This book surveys and summarizes the numerous approaches used to extract information on market expectations from option prices. The various approaches are thoroughly explained and many practical issues are discussed, including: data selection, data preparation, and presentation and interpretation of results. This enables the reader to easily implement these techniques in his own applied work. Most studies concerning uncertainty in financial markets focus on actual uncertainty as represented by historical volatility measures, variances etc. In contrast, using option prices allows us to study uncertainty in expectations, i.e. to take a forward looking perspective. In some applications we study how ECB-council meetings affect uncertainty in money market expectations. Most interesting among our results is a number of event studies which compare how uncertainty in market participants' expectations reacts to anticipated and unanticipated results of ECB-council meetings.

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This book is a slightly revised version of my doctoral dissertation which has been accepted by the Department of Economics and Business Administration of the Justus-Liebig-Universitat Giessen in July 2002. I am indebted to my advisor Prof. Dr. Volbert Alexander for encouraging and supporting my research. I am also grateful to the second member of the doctoral committee, Prof. Dr. Horst Rinne. Special thanks go to Dr. Ralf Ahrens for providing part of the data and to my colleague Carsten Lang, who spent much time reading the complete first draft. Wetzlar, January 2003 Martin Mandler Contents 1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Part I Theoretical Foundations 2 Arbitrage Pricing and Risk-Neutral Probabilities........ .. 7 2.1 Arbitrage Pricing in the Black/Scholes-Merton Model... . . .. . 7 2.2 The Equivalent Martingale Measure and Risk-Neutral Valuation ............................................... 11 2.3 Extracting Risk-Neutral Probabilities from Option Prices. . . .. 13 2.4 Summary............................................... 15 Appendix 2A: The Valuation Function in the Black/Scholes-Merton Model .................................................. 16 Appendix 2B: Some Further Details on the Replication Strategy ... 21 3 Survey of the Related Literature .......................... 23 3.1 The Information Content of Forward and Futures Prices. . . .. . 24 3.2 The Information Content of Implied Volatilities ............. 25 3.2.1 Implied Volatilities and the Risk-Neutral Probability Density .......................................... 27 3.2.2 The Term Structure of Implied Volatilities. . . . . . . .. . . 29 . 3.2.3 The Forecasting Information in Implied Volatilities. . .. 30 3.2.4 Implied Correlations as Forecasts of Future Correlations 43 VIII Contents 3.3 The Skewness Premium ..... . . . . . . . . . . . . . . . . . . .. . . 45 . . . . . . .

Inhalt

1 Introduction.- I Theoretical Foundations.- 2 Arbitrage Pricing and Risk-Neutral Probabilities.- 2.1 Arbitrage Pricing in the Black/Scholes-Merton Model.- 2.2 The Equivalent Martingale Measure and Risk-Neutral Valuation.- 2.3 Extracting Risk-Neutral Probabilities from Option Prices.- 2.4 Summary.- Appendix 2A: The Valuation Function in the Black/Scholes-Merton Model.- Appendix 2B: Some Further Details on the Replication Strategy.- 3 Survey of the Related Literature.- 3.1 The Information Content of Forward and Futures Prices.- 3.2 The Information Content of Implied Volatilities.- 3.2.1 Implied Volatilities and the Risk-Neutral Probability Density.- 3.2.2 The Term Structure of Implied Volatilities.- 3.2.3 The Forecasting Information in Implied Volatilities.- 3.2.4 Implied Correlations as Forecasts of Future Correlations.- 3.3 The Skewness Premium.- 3.4 Summary.- 4 Presenting and Interpreting Risk-Neutral Probabilities.- 4.1 Interpretation Problems Concerning Risk-Neutral Probabilities.- 4.2 Graphical Presentations of the Risk-Neutral Probability Density.- 4.3 Distributional Statistics and Percentiles.- 4.4 Summary.- 5 Techniques for Extracting Risk-Neutral Probabilities from Option Prices.- 5.1 The Direct Approach.- 5.2 Fitting Density Functions to Option Prices.- 5.2.1 Estimating Parametric Density Functions.- 5.2.2 Expansion Methods.- 5.2.3 Minimization of Deviations from a Prior Density.- 5.2.4 The Maximum-Smoothness Criterion.- 5.3 Estimating Option-Pricing Functions.- 5.3.1 Fitting Polynomials to the Volatility Smile.- 5.3.2 A Nonparametric Technique.- 5.3.3 The Maximum-Smoothness Criterion for the Volatility Smile.- 5.3.4 Further Extensions.- 5.4 Process-Based Techniques.- 5.4.1 Implied-Volatility Trees.- 5.4.2 Estimation of Stochastic Process Parameters.- 5.5 Data Selection and Preparation.- 5.6 Summary.- Appendix 5A: Restrictions to Ensure a Positive Density in the Gram-Charlier Expansion.- Appendix 5B: Deriving (5.120) and (5.123).- 6 The Advantages and Disadvantages of Selected Techniques.- 6.1 Implementation.- 6.2 Comparing the Results.- 6.3 Robustness.- 6.4 Summary.- II Empirical Applications.- 7 Important Empirical Applications - A Review.- 7.1 Exchange Rates.- 7.2 Interest Rates.- 7.3 Stock Indices.- 7.4 Risk Aversion.- 7.5 Summary.- 8 Central-Bank Council Meetings and Money Market Uncertainty.- 8.1 Estimation Method.- 8.2 Data.- 8.3 Results.- 8.4 Summary.- 9 Central-Bank Council Meetings - Event Studies.- 9.1 Methodology and Data.- 9.2 Results.- 9.3 Summary.- 10 Summary and Conclusions.- List of Figures.- List of Tables.