Studies in Computational Intelligence

Transcription

1 Studies in Computational Intelligence Volume 697 Series editor Janusz Kacprzyk, Polish Academy of Sciences, Warsaw, Poland

2 About this Series The series Studies in Computational Intelligence (SCI) publishes new developments and advances in the various areas of computational intelligence quickly and with a high quality. The intent is to cover the theory, applications, and design methods of computational intelligence, as embedded in the fields of engineering, computer science, physics and life sciences, as well as the methodologies behind them. The series contains monographs, lecture notes and edited volumes in computational intelligence spanning the areas of neural networks, connectionist systems, genetic algorithms, evolutionary computation, artificial intelligence, cellular automata, self-organizing systems, soft computing, fuzzy systems, and hybrid intelligent systems. Of particular value to both the contributors and the readership are the short publication timeframe and the worldwide distribution, which enable both wide and rapid dissemination of research output. More information about this series at

3 Fahed Mostafa Tharam Dillon Elizabeth Chang Computational Intelligence Applications to Option Pricing, Volatility Forecasting and Value at Risk 123

4 Fahed Mostafa Department of Computer Science and Computer Engineering La Trobe University Bundoora, VIC Australia Elizabeth Chang School of Business University of New South Wales Canberra, ACT Australia Tharam Dillon Department of Computer Science and Computer Engineering La Trobe University Bundoora, VIC Australia ISSN X ISSN (electronic) Studies in Computational Intelligence ISBN ISBN (ebook) DOI / Library of Congress Control Number: Springer International Publishing AG 2017 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, 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. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer International Publishing AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

5 Preface Increasingly there are many sources of uncertainty in markets. These sources of uncertainty can have adverse effects on the evaluation of portfolio risk exposure. This uncertainty in the market variables is known as market risk which characterises the potential loss of value of an asset due to movements in market factors. Quantitative techniques to analyse individual financial instruments and a portfolio of assets are essential for measuring market risk. Quantitative models seek to capture the trends and behaviours in the data which are then used to deduce future values. In this book, market risk is grouped into four main categories: volatility forecasting, option pricing, hedging and portfolio risk management. When developing these quantitative methods in this book, the focus has been twofold: first, to build on the existing methodologies such as the GARCH and Black Scholes models and second to develop approaches to overcome some of the disadvantages inherent in some of the models arising from some of the underlying assumptions which have been found to not properly reflect the behaviours inherent in the markets. For instance, a computation intelligence approach and more particularly a neural network is used to learn from data the Black Scholes implied volatility. The implied volatility forecasts, generated from the neural net, are converted to option price using the Black Scholes formula. The neural network option-pricing capabilities are shown to be superior to the Black Scholes and the GARCH option-pricing model. The neural network has also shown that it is able to reproduce the implied volatility well into the future whereas the GARCH option-pricing model shows deterioration in the implied volatility with time. A new method for delta hedging using this approach is also presented. The book has been structured to provide a systematic study of the issues involved in market risk and its organisation reflects that. Chapter 1 provides a broad introduction to some of the important concepts involved in market risk. Time series models are reviewed in Chap. 2. All financial time series models and concepts considered in this book are reviewed and explained. The weakness of each of the modelling techniques is highlighted and explained with reference to research. v

6 vi Preface Chapter 3 introduces options, existing option-pricing models and hedging. Chapter 4 provides a review of neural networks. Then a comprehensive review is provided on the neural networks research in forecasting volatility, option pricing, hedging and value-at-risk. In this review, the strength(s) and weakness(es) of each approach are explained. Chapter 5 outlines important problems in financial forecasting including volatility forecasting, options pricing and hedging. It provides a definition of important terms necessary to the considerations in the chapters that follow. Volatility forecasting models are considered and evaluated in Chap. 6 including the GARCH, EGARCH and mixture density models. This is followed by the explanation of the method adopted in this book including results, discussion and evaluation. Chapter 7 considers option-pricing models including GARCH Option-Pricing Model (GOPM), BSOPM model, implied volatility and existing neural net models. The method utilised in this book is explained, and results, discussions and evaluation are given. Value-at-risk is considered in Chap. 8 including definitions and models. Chapter 9 provides a recapitulation and conclusions. The book can be used by advanced undergraduate students and graduate students in its entirety. It is also of considerable importance to practitioners in the field. We hope that you have an enjoyable and profitable time from studying the book. Every reasonable effort has been made to acknowledge the owners of copyright material. I would be pleased to hear from any copyright owner who has been omitted or incorrectly acknowledged. Bundoora, Australia Bundoora, Australia Canberra, Australia Fahed Mostafa Tharam Dillon Elizabeth Chang

7 Contents 1 Introduction Volatility Forecasting Option Pricing Risk Management Methods Neural Networks Approach Book Layout Time Series Modelling Time Series Properties White Noise Stochastic Processes Stationarity in Time Series Autoregressive Models Time Series Models The Wiener Process Geometric Brownian Motion with Drift Itô Process Linear Time Series Models Moving Average Model Auto Regressive Moving Model (ARMA) Financial Time Series Modelling Distributional Properties of the Return Series Stylised Properties of Returns Conditional Mean Volatility Modelling Conditional Heteroscedasticity Models ARCH Model GARCH Model vii

8 viii Contents GARCH-in-Mean Exponential GARCH Time Varying Volatility Models Literature Review Options and Options Pricing Models Options Call Options Put Options Options Moneyness Intrinsic Value Time Value Option Pricing Models and Hedging The Black-Scholes Options Pricing Model Black-Schole Equation Implied Volatility Black-Scholes Option Pricing Model (BSOPM) GARCH Option Pricing Models Hedging Delta Hedging Neural Networks and Financial Forecasting Neural Net Models Preceptron Multi-layer Preceptron (MLP) Training MLP Back Propagation Mixture Density Networks Radial Base Function Network Neural Networks in Financial Forecasting Neural Networks for Time Series Forecasting Neural Networks in Conditional Volatility Forecasting Volatility Forecasting with MDN Application of Neural Networks Option Pricing Important Problems in Financial Forecasting Terms and Concepts Used Financial Time Series Options Problem Definition Volatility Forecasting Option Pricing Delta Hedging Choice of Methodology Research Method... 90

9 Contents ix 6 Volatility Forecasting Volatility Models GARCH Model EGARCH Model Mixture Density Networks Issues Investigated Solution Overview Forecast Evaluation Data Analysis Experimentation Results In-Sample Testing Out-of-Sample Forecast Performance One-Day Volatility Forecast and 30 Days Forecast Conclusion Option Pricing Option Pricing Models GARCH Option Pricing Model (GOPM) BSOPM Option Pricing Model Implied Volatility Artificial Neural Network (ANN) Neural Networks for Option Pricing My Option Pricing Model Issues Investigated New Option Pricing Model and Solution Overview Data Experimental Design GOPM Parameters Neural Network Training Methods Performance Measures Pricing Accuracy Delta Hedging Solution Overview New Method Developed Results The Empirical Dynamics of the Volatility Smile Summary and Conclusion Value-at-Risk Value-at-Risk Review Value-at-Risk Definition

10 x Contents 8.3 Modelling Value at Risk with Neural Networks Historical Simulation Method Variance-Covariance Method Monte Carlo Simulation Method Modelling Value-at-Risk with Neural Networks Value-at-Risk (VaR) Future Work Conclusion and Discussion Volatility Forecasting Option Pricing and Hedging Recapitulation Contributions of This Research Appendix A: Detailed Results References