Return distributions in finance

RETURN DISTRIBUTIONS IN FINANCE Butterworth-Heinemann Finance Aims and objectives * * * * * * books based on the work of ®nancial market practitioners and academics presenting cutting edge research to the professional/practitioner market combining intellectual rigour and practical application covering the interaction between mathematical theory and ®nancial practice to improve portfolio performance, risk management and trading book performance covering quantitative techniques market Brokers/Traders; Actuaries; Consultants; Asset Managers; Fund Managers; Regulators; Central Bankers; Treasury Ocials; Technical Analysts; and Academics for Masters in Finance and MBA market series editor Dr Steven Satchell Apart from being an economics/®nance academic at Trinity College, Cambridge with many publications to his credit, he also works in a consultative capacity to many ®rms and edits the journal Derivatives: use, trading and regulations published by Henry Stewart Publishers He has edited two ®nance books published by Butterworth-Heinemann: Forecasting Volatility with John Knight and Advanced Trading Rules with Emmanuel Acar He is currently writing, with Frank Sortino, a new book, Downside Risk in Financial Markets: theory, practice and implementation and editing a new book, with John Knight, Performance Measurement in Finance: ®rms, funds and managers His latest edited book with John Knight is Return Distributions in Finance He is a regular speaker at professional conferences series titles Return Distributions in Finance Downside Risk in Financial Markets: theory, practice and implementation Performance Measurement in Finance: ®rms, funds and managers Global Tactical Asset Allocation: theory and practice RETURN DISTRIBUTIONS IN FINANCE Edited by John Knight Stephen Satchell OXFORD AUCKLAND BOSTON JOHANNESBURG MELBOURNE NEW DELHI Butterworth-Heinemann Linacre House, Jordan Hill, Oxford OX2 8DP 225 Wildwood Avenue, Woburn, MA 01801-2041 A division of Reed Educational and Professional Publishing Ltd A member of the Reed Elsevier plc group First published 2001 # Reed Educational and Professional Publishing Ltd 2001 All rights reserved No part of this publication may be reproduced in any material form (including photocopying or storing in any medium by electronic means and whether or not transiently or incidentally to some other use of this publication) without the written permission of the copyright holder except in accordance with the provisions of the Copyright, Designs and Patents Acts 1988 or under the terms of a licence issued by the Copyright Licensing Agency Ltd, 90 Tottenham Court Road, London, England W1P 0LP Applications for the copyright holder's written permission to reproduce any part of this publication should be addressed to the publishers British Library Cataloguing in Publication Data Return distributions in ®nance Asset allocation Financial engineering Mathematics I Knight, John II Satchell, Stephen E 332.6'0151 ISBN 7506 4751 Printed and bound in Great Britain Investments Contents Preface List of contributors Modelling asset returns with hyperbolic distributions N H Bingham and RuÈdiger Kiesel 1.1 Introduction 1.2 Hyperbolic models of ®nancial markets and hyperbolic LeÂvy motion 1.3 Equivalent martingale measure 1.4 Case study 1.5 Conclusion References A review of asymmetric conditional density functions in autoregressive conditional heteroscedasticity models Shaun A Bond 2.1 Introduction 2.2 The literature on skewness 2.3 Dynamic volatility models 2.4 Empirical evidence 2.5 The role of distributions 2.6 Conclusion References The distribution of commercial real estate returns Colin Lizieri and Charles Ward 3.1 Introduction 3.2 De®nitional and measurement issues 3.3 The private, direct real estate market 3.4 The public, indirect real estate market ix xi 1 13 17 18 21 21 23 25 29 38 41 43 47 47 48 52 53 vi Contents 3.5 A property factor? Real estate and capital market integration 3.6 Non-linearity in real estate returns 3.7 The UK real estate market: models of return distributions 3.8 Conclusions References Appendix Modelling emerging market risk premia using higher moments Soosung Hwang and Stephen E Satchell 4.1 Introduction 4.2 Higher-moment CAPMs 4.3 Empirical tests 4.4 Higher-moment DGPs 4.5 Conclusion Appendix Appendix Appendix References Are stock prices driven by the volume of trade? Empirical analysis of the FT30, FT100 and certain British shares over 1988±1990 L.C.G Rogers, Stephen E Satchell and Youngjun Yoon 5.1 Introduction 5.2 Early research 5.3 Testing normality in the individual stocks 5.4 Conclusion Appendix References Testing for a ®nite variance in stock return distributions Jun Yu 6.1 Introduction 6.2 Proposed statistic and its properties 6.3 Candidate distributions for stock returns 6.4 Applications 6.5 Conclusions Appendix References Implementing option pricing models when asset returns are predictable and discontinuous George J Jiang 7.1 Introduction 55 57 58 68 70 73 75 75 78 84 107 111 112 113 114 115 118 118 119 123 138 138 141 143 143 145 149 156 160 161 163 165 166 Contents 7.2 Alternative model speci®cations and option pricing 7.3 Implications of model (mis)speci®cation on option prices 7.4 Discussion of related issues 7.5 Conclusion Appendix References The probability functions of option prices, risk-neutral pricing and Value-at-Risk John L Knight, Stephen E Satchell and Guoqiang Wang 8.1 Introduction and literature review 8.2 Models and approach 8.3 Results 8.4 Conclusion References Pricing derivatives written on assets with arbitrary skewness and kurtosis John L Knight and Stephen E Satchell 9.1 Introduction 9.2 RNVR relationships 9.3 Computing the RNVR 9.4 Option pricing 9.5 Conclusion Appendix References vii 170 182 207 217 218 224 229 229 233 240 246 250 252 252 254 258 260 261 262 274 10 The distribution of realized returns from moving average trading rules with application to Canadian stock market data Alexander Fritsche 10.1 Introduction 10.2 Moving average trading rules and technical analysis 10.3 Theoretical framework 10.4 Characteristics of the probability density functions 10.5 Application to TSE35 10.6 Conclusion References 276 278 280 284 300 304 305 Index 307 276 This Page Intentionally Left Blank Preface The purpose of this book is to bring together research on the question of how to model the probability of ®nancial asset price returns There is now a consensus that conventional models that assume normality need to be broadened to deal with such issues as tail probabilities, pricing derivatives and outliers, to name some more obvious cases The ®rst chapter, by Bingham and Kiesel, discusses the modelling of stock returns and interest rates using a family of stochastic processes called hyperbolic LeÂvy processes They demonstrate that such an approach can be estimated empirically and applied to option pricing problems Bond surveys and discusses the use of asymmetric density functions in ®nance and their usefulness in modelling conditional skewness Lizieri and Ward present a detailed investigation of UK commercial property returns Hwang and Satchell discuss how to build capital asset pricing models when the data is nonnormal and described by coecients of skewness and kurtosis They apply this methodology to emerging markets data Rogers, Satchell and Yoon present an analysis of returns when conditioned in various ways on volume By changing clocks from Newtonian time to volume time they ®nd that seemingly nonnormal data is, in e€ect, normal This work was completed some years ago but is being published in this volume as, recently, other scholars seem to be discovering this result afresh Jun Yu presents a chapter that addresses issues of hypothesis testing for asset returns In particular his test procedure allows one to discriminate between ®nite and in®nite variance distributions Jiang presents an analysis of option pricing when the underlying asset return process is both predictable and discontinuous This extends existing results in this literature and emphasizes how the properties of the underlying process can in¯uence the options price In a similar vein, Knight, Satchell and Wang investigate the impact of di€erent distributional assumptions on the future option prices and Value-at-Risk calculations Knight and Satchell discuss the pricing of options when the values of skewness and kurtosis of returns are †, then E‰q…t†Š ˆ 0; Var‰q…t†Š ˆ 2 =2 ‡ …t ÿ t0 †eÿ2 …tÿt0 †  As t0 ÿI, or t ÿ t0 ‡I, q…t† converges to the Ornstein±Uhlenbeck process with a Gaussian marginal density N…0; 2 =2 † Further di€erence from the constant drift jump-di€usion model with iid lognormal jump is that the Ornstein±Uhlenbeck process with an exponentially decaying jump no longer has independent increments even though its driving processes, the Brownian motion and compound Poisson, both Let r …t† ˆ Á p…t† ˆ p…t† ÿ p…t ÿ † ˆ  ‡ q…t† ÿ q…t ÿ †, we have E‰r Š ˆ ; Var‰r Š ˆ  …1 ÿ eÿ  † ‡ … ‡ …1 ÿ e  †2 …t ÿ  ÿ t0 ††eÿ2 …tÿt0 †  ; Implementing option pricing models 177  ÿ …ÿ† e …1 ÿ eÿ  †2 ‡… ‡ …1 ÿ e  †…t ÿ  ÿ  ÿ t0 † Cov‰r …t†; r …t ÿ †Š ˆ ÿ  ÿ …2tÿÿ2t0 † …1 ÿ e †e  for  !  Again as t0 ÿI, or t ÿ t0 ‡I, we have E‰r Š ˆ ; Var‰r Š  ... book with John Knight is Return Distributions in Finance He is a regular speaker at professional conferences series titles Return Distributions in Finance Downside Risk in Financial Markets: theory,... focus here on models including the hyperbolic distributions This family has been used to model Return Distributions in Finance ®nancial data by several authors, including Eberlein and Keller (1995)... Cataloguing in Publication Data Return distributions in ®nance Asset allocation Financial engineering Mathematics I Knight, John II Satchell, Stephen E 332.6'0151 ISBN 7506 4751 Printed and bound in