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著名的普林斯顿大学教授倾力打造的精品英文版的金融数学方面的精品教材。
内容简介
《数学名著系列丛书:计量金融精要》是一本关于金融计量方面的基础用书,提供了核心基础资料,包括金融研究日益增长的科学前沿和金融工业方面重要的发展情况。《数学名著系列丛书:计量金融精要》对资产定价理论、投资组合优化和风险管理方法提供了简洁的和紧凑的处理。提供了单因素和多因素情况下的时间序列模型技术,在分析财务数据上下文的时候介绍了他们的均值和方差。真实的数据分析贯穿全书,是《数学名著系列丛书:计量金融精要》的一个明显的特征。
作者简介
范剑青,美国普林斯顿大学统计与金融工程终身教授,The Annals of Statistics 杂志主编。1982年毕业于复旦大学数学系,随后考入中国科学院应用数学所攻读硕士。1986年进入美国加州柏克萊大学攻读博士学位,师从国际著名的统计学家 Bickel 教授和Donoho教授,在过去的十多年里,范教授发表了一百多篇论文,已经出版两本英文专著。于2004年任 The Annals of Statistics 的主编,成为该杂志创刊70多年来**的亚裔主编。他还当选为美国统计学会院士(Fellow)、国际数理研究院院士和国际统计研究院院士。2005年出任中国科学院数学与系统科学研究院统计科学研究中心主任,2006年获得国家杰出海外青年基金。
内页插图
目录
Preface to Mathematics Monograph Series
Preface
Chapter 1 Asset Returns
1.1 Returns
1.1.1 One-period simple returns and gross returns
1.1.2 Multiperiod returns
1.1.3 Log returns and continuously compounding
1.1.4 Adjustment for dividends
1.1.5 Bond yields and prices
1.1.6 Excess returns
1.2 Behavior of?nancial return data
1.2.1 Stylized features of?nancial returns
1.3 E±cient markets hypothesis and statistical models for returns
1.4 Tests related to e±cient markets hypothesis
1.4.1 Tests for white noise
1.4.2 Remarks on the Ljung-Box test
1.4.3 Tests for random walks
1.4.4 Ljung-Box test and Dickey-Fuller test
1.5 Appendix: Q-Q plot and Jarque-Bera test
1.5.1 Q-Q plot
1.5.2 Jarque-Bera test
1.6 Further reading and software implementation
1.7 Exercises
Chapter 2 Linear Time Series Models
2.1 Stationarity
2.2 Stationary ARMA models
2.2.1 Moving average processes
2.2.2 Autoregressive processes
2.2.3 Autoregressive and moving average processes
2.3 Nonstationary and long memory ARMA processes
2.3.1 Random walks
2.3.2 ARIMA model and exponential smoothing
2.3.3 FARIMA model and long memory processes
2.3.4 Summary of time series models
2.4 Model selection using ACF, PACF and EACF
2.5 Fitting ARMA models: MLE and LSE
2.5.1 Least squares estimation
2.5.2 Gaussian maximum likelihood estimation
2.5.3 Illustration with gold prices
2.5.4 A snapshot of maximum likelihood methods
2.6 Model diagnostics: residual analysis
2.6.1 Residual plots
2.6.2 Goodness-of-?t tests for residuals
2.7 Model identi?cation based on information criteria
2.8 Stochastic and deterministic trends
2.8.1 Trend removal
2.8.2 Augmented Dickey-Fuller test
2.8.3 An illustration
2.8.4 Seasonality
2.9 Forecasting
2.9.1 Forecasting ARMA processes
2.9.2 Forecasting trends and momentum of?nancial markets
2.10 Appendix: Time series analysis in R
2.10.1 Start up with R
2.10.2 R-functions for time series analysis
2.10.3 TSA{ an add-on package
2.11 Exercises
Chapter 3 Heteroscedastic Volatility Models
3.1 ARCH and GARCH models
3.1.1 ARCH models
3.1.2 GARCH models
3.1.3 Stationarity of GARCH models
3.1.4 Fourth moments
3.1.5 Forecasting volatility
3.2 Estimation for GARCH models
3.2.1 Conditional maximum likelihood estimation
3.2.2 Model diagnostics
……
Chapter 4 Multivariate Time Series Analysis
Chapter 5 Effcient Portfolios and Capital Asset Pricing Model
Chapter 6 Factor Pricing Models
Chapter 7 Portfolio Allocation and Risk Assessment
Chapter 8 Consumption based CAPM
Chapter 9 Present-value Models
References
Author Index
Subject Index
精彩书摘
《数学名著系列丛书:计量金融精要》:
Chapter 1
Asset Returns The primary goal of investing in a -nancial market is to make pro-ts without taking excessive risks. Most common investments involve purchasing -nancial assets such as stocks, bonds or bank deposits, and holding them for certain periods. Posi- tive revenue is generated if the price of a holding asset at the end of holding period is higher than that at the time of purchase (for the time being we ignore transaction charges). Obviously the size of the revenue depends on three factors: (i) the initial capital (i.e. the number of assets purchased), (ii) the length of holding period, and (iii) the changes of the asset price over the holding period. A successful investment pursues the maximum revenue with a given initial capital, which may be measured explicitly in terms of the so-called return . A return is a percentage de-ned as the change of price expressed as a fraction of the initial price. It turns out that asset returns exhibit more attractive statistical properties than asset prices themselves.
Therefore it also makes more statistical sense to analyze return data rather than price series.
1.1 Returns
Let Pt denote the price of an asset at time t. First we introduce various de-nitions for the returns for the asset.
1.1.1 One-period simple returns and gross returns
Holding an asset from time t ? 1 to t, the value of the asset changes from Pt?1 to Pt. Assuming that no dividends paid are over the period. Then the one-period simple return is de-ned as
It is the pro-t rate of holding the asset from time t ? 1 to t. Often we write Rt = 100Rt%, as 100Rt is the percentage of the gain with respect to the initial capital Pt?1. This is particularly useful when the time unit is small (such as a day or an hour); in such cases Rt typically takes very small values. The returns for lessrisky assets such as bonds can be even smaller in a short period and are often quoted in basis points , which is 10; 000Rt. The one period gross return is de-ned as Pt=Pt?1 = Rt 1. It is the ratio of the new market value at the end of the holding period over the initial market value. 1.1.2 Multiperiod returns
The holding period for an investment may be more than one time unit. For any integer k > 1, the returns for over k periods may be de-ned in a similar manner.
For example, the k-period simple return from time t ? k to t is and the k-period gross return is Pt=Pt?k = Rt(k) 1. It is easy to see that the multiperiod returns may be expressed in terms of one-period returns as follows:
If all one-period returns Rt; ;Rt?k 1 are small, (1.3) implies an approximation
This is a useful approximation when the time unit is small (such as a day, an hour or a minute).
1.1.3 Log returns and continuously compounding
In addition to the simple return Rt, the commonly used one period log return is
de-ned as
Note that a log return is the logarithm (with the natural base) of a gross return and log Pt is called the log price. One immediate convenience in using log returns is that the additivity in multiperiod log returns, i.e. the k period log return rt(k) ′
log(Pt=Pt?k) is the sum of the k one-period log returns:
An investment at time t ? k with initial capital A yields at time t the capitalwhere 1r = (rt rt?1 ¢ ¢ ¢ rt?k 1)=k is the average one-period log returns. In this book returns refer to log returns unless speci-ed otherwise.
Note that the identity (1.6) is in contrast with the approximation (1.4) which is only valid when the time unit is small. Indeed when the values are small, the two returns are approximately the same:
However, rt < Rt. Figure 1.1 plots the log returns against the simple returns for the Apple Inc share prices in the period of January 1985 { February 2011. The returns are calculated based on the daily close prices for the three holding periods: a day, a week and a month. The -gure shows that the two de-nitions result almost the same daily returns, especially for those with the values between ?0.2 and 0.2. However when the holding period increases to a week or a month, the discrepancy between the two de-nitions is more apparent with a simple return always greater than the corresponding log return.
……
前言/序言
计量金融精要:洞悉金融市场运作的数学利器 金融市场,一个充斥着海量数据、瞬息万变且充满风险的复杂系统。理解其内在规律、预测其未来走向、并在此基础上做出最优决策,是无数金融从业者、研究者和投资者的不懈追求。然而,传统定性分析往往难以捕捉金融市场的细微之处,其内在的随机性和非线性特征更是带来了巨大的挑战。《计量金融精要》正是应运而生,它以严谨的数学语言和精湛的统计工具,为读者构建起一座通往金融市场深层奥秘的桥梁,引领读者掌握洞悉金融市场运作的数学利器。 什么是计量金融? 计量金融(Financial Econometrics)是经济学、统计学和数学的交叉学科,它将计量经济学的理论和方法应用于金融领域,旨在通过数据分析来理解、建模、预测和检验金融市场的现象。与纯粹的理论经济学不同,计量金融更加注重实证,它依赖于真实的金融数据,通过统计模型来量化金融资产的价格波动、风险特征、市场效率以及各类经济变量对金融市场的影响。从宏观经济政策对股市的影响,到微观层面的资产定价,再到新兴的金融衍生品市场,计量金融都展现出其强大的解释力和预测力。 《计量金融精要》将带你深入探索什么? 本书并非对金融理论的简单罗列,而是聚焦于那些支撑起现代金融分析体系的核心数学和统计方法。它将带领你系统性地学习和理解以下关键领域: 时间序列分析(Time Series Analysis): 金融市场的数据几乎都是按时间顺序排列的,如股票价格、汇率、利率等。时间序列分析是处理这类数据的基础。本书将详细介绍各种时间序列模型,包括但不限于: 自回归模型 (AR)、移动平均模型 (MA) 和自回归移动平均模型 (ARMA): 学习如何捕捉时间序列数据的自相关性,并用以预测未来的数值。 自回归积分滑动平均模型 (ARIMA): 进一步处理非平稳时间序列,使其能够被建模和预测。 季节性 ARIMA 模型 (SARIMA): 识别和建模数据中的季节性规律,这对分析某些金融产品(如季度财报影响下的股票)至关重要。 GARCH 系列模型(ARCH, GARCH, EGARCH, GJR-GARCH 等): 金融市场最显著的特征之一是“波动率聚集”,即大的价格变动往往伴随着大的价格变动,小的变动则伴随着小的变动。GARCH 系列模型正是用来刻画和预测这种波动的,它们在风险管理、期权定价等领域具有不可替代的作用。 横截面数据分析(Cross-Sectional Data Analysis): 除了时间序列数据,我们也需要分析同一时间点上不同实体的数据,例如不同公司的财务报表、不同国家的宏观经济指标等。本书将涵盖: 线性回归模型(Linear Regression Models): 学习如何建立因变量与一个或多个自变量之间的线性关系,例如分析广告投入与公司销售额的关系。 多重回归与变量选择: 掌握如何在包含多个潜在解释变量时,选择最合适的变量集,避免多重共线性问题,并提高模型的解释力和预测能力。 异方差性(Heteroskedasticity)和自相关性(Autocorrelation)的诊断与处理: 在金融数据分析中,这两个问题非常普遍,需要专门的方法来识别和修正,以保证估计结果的有效性。 面板数据模型(Panel Data Models): 当我们同时拥有跨越多个实体(如公司、国家)且在多个时间点上收集的数据时,面板数据模型能够充分利用数据的维度,提供比单纯的时间序列或横截面分析更丰富的信息。本书将介绍: 固定效应模型(Fixed Effects Models)与随机效应模型(Random Effects Models): 学习如何处理个体特异性的、不随时间变化的因素,以及如何判断这些因素是固定还是随机的。 模型选择与检验(Model Selection and Testing): 任何统计模型都不是完美的,选择一个适合特定问题的模型至关重要。本书将教会读者如何: 信息准则(AIC, BIC): 利用信息准则来评估和比较不同模型的拟合优度。 假设检验(Hypothesis Testing): 学习如何对模型的参数和整体显著性进行检验,以得出统计上可靠的结论。 模型诊断(Model Diagnostics): 检查模型是否满足基本假设,例如残差的正态性、独立性等,并进行必要的调整。 金融市场中的具体应用: 本书的价值不仅在于理论的介绍,更在于将其与实际金融问题紧密结合。你将看到这些模型如何被应用于: 资产定价: 理解CAPM、APT等资产定价模型的计量检验,以及如何通过因子模型来解释资产收益。 风险管理: 使用VaR (Value at Risk)、CVaR (Conditional Value at Risk) 等度量指标,并利用GARCH模型进行风险暴露的预测。 金融衍生品定价: 为期权、期货等衍生品提供定价理论和计量模型的视角。 宏观经济与金融市场的联动: 分析通货膨胀、利率变动等宏观因素对股票、债券市场的影响。 为什么选择《计量金融精要》? 在充斥着各种金融读物的市场中,《计量金融精要》以其独特的视角和深刻的洞察力脱颖而出: 严谨的数学基础: 本书不回避复杂的数学推导,但会以清晰易懂的方式呈现,帮助读者建立扎实的理论根基。 精选的统计工具: 专注于那些在金融领域应用最广泛、最有效的计量方法,避免泛泛而谈。 理论与实践的融合: 每一章的讲解都力求与金融市场的实际应用相结合,让读者能学以致用。 循序渐进的学习路径: 从基础概念到复杂模型,内容编排合理,适合不同水平的读者逐步深入。 无论你是金融专业的学生,渴望夯实计量金融的理论基础;还是金融市场的从业者,希望提升分析和决策的精准度;抑或是对金融世界充满好奇的投资者,希望理解市场背后的数学逻辑,《计量金融精要》都将是你不可或缺的参考书。它将赋予你用数据说话、用模型洞察、用智慧驾驭金融市场的力量。