Computational methods for quantitative finance. Finite element methods for derivative pricing
type: Item
instance of: scholarly article
title: Computational methods for quantitative finance. Finite element methods for derivative pricing
zbMATH Open document ID: 1275.91005
DOI: 10.1007/978-3-642-35401-4
author: Norbert Hilber
author: Oleg Reichmann
author: Christoph Schwab
author: Christoph Winter
published in: Springer Finance
publication date: 2013-02-13T00:00:00Z
review text: This book is a comprehensive treatise on finite difference and finite element methods for financial derivative pricing. I appreciate that the introduction about mathematical finance, on which there are plenty of books, is very short; the authors basically assume that the stage for derivative pricing is set. After introductory chapters on the numerical schemes for PDEs, they are applied to European, American, and exotic options in the Black-Scholes model. The following chapters cover numerical schemes for stochastic volatility models, Lévy models, and combinations thereof, also in several dimensions. American options lead to boundary value problems, and Lévy models to partial integro-differential equations (PIDEs). Many results about discretization error estimates are included. The focus of the book is on pricing, to some extent also on computing Greeks; it seems that the authors do not comment on whether they also propose to use these methods for calibration. Each chapter begins with a succinct, but informative paragraph on the topics that are to be expected, and ends with suggestions for further reading. At least the methods for one-dimensional models should be accessible to practitioners, whereas the later chapters use more advanced concepts and tools (e.g., wavelet discretization, tensor product finite element spaces, Feller processes).
reviewed by: Stefan Gerhold
Mathematics Subject Classification ID: 91-02
Mathematics Subject Classification ID: 91G60
Mathematics Subject Classification ID: 91G20
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 65M60
Mathematics Subject Classification ID: 65M15
zbMATH DE Number: 6135854
zbMATH Keywords: finite element method
zbMATH Keywords: finite difference method
zbMATH Keywords: derivative pricing
zbMATH Keywords: partial differential equation
zbMATH Keywords: partial integro-differential equation
zbMATH Keywords: Lévy process
zbMATH Keywords: stochastic volatility model
zbMATH Keywords: Feller process
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/978-3-642-35401-4
OpenAlex ID: W4233476184
description: scientific article; zbMATH DE number 6135854