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著名的普林斯頓大學教授傾力打造的精品英文版的金融數學方麵的精品教材。
內容簡介
《數學名著係列叢書:計量金融精要》是一本關於金融計量方麵的基礎用書,提供瞭核心基礎資料,包括金融研究日益增長的科學前沿和金融工業方麵重要的發展情況。《數學名著係列叢書:計量金融精要》對資産定價理論、投資組閤優化和風險管理方法提供瞭簡潔的和緊湊的處理。提供瞭單因素和多因素情況下的時間序列模型技術,在分析財務數據上下文的時候介紹瞭他們的均值和方差。真實的數據分析貫穿全書,是《數學名著係列叢書:計量金融精要》的一個明顯的特徵。
作者簡介
範劍青,美國普林斯頓大學統計與金融工程終身教授,The Annals of Statistics 雜誌主編。1982年畢業於復旦大學數學係,隨後考入中國科學院應用數學所攻讀碩士。1986年進入美國加州柏剋萊大學攻讀博士學位,師從國際著名的統計學傢 Bickel 教授和Donoho教授,在過去的十多年裏,範教授發錶瞭一百多篇論文,已經齣版兩本英文專著。於2004年任 The Annals of Statistics 的主編,成為該雜誌創刊70多年來**的亞裔主編。他還當選為美國統計學會院士(Fellow)、國際數理研究院院士和國際統計研究院院士。2005年齣任中國科學院數學與係統科學研究院統計科學研究中心主任,2006年獲得國傢傑齣海外青年基金。
內頁插圖
目錄
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
精彩書摘
《數學名著係列叢書:計量金融精要》:
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
計量金融精要:洞悉金融市場運作的數學利器 金融市場,一個充斥著海量數據、瞬息萬變且充滿風險的復雜係統。理解其內在規律、預測其未來走嚮、並在此基礎上做齣最優決策,是無數金融從業者、研究者和投資者的不懈追求。然而,傳統定性分析往往難以捕捉金融市場的細微之處,其內在的隨機性和非綫性特徵更是帶來瞭巨大的挑戰。《計量金融精要》正是應運而生,它以嚴謹的數學語言和精湛的統計工具,為讀者構建起一座通往金融市場深層奧秘的橋梁,引領讀者掌握洞悉金融市場運作的數學利器。 什麼是計量金融? 計量金融(Financial Econometrics)是經濟學、統計學和數學的交叉學科,它將計量經濟學的理論和方法應用於金融領域,旨在通過數據分析來理解、建模、預測和檢驗金融市場的現象。與純粹的理論經濟學不同,計量金融更加注重實證,它依賴於真實的金融數據,通過統計模型來量化金融資産的價格波動、風險特徵、市場效率以及各類經濟變量對金融市場的影響。從宏觀經濟政策對股市的影響,到微觀層麵的資産定價,再到新興的金融衍生品市場,計量金融都展現齣其強大的解釋力和預測力。 《計量金融精要》將帶你深入探索什麼? 本書並非對金融理論的簡單羅列,而是聚焦於那些支撐起現代金融分析體係的核心數學和統計方法。它將帶領你係統性地學習和理解以下關鍵領域: 時間序列分析(Time Series Analysis): 金融市場的數據幾乎都是按時間順序排列的,如股票價格、匯率、利率等。時間序列分析是處理這類數據的基礎。本書將詳細介紹各種時間序列模型,包括但不限於: 自迴歸模型 (AR)、移動平均模型 (MA) 和自迴歸移動平均模型 (ARMA): 學習如何捕捉時間序列數據的自相關性,並用以預測未來的數值。 自迴歸積分滑動平均模型 (ARIMA): 進一步處理非平穩時間序列,使其能夠被建模和預測。 季節性 ARIMA 模型 (SARIMA): 識彆和建模數據中的季節性規律,這對分析某些金融産品(如季度財報影響下的股票)至關重要。 GARCH 係列模型(ARCH, GARCH, EGARCH, GJR-GARCH 等): 金融市場最顯著的特徵之一是“波動率聚集”,即大的價格變動往往伴隨著大的價格變動,小的變動則伴隨著小的變動。GARCH 係列模型正是用來刻畫和預測這種波動的,它們在風險管理、期權定價等領域具有不可替代的作用。 橫截麵數據分析(Cross-Sectional Data Analysis): 除瞭時間序列數據,我們也需要分析同一時間點上不同實體的數據,例如不同公司的財務報錶、不同國傢的宏觀經濟指標等。本書將涵蓋: 綫性迴歸模型(Linear Regression Models): 學習如何建立因變量與一個或多個自變量之間的綫性關係,例如分析廣告投入與公司銷售額的關係。 多重迴歸與變量選擇: 掌握如何在包含多個潛在解釋變量時,選擇最閤適的變量集,避免多重共綫性問題,並提高模型的解釋力和預測能力。 異方差性(Heteroskedasticity)和自相關性(Autocorrelation)的診斷與處理: 在金融數據分析中,這兩個問題非常普遍,需要專門的方法來識彆和修正,以保證估計結果的有效性。 麵闆數據模型(Panel Data Models): 當我們同時擁有跨越多個實體(如公司、國傢)且在多個時間點上收集的數據時,麵闆數據模型能夠充分利用數據的維度,提供比單純的時間序列或橫截麵分析更豐富的信息。本書將介紹: 固定效應模型(Fixed Effects Models)與隨機效應模型(Random Effects Models): 學習如何處理個體特異性的、不隨時間變化的因素,以及如何判斷這些因素是固定還是隨機的。 模型選擇與檢驗(Model Selection and Testing): 任何統計模型都不是完美的,選擇一個適閤特定問題的模型至關重要。本書將教會讀者如何: 信息準則(AIC, BIC): 利用信息準則來評估和比較不同模型的擬閤優度。 假設檢驗(Hypothesis Testing): 學習如何對模型的參數和整體顯著性進行檢驗,以得齣統計上可靠的結論。 模型診斷(Model Diagnostics): 檢查模型是否滿足基本假設,例如殘差的正態性、獨立性等,並進行必要的調整。 金融市場中的具體應用: 本書的價值不僅在於理論的介紹,更在於將其與實際金融問題緊密結閤。你將看到這些模型如何被應用於: 資産定價: 理解CAPM、APT等資産定價模型的計量檢驗,以及如何通過因子模型來解釋資産收益。 風險管理: 使用VaR (Value at Risk)、CVaR (Conditional Value at Risk) 等度量指標,並利用GARCH模型進行風險暴露的預測。 金融衍生品定價: 為期權、期貨等衍生品提供定價理論和計量模型的視角。 宏觀經濟與金融市場的聯動: 分析通貨膨脹、利率變動等宏觀因素對股票、債券市場的影響。 為什麼選擇《計量金融精要》? 在充斥著各種金融讀物的市場中,《計量金融精要》以其獨特的視角和深刻的洞察力脫穎而齣: 嚴謹的數學基礎: 本書不迴避復雜的數學推導,但會以清晰易懂的方式呈現,幫助讀者建立紮實的理論根基。 精選的統計工具: 專注於那些在金融領域應用最廣泛、最有效的計量方法,避免泛泛而談。 理論與實踐的融閤: 每一章的講解都力求與金融市場的實際應用相結閤,讓讀者能學以緻用。 循序漸進的學習路徑: 從基礎概念到復雜模型,內容編排閤理,適閤不同水平的讀者逐步深入。 無論你是金融專業的學生,渴望夯實計量金融的理論基礎;還是金融市場的從業者,希望提升分析和決策的精準度;抑或是對金融世界充滿好奇的投資者,希望理解市場背後的數學邏輯,《計量金融精要》都將是你不可或缺的參考書。它將賦予你用數據說話、用模型洞察、用智慧駕馭金融市場的力量。