Handbook of computational finance

Springer Handbooks of Computational Statistics Series Editors James E Gentle Wolfgang K Hăardle Yuichi Mori For further volumes: http://www.springer.com/series/7286 Jin-Chuan Duan James E Gentle Wolfgang Karl Hăardle Editors Handbook of Computational Finance 123 Editors Jin-Chuan Duan National University of Singapore Risk Management Institute 21 Heng Mui Keng Terrace, Level 119613 Singapore Singapore bizdjc@nus.edu.sg Prof James E Gentle George Mason University Department of Computational and Data Sciences University Drive 4400 22030 Fairfax Virginia USA jgentle@gmu.edu Prof.Dr Wolfgang Karl Hăardle Ladislaus von Bortkiewicz Chair of Statistics C.A.S.E Centre for Applied Statistics and Economics School of Business and Economics Humboldt-Universităat zu Berlin Unter den Linden 10099 Berlin Germany haerdle@wiwi.hu-berlin.de ISBN 978-3-642-17253-3 e-ISBN 978-3-642-17254-0 DOI 10.1007/978-3-642-17254-0 Springer Heidelberg Dordrecht London New York Library of Congress Control Number: 2011937712 c Springer-Verlag Berlin Heidelberg 2012 This work is subject to copyright All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer Violations are liable to prosecution under the German Copyright Law The use of general descriptive names, registered names, trademarks, etc in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use Cover design: WMXDesign GmbH Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com) Contents Part I Introduction Computational Finance: An Introduction Jin-Chuan Duan, James E Gentle, and Wolfgang Karl Hăardle Part II Asset Pricing Models Modeling Asset Prices James E Gentle and Wolfgang Karl Hăardle 15 Diffusion Models of Asset Prices J´erˆome Detemple and Marcel Rindisbacher 35 Jump-Diffusion Models Driven by L´evy Processes Jos´e E Figueroa-L´opez 61 Multivariate Time Series Models for Asset Prices Christian M Hafner and Hans Manner 89 Option Data and Modeling BSM Implied Volatility 117 Matthias R Fengler Interest Rate Derivatives Pricing with Volatility Smile 143 Haitao Li Volatility Investing with Variance Swaps 203 Wolfgang Karl Hăardle and Elena Silyakova Part III Statistical Inference in Financial Models Evaluation of Asset Pricing Models Using Two-Pass Cross-Sectional Regressions 223 Raymond Kan and Cesare Robotti v vi Contents 10 Parametric Estimation of Risk Neutral Density Functions 253 Maria Grith and Volker Krăatschmer 11 Nonparametric Estimation of Risk-Neutral Densities 277 Maria Grith, Wolfgang Karl Hăardle, and Melanie Schienle 12 Value at Risk Estimation 307 Ying Chen and Jun Lu 13 Volatility Estimation Based on High-Frequency Data 335 Christian Pigorsch, Uta Pigorsch, and Ivaylo Popov 14 Identifying Jumps in Asset Prices 371 Johan Bjursell and James E Gentle 15 Simulation-Based Estimation Methods for Financial Time Series Models 401 Jun Yu Part IV Computational Methods 16 Filtering Methods 439 Andras Fulop 17 Fitting High-Dimensional Copulae to Data 469 Ostap Okhrin 18 Numerical Methods for Nonlinear PDEs in Finance 503 Peter A Forsyth and Kenneth R Vetzal 19 Numerical Solution of Stochastic Differential Equations in Finance 529 Timothy Sauer 20 Lattice Approach and Implied Trees 551 Răudiger U Seydel 21 Efficient Options Pricing Using the Fast Fourier Transform 579 Yue Kuen Kwok, Kwai Sun Leung, and Hoi Ying Wong 22 Dynamic Programming and Hedging Strategies in Discrete Time 605 Shih-Feng Huang and Meihui Guo 23 Approximation of Dynamic Programs 633 Mich`ele Breton and Javier de Frutos 24 Computational Issues in Stress Testing 651 Ludger Overbeck Contents vii 25 Portfolio Optimization 675 J´erˆome Detemple and Marcel Rindisbacher 26 Low-Discrepancy Simulation 703 Harald Niederreiter 27 Introduction to Support Vector Machines and Their Applications in Bankruptcy Prognosis 731 Yuh-Jye Lee, Yi-Ren Yeh, and Hsing-Kuo Pao Part V Software Tools 28 MATLAB R as a Tool in Computational Finance 765 James E Gentle and Angel Martinez 29 R as a Tool in Computational Finance 781 John P Nolan • Contributors Johan Bjursell George Mason University, Fairfax, VA 22030, USA, cbjursel@ gmu.edu Mich`ele Breton GERAD, HEC Montr´eal, 3000, chemin de la Cˆote-SainteCatherine, Montr´eal, QC, Canada H3T 2A7, michele.breton@hec.ca Ying Chen Department of Statistics and Applied Probability, National University of Singapore, Singapore 117546, Singapore, stacheny@nus.edu.sg J´erˆome Detemple Boston University School of Management, Boston University, 595 Commonwealth Avenue, Boston, MA 02215, USA, detemple@bu.edu Jin-Chuan Duan National University of Singapore, Singapore 117546, Singapore, bizdjc@nus.edu.sg Matthias R Fengler University of St Gallen, Gallen, Switzerland, matthias fengler@unisg.ch Jos´e E Figueroa-L´opez Department of Statistics, Purdue University, West Lafayette, IN 47907-2066, USA, figueroa@stat.purdue.edu Peter A Forsyth Cheriton School of Computer Science, University of Waterloo, Waterloo, ON, Canada, paforsyt@uwaterloo.ca Javier de Frutos GERAD and Dpto de Matem´atica Aplicada, Universidad de Valladolid, Valladolid, Palencia, Soria and Segovia, Spain, frutos@mac.uva.es Andras Fulop ESSEC Business School, Paris, France, fulop@essec.fr James E Gentle George Mason University, Fairfax, VA 22030, USA, jgentle@gmu.edu Maria Grith Ladislaus von Bortkiewicz Chair of Statistics, Humboldt-Universităat zu Berlin, Spandauer Straòe 1, 10178 Berlin, Germany, gritmari@wiwi hu-berlin.de ix 790 J.P Nolan Histogram of v 100 100 80 80 Frequency Frequency Histogram of u 60 40 60 40 20 20 0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 u 0.6 0.8 1.0 v scatterplot of u and v Histogram of u + v 1.0 0.8 150 Frequency v 0.6 0.4 0.2 0.0 100 50 0.0 0.2 0.4 0.6 u 0.8 1.0 0.0 0.5 1.0 u+v 1.5 2.0 Fig 29.4 Multiplot showing histograms of u, v, u C v, and a scatter plot of u; v/ x