David Ruppert - Statistics and Data Analysis for Financial Engineering

Springer Science+Business Media New York 2015

David Ruppert 1 and David S. Matteson 2

This book is about the analysis of financial markets data. After this brief introductory chapter, we turn immediately in Chaps. cover a variety of more advanced statistical techniques: ARIMA models, regression, multivariate models, copulas, GARCH models, factor models, cointegration, Bayesian statistics, and nonparametric regression.

Much of finance is concerned with financial risk. The return on an investment is its revenue expressed as a fraction of the initial investment. If one invests at time t 1 in an asset with price and the price later at time t 2 is , then the net return for the holding period from t 1 to t 2 is . For most assets, future returns cannot be known exactly and therefore are random variables. Risk means uncertainty in future returns from an investment, in particular, that the investment could earn less than the expected return and even result in a loss, that is, a negative return. Risk is often measured by the standard deviation of the return, which we also call the volatility. Recently there has been a trend toward measuring risk by value-at-risk (VaR) and expected shortfall (ES). These focus on large losses and are more direct indications of financial risk than the standard deviation of the return. Because risk depends upon the probability distribution of a return, probability and statistics are fundamental tools for finance. Probability is needed for risk calculations, and statistics is needed to estimate parameters such as the standard deviation of a return or to test hypotheses such as the so-called random walk hypothesis which states that future returns are independent of the past.

In financial engineering there are two kinds of probability distributions that can be estimated. Objective probabilities are the true probabilities of events. Risk-neutral or pricing probabilities give model outputs that agree with market prices and reflect the markets beliefs about the probabilities of future events. The statistical techniques in this book can be used to estimate both types of probabilities. Objective probabilities are usually estimated from historical data, whereas risk-neutral probabilities are estimated from the prices of options and other financial instruments.

Finance makes extensive use of probability models, for example, those used to derive the famous BlackScholes formula. Use of these models raises important questions of a statistical nature such as: Are these models supported by financial markets data? How are the parameters in these models estimated? Can the models be simplified or, conversely, should they be elaborated?

After Chaps. cover other areas of statistics and finance such as GARCH models of nonconstant volatility, Bayesian statistics, risk management, and nonparametric regression.

Several related themes will be emphasized in this book: