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

The SABR/LIBOR Market Model: Pricing, Calibration and Hedging for Complex Interest-Rate DerivativesAuthors: Riccardo Rebonato, Kenneth McKay, Richard White
Publisher: Wiley
Category: Book

List Price: $105.00
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Seller: indoobestsellers
Rating: 4.0 out of 5 stars 1 reviews
Sales Rank: 135393

Media: Hardcover
Pages: 296
Number Of Items: 1
Shipping Weight (lbs): 1.5
Dimensions (in): 9.8 x 6.8 x 0.9

ISBN: 0470740051
Dewey Decimal Number: 332.8015118
EAN: 9780470740057
ASIN: 0470740051

Publication Date: April 27, 2009
Availability: Usually ships in 1-2 business days

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Product 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.

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



Customer Reviews:
4 out of 5 stars Lucid thinking about models. Model details of less general interest.   November 24, 2009
Un francais en angleterre (Londres, UK)
1 out of 1 found this review helpful

Having to deal with Exotic Interest Rates product professionally, I had to get the latest Rebonato's opum. I've found in the past that there is much to be annoyed with this author (he gets fairly deep into the details but not necessarily at the level where you can re-implement things yourself), but also very frequently insights you would not get anywhere else: in the case of this book, the couple of pages where he explains what makes a good model should be mandatory reading for any aspiring "quant" thinking about applying the tools of his trade to the dirty world of finance. This is much better stuff than the more common-place fare he served in his "plight of the fortune tellers". Recommended as such. If you're buying this for the specific model that Rebonato advocates, unless you're very deeply involved in Rates structured products, I don't think you're getting a bargain.


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