Optimal statistical inference in financial engineering



Optimal statistical inference in financial engineering

Masanobu Taniguchi, Junichi Hirukawa, Kenichiro Tamaki

Chapman & Hall/CRC, c2008

  • : hardcover

大学図書館所蔵 件 / 10



Includes bibliographical references (p. 355-362) and index



Until now, few systematic studies of optimal statistical inference for stochastic processes had existed in the financial engineering literature, even though this idea is fundamental to the field. Balancing statistical theory with data analysis, Optimal Statistical Inference in Financial Engineering examines how stochastic models can effectively describe actual financial data and illustrates how to properly estimate the proposed models. After explaining the elements of probability and statistical inference for independent observations, the book discusses the testing hypothesis and discriminant analysis for independent observations. It then explores stochastic processes, many famous time series models, their asymptotically optimal inference, and the problem of prediction, followed by a chapter on statistical financial engineering that addresses option pricing theory, the statistical estimation for portfolio coefficients, and value-at-risk (VaR) problems via residual empirical return processes. The final chapters present some models for interest rates and discount bonds, discuss their no-arbitrage pricing theory, investigate problems of credit rating, and illustrate the clustering of stock returns in both the New York and Tokyo Stock Exchanges. Basing results on a modern, unified optimal inference approach for various time series models, this reference underlines the importance of stochastic models in the area of financial engineering.


PREFACE INTRODUCTION ELEMENTS OF PROBABILITY Probability and Probability Distribution Vector Random Variable and Independence Expectation and Conditional Distribution Convergence and Central Limit Theorems STATISTICAL INFERENCE Sufficient Statistics Unbiased Estimators Efficient Estimators Asymptotically Efficient Estimators VARIOUS STATISTICAL METHODS Interval Estimation Most Powerful Test Various Tests Discriminant Analysis STOCHASTIC PROCESSES Elements of Stochastic Processes Spectral Analysis Ergodicity, Mixing, and Martingale Limit Theorems for Stochastic Processes Exercise TIME SERIES ANALYSIS Time Series Model Estimation of Time Series Models Model Selection Problems Nonparametric Estimation Prediction of Time Series Regression for Time Series Long Memory Processes Local Whittle Likelihood Approach Nonstationary Processes Semiparametric Estimation Discriminant Analysis for Time Series INTRODUCTION TO STATISTICAL FINANCIAL ENGINEERING Option Pricing Theory Higher Order Asymptotic Option Valuation for Non-Gaussian Dependent Returns Estimation of Portfolio Value-at-Risk (VaR) Problems TERM STRUCTURE Spot Rates and Discount Bonds Estimation Procedures for Term Structure CREDIT RATING Parametric Clustering for Financial Time Series Nonparametric Clustering for Financial Time Series Credit Rating Based on Financial Time Series APPENDIX REFERENCES INDEX

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