Pricing in (In)Complete Markets

In this book, the authors investigate structural aspects of no arbitrage pricing of contingent claims and applications of the general pricing theory in the context of incomplete markets. A quasi-closed form pricing equation in terms of artificial probabilities is derived for arbitrary payoff structures. Moreover, a comparison between continuous and discrete models is presented, highlighting the major similarities and key differences. As applications, two sources of market incompleteness are considered, namely stochastic volatility and stochastic liquidity. Firstly, the general theory discussed before is applied to the pricing of power options in a stochastic volatility model. Secondly, the issue of liquidity risk is considered by focusing on the aspect of how asset price dynamics are affected by the trading strategy of a large investor.

1 Motivation and Overview.- 2 Pricing by Change of Measure and Numeraire.- 2.1 Introduction.- 2.2 Model Setup.- 2.3 Equivalent Measures.- 2.4 Derivation of a General Pricing Equation.- 2.5 Is Every Equivalent Measure a Martingale Measure?.- 2.6 Conclusion.- 3 Comparison of Discrete and Continuous Models.- 3.1 Introduction.- 3.2 Dynamics of the Underlying Processes.- 3.3 Model-Specific Change of Measure.- 3.4 Normalized Price Processes.- 3.5 Examples.- 3.6 Conclusion.- 4 Valuation of Power Options.- 4.1 Introduction.- 4.2 General Pricing Equation.- 4.3 Examples.- 4.4 Conclusion.- 5 Modeling Feedback Effects Using Stochastic Liquidity.- 5.1 Introduction.- 5.2 The Liquidity Framework.- 5.3 Examples.- 5.4 Conclusion.- 6 Summary and Outlook.- A Power Options in Stochastic Volatility Models.- A.1 Calculations of the Characteristic Functions.- A.2 Ornstein-Uhlenbeck Process for Volatility.- References.- Abbreviations.- List of Symbols.- List of Figures.- List of Tables.