Optimal Statistical Inference in Financial Engineering: 1st Edition (Hardback) book cover

Optimal Statistical Inference in Financial Engineering

1st Edition

By Masanobu Taniguchi, Junichi Hirukawa, Kenichiro Tamaki

Chapman and Hall/CRC

384 pages | 61 B/W Illus.

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Description

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.

Reviews

This book can be recommended to scholars and PhD students interested in finance and time series.

Journal of Times Series Analysis, April 2010

Table of Contents

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

Subject Categories

BISAC Subject Codes/Headings:
BUS027000
BUSINESS & ECONOMICS / Finance
MAT000000
MATHEMATICS / General
MAT029000
MATHEMATICS / Probability & Statistics / General