1st Edition

Optimal Statistical Inference in Financial Engineering

    378 Pages 61 B/W Illustrations
    by Chapman & Hall

    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