## Pricing in (In)Complete Markets: Structural Analysis and ApplicationsIn 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. |

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### Contents

Motivation and Overview | 1 |

Pricing by Change of Measure and Numeraire | 9 |

22 Model Setup | 10 |

23 Equivalent Measures | 11 |

232 Martingale Measures | 12 |

233 Change of Numeraire | 14 |

24 Derivation of a General Pricing Equation | 16 |

25 Is Every Equivalent Measure a Martingale Measure? | 19 |

422 Powered Option | 59 |

423 Capped Power Option | 60 |

43 Examples | 61 |

4312 Numeraire Portfolio | 63 |

432 Stochastic Volatility Models | 64 |

4322 QuasiClosed Form Pricing Equation | 65 |

44 Conclusion | 67 |

Modeling Feedback Effects Using Stochastic Liquidity | 69 |

252 Incomplete Market | 20 |

253 Review of the Pricing Equation | 21 |

Comparison of Discrete and Continuous Models | 23 |

32 Dynamics of the Underlying Processes | 24 |

322 Discrete Model | 25 |

33 ModelSpecific Change of Measure | 26 |

331 Diffusion Model | 27 |

332 Discrete Model | 28 |

34 Normalized Price Processes | 32 |

341 Discounted Price Processes and RiskNeutral Measure | 33 |

3412 Discrete Model | 35 |

342 Price Processes Normalized by a Risky Basis Asset | 37 |

3422 Discrete Model | 40 |

343 Price Processes Normalized by a Portfolio | 43 |

3432 Discrete Model | 46 |

35 Examples | 47 |

351 Complete Market with Two Basis Assets in the Discrete Setup | 48 |

352 Binomial Tree | 49 |

353 Two Correlated Assets | 51 |

354 Stochastic Volatility Setup | 53 |

36 Conclusion | 54 |

Valuation of Power Options | 55 |

42 General Pricing Equation | 56 |

52 The Liquidity Framework | 70 |

522 Stochastic Liquidity | 72 |

5222 Stock Price Dynamics with Feedback Effects | 74 |

5223 RiskNeutral Dynamics | 80 |

53 Examples | 81 |

531 Numerical Analysis of the Effective Stock Price Dynamics for Two Trading Strategies | 82 |

5312 Parameter Specifications for the Sample Paths | 84 |

5313 Positive Feedback Strategy | 85 |

5314 Contrarian Feedback Strategy | 86 |

532 Liquidity Insurance | 87 |

5321 Specification and Pricing of the Contract | 88 |

5322 Alternative Scenario | 91 |

54 Conclusion | 92 |

Summary and Outlook | 95 |

Power Options in Stochastic Volatility Models | 97 |

A2 OrnsteinUhlenbeck Process for Volatility | 100 |

References | 105 |

Abbreviations | 109 |

List of Symbols | 111 |

List of Figures | 117 |

List of Tables | 119 |

121 | |

### Other editions - View all

Pricing in (In)Complete Markets: Structural Analysis and Applications Angelika Esser Limited preview - 2004 |

Pricing in (In)Complete Markets: Structural Analysis and Applications Angelika Esser Limited preview - 2012 |

Pricing in (In)Complete Markets: Structural Analysis and Applications Angelika Esser No preview available - 2011 |