Pricing in (In)Complete Markets: Structural Analysis and Applications

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Springer Science & Business Media, Jan 23, 2004 - Business & Economics - 122 pages
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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.

 

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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
Index
121
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Page 107 - Pham, H., Touzi, N., 1996. Equilibrium state prices in a stochastic volatility model. Mathematical Rilstone, P., 1996.

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