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  本文選題：q-微積分　切入點：q-正態(tài)分布　出處：《武漢理工大學》2012年碩士論文

【摘要】：股票市場作為金融市場的重要部分,其較大的波動性和交易量使其成為風險管理的主體。中國的股票市場正處于摸索階段,仍存在著市場風險管理的方法和技術(shù)比較落后、市場風險信息披露制度不健全、風險管理體系不夠完善等缺陷和不足。如何對股票市場進行有效的計量和管理,是市場各方面必須面對的重要課題。風險價值VaR模型作為目前度量風險的主流方法之一在20世紀90年代的迅速發(fā)展,使得各種金融工具和不同的市場風險獲得了統(tǒng)一衡量和綜合管理。VaR模型成為市場風險管理的一種共同標準,這種影響和變化甚至被稱為風險管理的VaR革命。 本文在國內(nèi)外學者的研究基礎(chǔ)上,首先簡單介紹了金融風險管理的理論基礎(chǔ)及VaR的傳統(tǒng)計算方法的優(yōu)缺點,并指出了VaR應(yīng)用于中國股票市場的必要性。其次運用q-微積分的理論知識推導出相應(yīng)的部分q-統(tǒng)計分布(q-正態(tài)分布、q-指數(shù)分布、q-均勻分布)的密度函數(shù)和部分特征數(shù)(數(shù)學期望、方差、k階矩),將q-正態(tài)分布應(yīng)用于以上證指數(shù)1A0001的原始數(shù)據(jù)為樣本數(shù)據(jù)的VaR值的估計計算中,指出了該統(tǒng)計分布的實用性,進一步證明了上證指數(shù)1A0001的口對數(shù)收益率服從此q-正態(tài)分布；最后將計算的VaR值與Tsallisq'-標準正態(tài)分布計算出的VaR值進行比較,說明了q-正態(tài)分布和適用于此樣本數(shù)據(jù)。 研究表明,q-正態(tài)分布能夠更好的描述股票收益率的特征,并且適應(yīng)于VaR值的估計中,更好的解決了股票收益率的“厚尾”特征并提高了精確度。
[Abstract]:As an important part of the financial market, the stock market is subject to risk management due to its high volatility and trading volume. The market risk information disclosure system is not perfect, the risk management system is not perfect, and so on. How to effectively measure and manage the stock market, VaR model of risk value, as one of the mainstream methods to measure risk, developed rapidly in 1990s. It makes all kinds of financial instruments and different market risks get unified measurement and integrated management. VaR model becomes a common standard of market risk management. This kind of influence and change is even called the VaR revolution of risk management. Based on the research of domestic and foreign scholars, this paper firstly introduces the theoretical basis of financial risk management and the advantages and disadvantages of traditional VaR calculation methods. The necessity of applying VaR to Chinese stock market is pointed out. Secondly, the density function and partial special distribution of partial q-statistic distribution and q-exponential distribution are derived by using the theory of q-calculus. Sign number (mathematical expectation, The q-normal distribution is applied to the estimation of the VaR value based on the original data of the 1A0001 index of Shanghai Stock Exchange, and the practicability of the statistical distribution is pointed out. It is further proved that the logarithmic rate of return of 1A0001 is derived from the q-normal distribution, and the calculated VaR value is compared with the VaR value calculated by Tsallisq-standard normal distribution, which shows the q-normal distribution and its applicability to the sample data. The research shows that Q-normal distribution can better describe the characteristics of stock return, and adapt to the estimation of VaR value, better solve the "thick tail" feature of stock yield and improve the accuracy.
【學位授予單位】：武漢理工大學
【學位級別】：碩士
【學位授予年份】：2012
【分類號】：F224;F832.51

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相關(guān)期刊論文 前2條

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2 陳立新;VaR風險測量模型在我國股票市場中的應(yīng)用[J];大連鐵道學院學報;2004年02期

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本文編號：1657678