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Numerical Methods in Finance : Bordeaux, June 2010 / edited by René A. Carmona, Pierre Del Moral, Peng Hu, Nadia Oudjane
Contributor(s): Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Series: Springer Proceedings in Mathematics ; 12 | SpringerLink BücherPublisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 2012Description: Online-Ressource (XVII, 471p. 88 illus., 58 illus. in color, digital)ISBN:- 9783642257469
- 300
- 519
- HB144 QA269-272
- HB144
- QA269-272
Contents:
Summary: Part I: Particle Methods in Finance -- 1 R. Carmona, P. Del Moral, P. Hu, N, Oudjane: An Introduction to Particle Methods with Financial Applications -- 2.Bhojnarine R. Rambharat: American option valuation with particle filters -- 3.Michael Ludkovski: Monte Carlo Methods for Adaptive Disorder Problems -- Part II: Numerical methods for backward conditional expectations -- 4.Pierre Del Moral, Bruno Rémillard, Sylvain Rubenthale: Monte Carlo approximations of American options that preserve monotonicity and convexity -- 5.Bruno Rémillard, Alexandre Hocquard, Hugues Langlois, and Nicolas Papageorgiou: Optimal Hedging of American Options in Discrete Time -- 6.Gilles Pagès and Benedikt Wilbertz: Optimal Delaunay and Voronoi quantization schemes for pricing American style options -- 7.Bruno Bouchard, Xavier Warin: Monte-Carlo valuation of American options: facts and new algorithms to improve existing methods -- 8.Christian Bender and Jessica Steiner: Least-squares Monte Carlo for backward SDEs -- 9.Lisa J. Powers, Johanna Nešlehová, and David A. Stephens: Pricing American Options in an infinite activity Lévy market: Monte Carlo and deterministic approaches using a diffusion approximation -- 10.Bowen Zhang and Cornelis W. Oosterlee: Fourier Cosine Expansions and Put–Call Relations for Bermudan Options -- Part III: Numerical methods for energy derivatives -- 11.Klaus Wiebauer: A practical view on valuation of multi-exercise American style options in gas and electricity markets -- 12. Marie Bernhart, Huyen Pham, Peter Tankov and Xavier Warin: Swing Options Valuation: a BSDE with Constrained Jumps Approach -- 13.François Turboult and Yassine Youlal: Swing option pricing by optimal exercise boundary estimation -- 14.Xavier Warin: Gas Storage Hedging -- 15.J.Frédéric Bonnans, Zhihao Cen, Thibault Christel: Sensitivity analysis of energy contracts by stochastic programming techniques. .Summary: Numerical methods in finance have emerged as a vital field at the crossroads of probability theory, finance and numerical analysis. Based on presentations given at the workshop Numerical Methods in Finance held at the INRIA Bordeaux (France) on June 1-2, 2010, this book provides an overview of the major new advances in the numerical treatment of instruments with American exercises. Naturally it covers the most recent research on the mathematical theory and the practical applications of optimal stopping problems as they relate to financial applications. By extension, it also provides an original treatment of Monte Carlo methods for the recursive computation of conditional expectations and solutions of BSDEs and generalized multiple optimal stopping problems and their applications to the valuation of energy derivatives and assets. The articles were carefully written in a pedagogical style and a reasonably self-contained manner. The book is geared toward quantitative analysts, probabilists, and applied mathematicians interested in financial applications.PPN: PPN: 165139864XPackage identifier: Produktsigel: ZDB-2-SEB | ZDB-2-SXMS | ZDB-2-SMA
Numerical Methods in Finance; Preface; References; Contents; Contributors; Part I Particle Methods in Finance; An Introduction to Particle Methods with Financial Applications; 1 Introduction; 2 Option Prices and Feynman-Kac Formula; 2.1 Discrete Time Models; 2.1.1 European Barrier Option; 2.1.2 Asian Option; 2.2 Continuous Time Models; 3 Interacting Particle Approximations; 3.1 Feynman-Kac Semigroups; 3.2 Interacting Particle Methodologies; 3.3 Path Space Models; 3.3.1 Genealogical Tree Based Algorithms; 3.3.2 Backward Markov Chain Model; 3.4 Parallel Island Particle Models
4 Application in Credit Risk Analysis4.1 Change of Measure for Rare Events and Feynman-Kac Formula; 4.2 On the Choice of the Potential Functions; 5 Sensitivity Computation; 5.1 Likelihood Ratio: Application to Dynamic Parameter Derivatives; 5.2 Tangent Process: Application to Initial State Derivatives; 6 American-Style Option Pricing; 6.1 Description of the Model; 6.2 A Perturbation Analysis; 6.3 Particle Approximations; 7 Pricing Models with Partial Observation Models; 7.1 Abstract Formulation and Particle Approximation; 7.2 Optimal Stopping with Partial Observation
7.3 Parameter Estimation in Hidden Markov Chain ModelsReferences; American Option Valuation with Particle Filters; 1 Introduction; 2 Valuation Framework; 2.1 A Risk-Neutral Stochastic Volatility Model; 2.2 Simulation Methodology; 2.3 Latent Volatility; 2.4 Risk Quantification; 3 American Options and Particle Filters; 3.1 Filter Statistics; 3.2 Pricing Algorithm; 4 Benchmark Analysis; 5 Application to Index Options; 5.1 Data Description; 5.2 Parameter Estimation; 5.3 Volatility Risk Premium; 6 Concluding Remarks; References; Monte Carlo Methods for Adaptive Disorder Problems; 1 Introduction
2 Problem Formulation2.1 Canonical Setup; 2.2 Physical Probability P; 2.3 Bayes Risk; 3 Filtering; 3.1 Conditional Moments; 3.2 Particle Filters; 3.3 Particle Degeneracy; 4 Solving the Optimal Stopping Problem; 4.1 Integrated Algorithm; 4.2 Error Analysis; 5 Numerical Examples; 5.1 Analysis of Particle Filter; 5.2 Example 1; 5.3 Example 2; 6 Extensions; 6.1 Compound Poisson Process Observations; 6.2 Jump Markov Signal; References; Part II Numerical Methods for Backward Conditional Expectations; Monte Carlo Approximations of American Options that Preserve Monotonicity and Convexity
1 Introduction2 A Brief Review of Algorithms for Valuation of American Options; 2.1 Snell Envelope; 2.2 Classes of Algorithms for Valuation of American Options; 2.3 Carriere Algorithm; 2.4 Longstaff-Schwartz Algorithm; 2.5 Primal-Dual Approach; 2.5.1 Algorithm for the Lower Bound; 3 Approximation of the Snell Envelope; 3.1 Properties of U and V; 3.2 Description of the Algorithm and Justification; 3.2.1 Algorithm; 4 Implementation Issues; 4.1 Geometric Brownian Motion; 4.1.1 Numerical Illustration for the American Call Option
4.1.2 Numerical Illustration for the American Call-on-max Option on Two Assets
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