Chapman and Hall/CRC
384 pages | 61 B/W Illus.
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.
This book can be recommended to scholars and PhD students interested in finance and time series.
—Journal of Times Series Analysis, April 2010
ELEMENTS OF PROBABILITY
Probability and Probability Distribution
Vector Random Variable and Independence
Expectation and Conditional Distribution
Convergence and Central Limit Theorems
Asymptotically Efficient Estimators
VARIOUS STATISTICAL METHODS
Most Powerful Test
Elements of Stochastic Processes
Ergodicity, Mixing, and Martingale
Limit Theorems for Stochastic Processes
TIME SERIES ANALYSIS
Time Series Model
Estimation of Time Series Models
Model Selection Problems
Prediction of Time Series
Regression for Time Series
Long Memory Processes
Local Whittle Likelihood Approach
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
Spot Rates and Discount Bonds
Estimation Procedures for Term Structure
Parametric Clustering for Financial Time Series
Nonparametric Clustering for Financial Time Series
Credit Rating Based on Financial Time Series