Springer Finance. Springer-Verlag Berlin Heidelberg GmbH

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1 Springer Finance Springer-Verlag Berlin Heidelberg GmbH

2 Springer Finance Springer Finance is a new programme ofbooks aimed at students, academics and practitioners working on increasingly technical approaches to the analysis of financial markets. It aims to cover a variety of topics, not only mathematical finance but foreign exchanges, term structure, risk management, portfolio theory, equity derivatives, and financial economics. Credit Risk Valuation: Risk-Neutral Valuation: Pricing and Hedging of Finance Derivatives Bingham, N. H. and Kiesel, R. ISBN (1998) Visual Explorations in Finance with Self-Organizing Maps Deboeck, G. and Kohonen, T. (Editors) ISBN (1998) Mathematical Models of Financial Derivatives Kwok, Y.-K. ISBN (1998) Mathematics of Financial Markets Elliott, R. ]. and Kopp, P. E. ISBN (1999) Efficient Methods for Valuing Interest Rate Derivatives Pelsser, A. ISBN (2000) Methods, Models and Applications Ammann,M. ISBN (2001) Credit Risk: Modelling, Valuation and Hedging Bielecki, T. R. and Rutkowski, M. ISBN (2001) Mathematical Finance - Bachelier Congress Selected Papers from the First World Congress of the Bachelier Finance Society, held in Paris, June 29-July 1,2000 Geman, H., Madan, D. S., PIiska R. and Vorst, T. (Editors) ISBN X (2001) Financial Markets Theory: Equilibrium, Efficiency and Information Barucci, E. ISBN X (2003) Financial Markets in Continuous Time Dana, R.-A. and ]eanblanc, M. ISBN (2003) Weak, Convergence of Financial Markets Prigent, ].-L. ISBN (2003) Incomplete Information and Heterogenous Beliefs in Continuous-time Finance Ziegler, A. ISBN (2003) Stochastic Calculus Models for Finance: Volume 1: The Binominal Assett Pricing Model Shreve, S. E. ISBN (2004) Irrational Exuberance Reconsidered: The Cross Section of Stock Returns Külpmann, M. ISBN (2004) Credit Risk Pricing Models: Theory and Practice Schmid, B. ISBN X (2004) AGame Theory Analysis of Options Ziegler, A. ISBN X (2004) Asset Pricing: Modeling and Estimation Kellerhals, B. P. ISBN (2004) Exponential Functionals of Brownian Motion and Related Processes Yor,M. ISBN (2001)

3 B. Philipp Kellerhals Asset Pricing Modeling and Estimation Second Edition with 10 Figures and 30 Tables Springer

4 Dr. B. Philipp Kellerhals dit I Allianz Dresdner Asset Management Mainzer Landstrasse Frankfurt am Main Germany Mathematics Subject Classification (2000): 91B28 Originally published as volume 506 in the series "Lecture Notes in Economics and Mathematical Systems" ISBN ISBN (ebook) DOI / Bibliographic information published by Die Deutsche Bibliothek Die Deutsche Bibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographie data available in the internet at http.!ldnb_ddb_de 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 permiued only under the provisions of the German Copyright Law of September in its current version. and permission for use must always be obtained from Springer-Verlag. Violations are liable for prosecution under the German Copyright Law. Springer-Verlag Berlin Heidelberg 2004 Originally published by Springer-Verlag Berlin Heidelberg New York in 2004 Softcover reprint of the hardcover 2nd edition 2004 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: design & production. Heidelberg

5 To Gerhard and Susanne.

6 Preface The modern field of asset pricing asks for sound pricing models grounded on the theory of financial economies a la Ingersoll (1987) as weil as for accurate estimation techniques a la Hamilton (1994b) when it comes to empirical inferences of the specified model. The idea behind this book on hand is to provide the reader with a canonical framework that shows how to bridge the gap between the continuous-time pricing practice in financial engineering and the capital market data inevitably only available at discrete time intervals. Three major financial markets are to be examined for which we select the equity market, the bond market, and the electricity market. In each market we derive new valuation models to price selected financial instruments in continuous-time. The decision criterium for choosing a continuous-time modeling framework is the richness of the stochastic theory available for continuoustime processes with Merton's pioneering contributions to financial economics, collected in Merton (1992). The continuous-time framework, reviewed and assessed by Sundaresan (2000), allows us to obtain analytical pricing formulae that would be unavailable in a discrete time setting. However, at the time of implementing the derived theoretical pricing models on market data, that is necessarily sampled at discrete time intervals, we work with so-called exact discrete time equivalents a la Bergstrom (1984). We show how to conveniently work within astate space framework which we derive in a general setting as weil as explicitly for each of the three applications. Thereupon we perform empirical maximum likelihood inferences implementing linear and extended specifications of Kaiman filter algorithms. The Kalman filter framework was originally developed by KaIman (1960) and KaIman and Bucy (1961) for applications in aerospace engineering (part of the astronautical guidance system of the Apollo project) and has successfully been used in electrical engineering. Only in the last decade, marked by Harvey (1989), Kalman filters have found ground as econometric tool for economic and financial estimation problems.

7 VIII Preface The technique of Kalman filtering generally leads to more efficient parameter estimates since it imposes greater theoretical modeling restrictions on the data than other commonly used methods. Given a hypothesized financial pricing model, the estimation procedure of Kalman filtering imposes cross-sectional as weil as time-series restrictions, making it a true maximum likelihood method. We use different types of Kalman filter algorithms, which we introduce in chapter 2 of this book, to empirically estimate current pricing problems in the field of financial economics. The selected pricing issues within the chosen financial markets are presented in the three distinct parts II, III, and IV of this book: In part II we investigate the pricing of equities. Within this asset class we specialize in the valuation of closed-end funds which share distinct financial characteristics of common joint-stock companies and mutual fund investment companies. In building our stochastic pricing model we especially draw our attention on the market anomaly that the market value of closed-end funds determined on organized exchanges differs dynamically over time from the reported value on their underlying investment port folios by a discount or a premium. In light of this anomaly we develop a two-factor valuation model of closed-end funds that takes into account both the price risk of the funds as weil as the risk associated with altering discounts. Based on astate space formulation of the pricing model we estimate the relevant model parameters using a Kalman filter framework. Having validated our pricing model on a sampie of emerging market closed-end funds traded on the New York Stock Exchange, we further assess the quality of the developed model for investor applications. There, we test the forecasting power of the valuation model to predict closed-end fund market prices and implement portfolio strategies using trading rules. The results of these applications indicate that the pricing model generates valuable investment information. For pricing Jixed-income securities we present a new dynamic term structure model in part III which belongs to the affine term structure models. Motivated by the incomplete market situation of fixed-income instruments we propose a pricing model that shifts from modeling static tastes to beliefs of the dynamic behavior of tastes. Besides a stochastic short interest rate the proposed two-factor term structure model allows for a stochastic behavior of the market price of interest rate risk. Given the theoretical term structure model we derive a closed-form expression for valuing discount bonds and examine the implied term structures of interest rates and volatilities as initial characteristic results. We further show how to apply the term structure model in a consistent framework to manage interest rate risk and price interest rate

8 Preface IX derivative securities. There we start with the concept of immunization using factor duration and price bond options, swap contracts, and interest rate caps and floors as the most relevant derivative contracts in risk management. Using US market data on Treasury Securities, LIBOR rates, and swap rates we implement the theoretical pricing model based on a corresponding state space form. Linear and extended Kalman filter routines give us the possibility of estimating the model as well as extracting the time-series of the underlying state variables. In part IV we present a continuous-time pricing model for the valuation of electricity derivatives. From investigating more mature commodity markets than the electricity market, we gather information on the price behavior of commodities and pricing models for commodity futures. For electricity prices we especially examine the most relevant idiosyncratic price patterns which are considered to be their seasonality, mean-reversion, and extreme volatility. From properly chosen model assumptions, especially capturing the unique characteristic of non-storability of electricity and the marked volatility in electricity prices being both high and variable over time, we build an appropriate valuation model to price electricity forwards. The proposed stochastic volatility pricing model yields a closed-form solution to electricity forwards using risk neutral pricing techniques. Next, we empirically adapt the theoretical pricing model in state space form dealing with state variables that follow a non-gaussian distribution; thereupon we implement an extended Kalman filter algorithm to estimate the model by means of maximum likelihood. Finally, we report empirical results of the pricing model based on electricity data from the largely deregulated Californian power market. Each of these three application parts can be read independently and contains an introductory survey chapter which motivates the presented research and clears its context in the respective literature. Furthermore, each part concludes with a summary chapter where we finally present our findings. The asset pricing framework common to all three modeling and estimation applications is comprehensively described in part I of this book. Although this preface is modified somewhat from that of the first edition, some additional remarks will clarify how the second edition differs from the first, Kellerhals (2001). Chapters 3, 4, and 5 from the first edition are merged into one chapter, Estimation Principles. The references have been thoroughly updated, and nontrivial changes and improvements have been made throughout the chapters. Recent research contributions in the three covered fields of equities with closed-end funds, fixed-income products, and electricity derivatives are integrated in the text. The newly incorporated chap-

9 x Preface ter Financial Modeling especially provides a comprehensive treatment of the arbitrage pricing theory in continuous-time as formidable dynamic asset pricing background for the applications presented in parts II, III, and IV of this book. Finally, I am grateful to have had the chance to extensively work in the field of dynamic asset pricing theory as weil as on aspects of econometric modeling, empirical estimation and calibration of applied financial models as a researcher and lecturer in the Department of Finance at the Eberhard-Karls University Tübingen, Germany, in particular with my academic supervisor Rainer Schöbel. The undergone research presented in the second edition in continuation of the first edition extensively profited from seminars, lectures, suggestions, and discussions from and with Yacine Ait-Sahaliah, Günter Bamberg, Michael Brennan, Wolfgang Bühler, Tarun Chordia, Roland Demmel, Gordon Gemmill, Stephan Heilig, Herbert Heyer, Olaf Kom, Roman Liesenfeld, Hartmut Nagel, Wemer Neus, Ariane Reiss, Gerd Ronning, Christian Schlag, Manfred Stadler, Marliese Uhrig-Homburg, Nick Webber, and Jianwei Zhu. I rededicate this book to my parents. Frankfurt am Main, J anuary 2004 B. Philipp Kellerhals

10 Contents Part lasset Pricing Framework 1 Financial Modeling Continuous-Time Stochastics Stochastic Processes and Brownian Motion Martingales, Itö Calculus, and Changes of Measure Arbitrage Pricing in Continuous Time PDE Approach...,..., EMM Approach..., 15 2 Estimation Principles State Space Notation Filtering Algorithms Filtering Objective..., Optimal Estimator Filter Recursions..., Extended KaIman Filtering Parameter Estimation Part 11 Pricing Equities 3 Introduction and Survey..., Opening Remarks..., Closed-End Funds: Survey and Hypotheses Valuation Model..., Characteristics of Closed-End Funds Economic Foundation..., 53

11 XII Contents 4.3 Pricing Closed-End Fund Shares... " 56 5 First Empirical Results Sarnple Data Implemented ModeL State Space Form Closed-End Fund Analysis Implications for Investment Strategies Testing the Forecasting Power Setup of Forecasting Study Evidence on Forecasting Quality Implementing Trading Rules Experimental Design..., Test Results on Trading Strategies Summary and Conclusions Part III Pricing Fixed-Income Securites 8 Introduction and Survey Overview Bond Prices and Interest Rates Dynamic Term Structure Models rerm Structure ~odel... '" Modeling an Incomplete Market Motivation for a Stochastic Risk Premium... " Economic Model Initial Characteristic Results Valuing Discount Bonds Term Structures of Interest Rates and Volatilities Spot and Forward Rate Curves Term Structure of Volatilities Analysis of Limiting Cases Reducing to an Ornstein-Uhlenbeck Process Examining the Asymptotic Behavior Possible Shapes of the Term Structures

12 Contents XIII Influences of the State Variables Choosing the Model Parameters Risk Management and Derivatives Pricing Management ofinterest Rate Risk Pricing Interest Rate Derivatives Bond Options... " Swap Contracts Interest Rate Caps and Floors Calibration to Standard Instruments Estimation Techniques for Term Structure Models Discrete Time Distribution of the State Variables US Treasury Securities Data Analysis Parameter Estimation Analysis of the State Variables Other Liquid Markets Appropriate Filtering Algorithm Sampie Data and Estimation Results Summary and Conclusions Part IV Pricing Electricity Forwards 14 Introduction and Survey Overview Commodity Futures Markets Pricing Commodity Futures Asset Pricing in Electricity Markets Electricity Pricing Model Model Assumptions and Risk-Neutral Pricing Valuation of Electricity Forwards Empirical Inference Estimation Model Distribution of the State Variables State Space Formulation and KaIman Filter Setup

13 XIV Contents 16.2 Data Analysis and Estimation Results Summary and Conclusions List of Symbols and Notation List of Tables List of Figures References Index