{"product_id":"the-sabr-libor-market-model-isbn-9780470740057","title":"The SABR\/LIBOR Market Model","description":"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.\u003cbr\u003e \u003cbr\u003e 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.\u003cbr\u003e \u003cbr\u003e Contents\u003cbr\u003e THE THEORETICAL SET-UP\u003cbr\u003e The Libor Market model\u003cbr\u003e The SABR Model\u003cbr\u003e The LMM-SABR Model\u003cbr\u003e \u003cbr\u003e IMPLEMENTATION AND CALIBRATION\u003cbr\u003e Calibrating the LMM-SABR model to Market Caplet prices\u003cbr\u003e Calibrating the LMM\/SABR model to Market Swaption Prices\u003cbr\u003e Calibrating the Correlation Structure\u003cbr\u003e \u003cbr\u003e EMPIRICAL EVIDENCE\u003cbr\u003e The Empirical problem\u003cbr\u003e Estimating the volatility of the forward rates\u003cbr\u003e Estimating the correlation structure\u003cbr\u003e Estimating the volatility of the volatility\u003cbr\u003e \u003cbr\u003e HEDGING\u003cbr\u003e Hedging the Volatility Structure\u003cbr\u003e Hedging the Correlation Structure\u003cbr\u003e Hedging in conditions of market stress \u003cp\u003eAcknowledgements xi\u003c\/p\u003e \u003cp\u003e1 Introduction 1\u003c\/p\u003e \u003cp\u003e\u003cb\u003eI The Theoretical Set-Up 7\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2 The LIBOR Market Model 9\u003c\/p\u003e \u003cp\u003e3 The SABR Model 25\u003c\/p\u003e \u003cp\u003e4 The LMM-SABR Model 51\u003c\/p\u003e \u003cp\u003e\u003cb\u003eII Implementation and Calibration 79\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5 Calibrating the LMM-SABR Model to Market Caplet Prices 81\u003c\/p\u003e \u003cp\u003e6 Calibrating the LMM-SABR Model to Market Swaption Prices 101\u003c\/p\u003e \u003cp\u003e7 Calibrating the Correlation Structure 125\u003c\/p\u003e \u003cp\u003e\u003cb\u003eIII Empirical Evidence 141\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8 The Empirical Problem 143\u003c\/p\u003e \u003cp\u003e9 Estimating the Volatility of the Forward Rates 159\u003c\/p\u003e \u003cp\u003e10 Estimating the Correlation Structure 181\u003c\/p\u003e \u003cp\u003e\u003cb\u003eIV Hedging 203\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e11 Various Types of Hedging 205\u003c\/p\u003e \u003cp\u003e12 Hedging against Moves in the Forward Rate and in the Volatility 221\u003c\/p\u003e \u003cp\u003e13 (LMM)-SABR Hedging in Practice: Evidence from Market Data 231\u003c\/p\u003e \u003cp\u003e14 Hedging the Correlation Structure 247\u003c\/p\u003e \u003cp\u003e15 Hedging in Conditions of Market Stress 257\u003c\/p\u003e \u003cp\u003eReferences 271\u003c\/p\u003e \u003cp\u003eIndex 275\u003c\/p\u003e  \u003cp\u003e\u003cb\u003eRICCARDO REBONATO\u003c\/b\u003e is Global Head of Market Risk and Global Head of the Quantitative Research Team at RBS. He is a visiting lecturer at Oxford University (Mathematical Finance) and adjunct professor at Imperial College (Tanaka Business School). He sits on the Board of Directors of ISDA and on the Board of Trustees for GARP. He is an editor for the \u003ci\u003eInternational Journal of Theoretical and Applied Finance\u003c\/i\u003e, for \u003ci\u003eApplied Mathematical Finance\u003c\/i\u003e, for the \u003ci\u003eJournal of Risk\u003c\/i\u003e and for the \u003ci\u003eJournal of Risk Management in Financial Institutions\u003c\/i\u003e. He holds doctorates in Nuclear Engineering and in Science of Materials\/Solid State Physics. He was a research fellow in Physics at Corpus Christi College, Oxford, UK. \u003c\/p\u003e\u003cp\u003e\u003cb\u003eKENNETH MCKAY\u003c\/b\u003e is a PhD student at the London School of Economics following a first class honours degree in Mathematics and Economics from the LSE and an MPhil in Finance from Cambridge University. He has been working on interest rate derivative-related research with Riccardo Rebonato for the past year. \u003c\/p\u003e\u003cp\u003e\u003cb\u003eRICHARD WHITE\u003c\/b\u003e holds a doctorate in Particle Physics from Imperial College London, and a first class honours degree in Physics from Oxford University. He held a Research Associate position at Imperial College before joining RBS in 2004 as a Quantitative Analyst. His research interests include option pricing with Levy Processes, Genetic Algorithms for portfolio optimisation, and Libor Market Models with stochastic volatility. He is currently taking a fortuitously timed sabbatical to pursue his joint passion for travel and scuba diving.   \u003c\/p\u003e\u003cp\u003e\u003cb\u003ethe SABR\/LIBOR Market Model\u003cbr\u003e PRICING, CALIBRATION AND HEDGING FOR COMPLEX INTEREST-RATE DERIVATIVES\u003c\/b\u003e \u003c\/p\u003e\u003cp\u003e\u003ci\u003e\"This is the best of Rebonato's books. The conversational spirit of the previous manuscripts is here pleasantly retained. But, the value added is the mathematical rigor that permeates the description of the proposed model. Definitely a must.\"\u003c\/i\u003e\u003cbr\u003e \"\u003cb\u003eFabio Mercurio\u003c\/b\u003e, Senior Quantitative Analyst, Bloomberg New York \u003c\/p\u003e\u003cp\u003e\u003ci\u003e\"A book that has all the hallmarks of Riccardo Rebonato: rigorous theory, up-to-date market knowledge, practical application, and empirical testing to destruction. This time, with co-authors, he applies himself to the most central banking market: LIBOR-related contracts.\"\u003c\/i\u003e\u003cbr\u003e \"\u003cb\u003eIan Cooper\u003c\/b\u003e, Professor of Finance, London Business School \u003c\/p\u003e\u003cp\u003e\u003ci\u003e\"In this concise book Riccardo Rebonato and his co-authors introduce a new financially motivated model combining the best features of the Libor Market and SABR models. The authors provide a useful roadmap to pricing, calibrating, and hedging interest rate derivatives in the new framework. The book will be of interest to practitioners and academics alike.\"\u003c\/i\u003e\u003cbr\u003e \"\u003cb\u003eAlexander Lipton\u003c\/b\u003e, Managing Director, Merrill Lynch and Visiting Professor, Imperial College\u003c\/p\u003e","brand":"Wiley","offers":[{"title":"Default Title","offer_id":47990334030053,"sku":"NP9780470740057","price":125.0,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9780470740057.jpg?v=1761787399","url":"https:\/\/k12savings.com\/es\/products\/the-sabr-libor-market-model-isbn-9780470740057","provider":"K12savings","version":"1.0","type":"link"}