost exactly and simultaneously gives a reasonable future evolution for the smile surface. The authors take the SABR model as the starting point for their extension of the LMM because it is a good model for European options.The problem, however with SABR is that it treats each European option in isolation and the processes for the various underlyings (forward and swap rates) do not talk to each other so it isn't obvious how to relate these processes into the dynamics of the whole yield curve. With this new model, the authors bring the dynamics of the various forward rates and stochastic volatilities under a single umbrella. To ensure the absence of arbitrage they derive drift adjustments to be applied to both the forward rates and their volatilities. When this is completed, complex derivatives that depend on the joint realisation of all relevant forward rates can now be priced.Contents THE THEORETICAL SET-UP The Libor Market model The SABR Model The LMM-SABR Model IMPLEMENTATION AND CALIBRATION Calibrating the LMM-SABR model to Market Caplet prices Calibrating the LMM/SABR model to Market Swaption Prices Calibrating the Correlation Structure EMPIRICAL EVIDENCE The Empirical problem Estimating the volatility of the forward rates Estimating the correlation structure Estimating the volatility of the volatility HEDGING Hedging the Volatility Structure Hedging the Correlation Structure Hedging in conditions of market stress. Seller Inventory # AAH9780470740057

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Book Description John Wiley and Sons Ltd, United Kingdom, 2009. Hardback. Condition: New. 1. Auflage. Language: English . Brand New Book. This book presents a major innovation in the interest rate space. It explains a financially motivated extension of the LIBOR Market model which accurately reproduces the prices for plain vanilla hedging instruments (swaptions and caplets) of all strikes and maturities produced by the SABR model. The authors show how to accurately recover the whole of the SABR smile surface using their extension of the LIBOR market model. This is not just a new model, this is a new way of option pricing that takes into account the need to calibrate as accurately as possible to the plain vanilla reference hedging instruments and the need to obtain prices and hedges in reasonable time whilst reproducing a realistic future evolution of the smile surface. It removes the hard choice between accuracy and time because the framework that the authors provide reproduces today s market prices of plain vanilla options almost exactly and simultaneously gives a reasonable future evolution for the smile surface. The authors take the SABR model as the starting point for their extension of the LMM because it is a good model for European options. The problem, however with SABR is that it treats each European option in isolation and the processes for the various underlyings (forward and swap rates) do not talk to each other so it isn t obvious how to relate these processes into the dynamics of the whole yield curve. With this new model, the authors bring the dynamics of the various forward rates and stochastic volatilities under a single umbrella. To ensure the absence of arbitrage they derive drift adjustments to be applied to both the forward rates and their volatilities. When this is completed, complex derivatives that depend on the joint realisation of all relevant forward rates can now be priced. Contents THE THEORETICAL SET-UP The Libor Market model The SABR Model The LMM-SABR Model IMPLEMENTATION AND CALIBRATION Calibrating the LMM-SABR model to Market Caplet prices Calibrating the LMM/SABR model to Market Swaption Prices Calibrating the Correlation Structure EMPIRICAL EVIDENCE The Empirical problem Estimating the volatility of the forward rates Estimating the correlation structure Estimating the volatility of the volatility HEDGING Hedging the Volatility Structure Hedging the Correlation Structure Hedging in conditions of market stress. Seller Inventory # AAH9780470740057

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Book Description John Wiley and Sons Ltd, United Kingdom, 2009. Hardback. Condition: New. 1. Auflage. Language: English. Brand new Book. This book presents a major innovation in the interest rate space. It explains a financially motivated extension of the LIBOR Market model which accurately reproduces the prices for plain vanilla hedging instruments (swaptions and caplets) of all strikes and maturities produced by the SABR model. The authors show how to accurately recover the whole of the SABR smile surface using their extension of the LIBOR market model. This is not just a new model, this is a new way of option pricing that takes into account the need to calibrate as accurately as possible to the plain vanilla reference hedging instruments and the need to obtain prices and hedges in reasonable time whilst reproducing a realistic future evolution of the smile surface. It removes the hard choice between accuracy and time because the framework that the authors provide reproduces today's market prices of plain vanilla options almost exactly and simultaneously gives a reasonable future evolution for the smile surface. The authors take the SABR model as the starting point for their extension of the LMM because it is a good model for European options.The problem, however with SABR is that it treats each European option in isolation and the processes for the various underlyings (forward and swap rates) do not talk to each other so it isn't obvious how to relate these processes into the dynamics of the whole yield curve. With this new model, the authors bring the dynamics of the various forward rates and stochastic volatilities under a single umbrella. To ensure the absence of arbitrage they derive drift adjustments to be applied to both the forward rates and their volatilities. When this is completed, complex derivatives that depend on the joint realisation of all relevant forward rates can now be priced.Contents THE THEORETICAL SET-UP The Libor Market model The SABR Model The LMM-SABR Model IMPLEMENTATION AND CALIBRATION Calibrating the LMM-SABR model to Market Caplet prices Calibrating the LMM/SABR model to Market Swaption Prices Calibrating the Correlation Structure EMPIRICAL EVIDENCE The Empirical problem Estimating the volatility of the forward rates Estimating the correlation structure Estimating the volatility of the volatility HEDGING Hedging the Volatility Structure Hedging the Correlation Structure Hedging in conditions of market stress. Seller Inventory # BTE9780470740057

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