1st Edition

# Optimal Statistical Inference in Financial Engineering

378 Pages 61 B/W Illustrations
by Chapman & Hall

384 Pages
by Chapman & Hall

Also available as eBook on:

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

### Biography

Masanobu Taniguchi, Junichi Hirukawa, Kenichiro Tamaki

This book can be recommended to scholars and PhD students interested in finance and time series.
Journal of Times Series Analysis, April 2010