Hull-White On Derivatives [Paperback]

Alan White; John Hull (Author), Alan White (Author), John Hull (Author)

Book Description

Publication Date: June 1, 1996

This book brings together classic papers on derivatives theory and implementation written by Professor John Hull and Alan White of the University of Toronto. The authors are two of the derivative industry's leading experts and together created the standard Hull-White model for pricing interest rate options. Professor Hull and White have provided introductions for each of the book's five main sections, clarifying the importance of each chapter to industry practitioners. Parts I and II provide you with a comprehensive treatment of stochastic volatility and its effect on option pricing and hedging, and describe some of the best numerical procedures for valuing derivatives. Part III looks at how to approach a key concern in the derivatives industry today - the assessment and valuation of the credit risk generated by derivatives portfolios. The final two sections offer an expansive treatment of the Hull-White approach to modeling the yield curve and valuing interest rate derivatives. With full explanations of both the theoretical background, and the necessary numerical procedures for implementing one- and two-factor models - essential reading for all those involved in the interest rate markets.

Editorial Reviews

Review

John Hull's book, Options, Futures and Other Derivative Securities, is one of the rare hits of financial literature. Hull's more advanced work, always written with Alan White, has appeared as academic papers in various publications. Hull-White on Derivatives organises these papers into five main themes, each with an added introduction that justifies the purchase of the book even for those who already have the 15 papers in it. 1. Stochastic volatility. Hull & White made clear that when the dynamics of volatility do not depend on the spot, the option price is an average of Black-Scholes prices with different volatilities, which generates a mild symmetric smile. To get market skews, one needs to introduce correlation between changes in spot and changes in volatility. Analytical expansions (for square root volatility processes) and hedging (no major changes in delta) are considered. 2. Numerical procedures. Links between trinomial trees and explicit discretisations of partial differential equations are shown. Tricks such as changing variables to normalise the volatility and changing the branching scheme to follow the drift are detailed. The idea of control variate techniques is presented: if you have a good approximation, try to estimate the error (through Monte Carlo, for instance) and add it to the approximation. The last paper explains the use of two-dimensional trees to compute the price of an option whose path-dependency is captured by a single variable. 3. Credit risk. The loss incurred in case of default of a counterparty is interpreted as an option payout and is valued following option pricing principles. The discount that should be demanded of a risky counterparty which sells an option is calculated through implied default probabilities read from risky bond prices. 4. Term-structure models: theory. Hull & White present a class of yield curve models, the most popular of which is the extended Vasicek model (a Markov Gaussian model on the short-term rate, which is fitted to the initial yield curve). Analytical formulas are given for yield curve reconstruction and option prices. 5. Term-structure models: implementation. This makes a nice case for the use of trinomial trees. Their application to the two-dimensional case is described as well as procedures to calibrate them to market prices. Hull & White have profoundly influenced the derivatives market, not least because they have a flair for addressing the right questions at the right time (any researcher knows that it is often harder to identify the problem than to solve it once it is well posed), a straightforward approach and a clear pedagogical talent. Hull & White are not the most theoretical people but their familiarity with practitioners makes their work quite usable. Some of their contributions carve in stone what some banks have been working on for years (trinomial trees, Gaussian yield curve models, numerical schemes for path dependent options, etc). Though this book offers a vast panorama, it cannot be considered as a second and definitive volume to Options, Futures and Other Derivative Securities. For instance, it does not deal with powerful tools such as changes of numeraire and measures, calibration to volatility smiles and low discrepancy sequences. It must be added, however, that this is not the aim of this book, which is a remarkable piece of work all the same. -- Bruno Dupire, Nikko Europe

Product Details

• Paperback: 356 pages
• Publisher: Risk Books; 1 edition (June 1, 1996)
• Language: English
• ISBN-10: 1899332456
• ISBN-13: 978-1899332458
• Product Dimensions: 9 x 5.8 x 0.7 inches
• Shipping Weight: 1.2 pounds (View shipping rates and policies)
• Amazon Best Sellers Rank: #1,465,859 in Books (See Top 100 in Books)

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