Nonlinear Option Pricing

Julien Guyon, Pierre Henry-Labordere

December 19, 2013 by Chapman and Hall/CRC
Reference - 484 Pages - 55 B/W Illustrations
ISBN 9781466570337 - CAT# K16480
Series: Chapman and Hall/CRC Financial Mathematics Series

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  • Provides practitioners with a guide to developing their analytical and numerical skills
  • Proposes novel methods for pricing options, calibrating models, and more
  • Illustrates all the mathematical methods with practical nonlinear option pricing problems
  • Contains implementation details and sketches of proofs where appropriate
  • Includes exercises, many from real problems in trading, to reinforce readers’ understanding


New Tools to Solve Your Option Pricing Problems

For nonlinear PDEs encountered in quantitative finance, advanced probabilistic methods are needed to address dimensionality issues. Written by two leaders in quantitative research—including Risk magazine’s 2013 Quant of the Year—Nonlinear Option Pricing compares various numerical methods for solving high-dimensional nonlinear problems arising in option pricing. Designed for practitioners, it is the first authored book to discuss nonlinear Black-Scholes PDEs and compare the efficiency of many different methods.

Real-World Solutions for Quantitative Analysts

The book helps quants develop both their analytical and numerical expertise. It focuses on general mathematical tools rather than specific financial questions so that readers can easily use the tools to solve their own nonlinear problems. The authors build intuition through numerous real-world examples of numerical implementation. Although the focus is on ideas and numerical examples, the authors introduce relevant mathematical notions and important results and proofs. The book also covers several original approaches, including regression methods and dual methods for pricing chooser options, Monte Carlo approaches for pricing in the uncertain volatility model and the uncertain lapse and mortality model, the Markovian projection method and the particle method for calibrating local stochastic volatility models to market prices of vanilla options with/without stochastic interest rates, the a + bλ technique for building local correlation models that calibrate to market prices of vanilla options on a basket, and a new stochastic representation of nonlinear PDE solutions based on marked branching diffusions.


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