1;Foreword;6 2;Acknowledgements;7 3;Contents;8 4;Acronyms;10 5;Chapter 1 Introduction;12 6;Chapter 2 Fractional Integration Calculus;16 6.1;2.1 The Stochastic Process of Fractional Brownian Motion;18 6.2;2.2 Serial Correlation: The Role of the Hurst Parameter;24 6.3;2.3 The Wick-Based Approach to Fractional Integration;28 6.4;2.4 Pathwise and Stratonovich Integrals;33 6.5;2.5 Some Important Results of the Wick Type Fractional Integration Calculus;36 6.6;2.6 The S-Transform Approach;39 7;Chapter 3 Fractional Binomial Trees;43 7.1;3.1 Binomial Approximation of an Arithmetic Fractional Brownian Motion Process;44 7.2;3.2 Binomial Approximation of the Conditional Moments of Fractional Brownian Motion;50 7.3;3.3 Binomial Approximation of a Geometric Fractional Price Process;54 7.4;3.4 Arbitrage in the Fractional Binomial Market Setting and Its Exclusion;59 8;Chapter 4 Characteristics of the Fractional Brownian Market: Arbitrage and Its Exclusion;66 8.1;4.1 Arbitrage in the Unrestricted Continuous Time Setting;67 8.2;4.2 Diverse Approaches to Exclude Arbitrage;71 8.3;4.3 On the Non-compatibility of Fractional Brownian Motion and Continuous Tradability;78 8.4;4.4 Renouncement of Continuous Tradability, Exclusion of Arbitrage and Transition to Preference-Based Pricing;86 9;Chapter 5 Risk Preference-Based Option Pricing in a Continuous Time Fractional Brownian Market;88 9.1;5.1 Motivation and Setup of the Model;88 9.2;5.2 The Conditional Distribution of Fractional Brownian Motion 5.2.1 Prediction Based on an Infinite Knowledge About the Past;90 9.3;5.3 A Conditional Fractional It_o Theorem;98 9.4;5.4 Fractional European Option Prices;101 9.5;5.5 The Influence of the Hurst Parameter;108 9.6;5.6 The Influence of Maturity and the Term Structure of Volatility;115 10;Chapter 6 Risk Preference-Based Option Pricing in the Fractional Binomial Setting;120 10.1;6.1 The Two-Time Total Equilibrium Approach;122 10.2;6.2 The Two-Time Relative Equilibrium Approach;125 10.3;6.3 Multi-Time Equilibrium Approaches;130 10.4;6.4 Deeper Insights Provided by Discretization: The Continuous Time Case Reconsidered;137 11;Chapter 7 Conclusion;140 12;References;144