Separating Information Maximum Likelihood Method for High-Frequency Financial Data
by Naoto Kunitomo (Author), Seisho Sato (Author), Daisuke Kurisu (Author)

About the Author
Naoto Kunitomo, Meiji University
Seisho Sato, The University of Tokyo
Daisuke Kurisu, Tokyo Institute of Technology

About this book
This book presents a systematic explanation of the SIML (Separating Information Maximum Likelihood) method, a new approach to financial econometrics.
Considerable interest has been given to the estimation problem of integrated volatility and covariance by using high-frequency financial data. Although several new statistical estimation procedures have been proposed, each method has some desirable properties along with some shortcomings that call for improvement. For estimating integrated volatility, covariance, and the related statistics by using high-frequency financial data, the SIML method has been developed by Kunitomo and Sato to deal with possible micro-market noises.
The authors show that the SIML estimator has reasonable finite sample properties as well as asymptotic properties in the standard cases. It is also shown that the SIML estimator has robust properties in the sense that it is consistent and asymptotically normal in the stable convergence sense when there are micro-market noises, micro-market (non-linear) adjustments, and round-off errors with the underlying (continuous time) stochastic process. Simulation results are reported in a systematic way as are some applications of the SIML method to the Nikkei-225 index, derived from the major stock index in Japan and the Japanese financial sector.

Table of contents
1 Introduction
    References
2 Continuous-Time Models and Discrete Observations for Financial Data
    2.1 Developments in Quantitative Finance
    2.2 On Financial Derivatives and the Black–Scholes formula
    2.3 Diffusion, Realized Volatility, and Micro-Market Noise
    References
3 The SIML Estimation of Volatility and Covariance with Micro-market Noise
    3.1 Statistical Models in Continuous-Time and Discrete-Time
    3.2 Basic Case
    3.3 Asymptotic Properties of the SIML Estimator in the Basic Case
    3.4 An Optimal Choice of mn
    3.5 Asymptotic Properties of the SIML Estimator When Instantaneous Volatility is Time Varying
    3.6 Discussion
    References
4 An Application to Nikkei-225 Futures and Some Simulation
    4.1 Introduction
    4.2 Basic Simulation Results
    4.3 Realized Hedging
    References
5 Mathematical Derivations
    5.1 Some Lemmas
    5.2 Proofs of Theorems
    References
6 Extensions and Robust Estimation (1)
    6.1 Introduction
    6.2 A General Formulation
    6.3 The Basic Round-Off Error Model
    6.4 A Micro-market Price Adjustment Model
    6.5 Round-Off Errors and Nonlinear Price Adjustment Models
    6.6 Asymptotic Robustness of SIML for the Round-Off Error and Price Adjustment Models
    6.7 Simulations
    6.8 Derivation of Theorems
    References
7 Extensions and Robust Estimation (2)
    7.1 Introduction
    7.2 A Two-Dimensional Model
    7.3 Asymptotic Properties of SIML Estimation
    7.4 Further Simulations
    7.5 On Mathematical Derivations
    References
8 Local SIML Estimation of Brownian Functionals
    8.1 Introduction
    8.2 Estimation of Brownian Functionals
    8.3 Local SIML Estimation
    8.4 Simulation
    References
9 Estimating Quadratic Variation Under Jumps and Micro-market Noise
    9.1 Introduction
    9.2 SIML Estimation of Quadratic Covariation
    9.3 An Outline of the Derivation of Proposition 9.1
    9.4 Some Numerical Analysis
    References
10 Concluding Remarks
    References

Series: SpringerBriefs in Statistics
Length: 114 pages
Publisher: Springer; 1st ed. 2018 edition (June 15, 2018)
Language: English
ISBN-10: 4431559280
ISBN-13: 978-4431559283