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Sommaire :

I Preliminary Material

1 From Diffusions to Semimartingales
1.1 Diffusions
1.2 Lévy Processes
1.3 Semimartingales
1.4 Ito Semimartingales
1.5 Processes with Conditionally Independent Increments

2 Data Considerations
2.1 Mechanisms for Price Determination
2.2 High-Frequency Data Distinctive Characteristics
2.3 Models for Market Microstructure Noise
2.4 Strategies to Mitigate the Impact of Noise

II Asymptotic concepts

3 Introduction to Asymptotic Theory: Volatility Estimation for a Continuous Process
3.1 Estimating Integrated Volatility in Simple Cases
3.2 Stable Convergence in Law
3.3 Convergence for Stochastic Processes
3.4 General Stochastic Volatility
3.5 What If the Process Jumps?

4 With Jumps: An Introduction to Power Variations
Power Variations
4.2 Estimation in a Simple Parametric Example: Merton's Model
4.3 References

5 High-Frequency Observations: Identifiability and Asymptotic Efficiency
5.1 Classical Parametric Models
5.2 Identifiability for L évy Processes and the Blumenthal-Getoor Indices
5.3 Discretely Observed Semimartingales: Identifiable Parameters
5.4 Tests: Asymptotic Properties
5.5 Back to the L évy Case: Disentangling the Diffusion Part from Jumps
5.6 Blumenthal-Getoor Indices for L évy Processes: Efficiency via Fisher's Information
5.7 References

III Volatility

6 Estimating Integrated Volatility: The Base Case with
No Noise and Equidistant Observations
6.1 When the Process Is Continuous
6.2 When the Process Is Discontinuous
6.3 Other Methods
6.4 Finite Sample Refinements for Volatility Estimators
6.5 References

7 Volatility and Microstructure Noise
7.1 Models of Microstructure Noise
7.2 Assumptions on the Noise
7.3 Maximum-Likelihood and Quasi Maximum-Likelihood Estimation
7.4 Quadratic Estimators
7 .5 Subsampling and Averaging: Two-Scales Realized Volatility
7.6 The Pre-averaging Method
7.7 Flat Top Realized Kernels
7.8 Multi-scales Estimators
7.9 Estimation of the Quadratic Covariation
7.10 References

8 Estimating Spot Volatility
8.1 Local Estimation of the Spot Volatility
8.2 Global Methods for the Spot Volatility
8.3 Volatility of Volatility
8.4 Leverage: The Covariation between X and c
8.5 Optimal Estimation of a Function of Volatility
8.6 State-Dependent Volatility
8.7 Spot Volatility and Microstructure Noise
8.8 References

9 Volatility and Irregularly Spaced Observations
9.1 Irregular Observation Times: The One-Dimensional Case
9.2 The Multivariate Case: Non-synchronous Observations
9.3 References

IV Jumps
10 Testing for Jumps
10.1 Introduction
10.2 Relative Sizes of the Jump and Continuous Parts and Testing for Jumps
10.3 A Symmetrical Test for Jumps
10.4 Detection of
10.5 Detection of Volatility Jumps
10.6 Microstructure Noise and Jumps
10.7 References

11 Finer Analysis of Jumps: The Degree of Jump Activity
11.3 Successive BG
11.4 References
12 Finite or Infinite Activity for Jumps?
12.1 When the Null Hypothesis Is Finite Jump Activity
12.2 When the Null Hypothesis Is Infinite Jump Activity
12.3 References
13 Is Brownian Motion Really Necessary?
13.1 Tests for the Null Hypothesis That the Brownian Is
Present
13.2 Tests for the Null Hypothesis That the Brownian Is Absent
13.3 References
14 Co-jumps
14.1 Co-jumps for the Underlying Process
14.2 Co-jumps between the Process and Its
14.3 References

A Asymptotic Results for Power Variations
B Miscellaneous Proofs

Bibliography

Langue : Anglais

Localisation : Bibliothèque Campus de Nice

Support : Numérique

Etat : Présent

Propriétaire : Bibliothèque