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基本説明
Develops the statistics for financial engineering based on the optimal statistical inference for non-Gaussian dependent processes. Introduces stochastic processes such as the spectral theory for stationary processes, ergodicity, mixing properties, and the martingale and central limit theorems.
Full 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.
Contents
Preface. Introduction. Elements of Probability. Statistical Inference. Various Statistical Methods. Stochastic Processes. Time Series Analysis. Introduction to Statistical Financial Engineering. Term Structure. Credit Rating. Appendix. References. Index.
