本文選題：跳躍間隔　切入點(diǎn)：多參指數(shù)分布　出處：《云南財(cái)經(jīng)大學(xué)》2017年碩士論文　論文類型：學(xué)位論文

【摘要】：近年來(lái),跳躍擴(kuò)散模型在實(shí)證研究中取得顯著效果,然而研究大多針對(duì)跳躍擴(kuò)散模型的跳躍間隔和跳躍幅度進(jìn)行概率分布假設(shè),鮮有從統(tǒng)計(jì)角度分析跳躍特征的實(shí)際分布情況。已有研究中,跳躍間隔一般假設(shè)為指數(shù)分布,也有少數(shù)學(xué)者利用冪律分布分析跳躍間隔特征�；谔S間隔服從指數(shù)分布的假設(shè),跳躍發(fā)生次數(shù)將呈泊松過(guò)程。然而,實(shí)證研究也發(fā)現(xiàn),指數(shù)分布極大地低估了長(zhǎng)間隔跳躍的概率。相較于指數(shù)分布,利用冪律分布描述跳躍間隔特征可以更好地捕捉價(jià)格跳躍的“時(shí)變性”和“厚尾性”,但同時(shí),也低估了短間隔的跳躍發(fā)生概率。整體而言,指數(shù)分布和冪律分布在跳躍間隔描述中各有優(yōu)劣�；谏鲜鰡�(wèn)題,本文立足跳躍與波動(dòng)理論,引入多參指數(shù)分布刻畫跳躍間隔特征,試圖給出最合適的跳躍間隔概率分布,并構(gòu)建多參跳躍擴(kuò)散模型。首先,本文總結(jié)了資產(chǎn)價(jià)格跳躍間隔特征,得到時(shí)變性、遞減性、驟降性和厚尾性四個(gè)性質(zhì)。其次,針對(duì)四種跳躍間隔性質(zhì),利用多參指數(shù)分布描述跳躍間隔特征,并構(gòu)建多參跳躍擴(kuò)散模型。此外,結(jié)合指數(shù)分布、冪律分布和多參指數(shù)分布進(jìn)行跳躍間隔特征的實(shí)證分析,并對(duì)比一般跳躍擴(kuò)散模型和多參跳躍擴(kuò)散模型的資產(chǎn)定價(jià)精度。結(jié)果顯示,多參指數(shù)分布相對(duì)于指數(shù)分布和冪律分布能更好地描述跳躍擴(kuò)散時(shí)變性、遞減性、驟降性和厚尾性四個(gè)性質(zhì);多參跳躍擴(kuò)散模型具有高于一般跳躍擴(kuò)散模型的定價(jià)精度。最后,根據(jù)實(shí)證結(jié)果,建議跳躍擴(kuò)散模型中使用多參指數(shù)分布代替冪律分布或指數(shù)分布作為跳躍間隔的概率分布。
[Abstract]:In recent years, the jump diffusion model has achieved remarkable results in empirical research. However, most of the studies are based on the hopping interval and the jump amplitude of the jump diffusion model for the probability distribution hypothesis. It is rare to analyze the actual distribution of jump characteristics from a statistical point of view. In previous studies, the jump interval is generally assumed to be exponential distribution. There are also a few scholars using power law distribution to analyze the characteristics of jump interval. Based on the assumption of exponential distribution of jump-spacer clothing, the number of jumps will be Poisson process. However, empirical research also found that, The exponential distribution greatly underestimates the probability of the long jump. Compared with the exponential distribution, the power law distribution can better capture the "time-varying" and "thick tail" of the price jump, but at the same time, the power law distribution can better capture the "time-varying" and "thick tail" of the price jump. On the whole, exponential distribution and power law distribution have advantages and disadvantages in the description of jump interval. Based on the above problems, this paper bases on the theory of jump and fluctuation. The multiparameter exponential distribution is introduced to characterize the jump interval characteristics, and the most suitable jump interval probability distribution is proposed, and the multi-parameter jump diffusion model is constructed. Firstly, the characteristics of the jump interval in asset prices are summarized, and the time-varying and decreasing properties are obtained. There are four properties of sudden drop and thick tail. Secondly, for the four properties of jump interval, the multiparameter exponential distribution is used to describe the characteristics of jump interval, and a multi-parameter jump diffusion model is constructed. In addition, the exponential distribution is combined with the exponential distribution. The power law distribution and multi-parameter exponential distribution are used to analyze the characteristics of jump interval, and the asset pricing accuracy of general jump diffusion model and multi-parameter jump diffusion model is compared. Compared with exponential distribution and power law distribution, the multiparameter exponential distribution can better describe the four properties of jump diffusion time variability, decrement, sudden drop and thick tail, and the multiparameter jump diffusion model has higher pricing accuracy than the general jump diffusion model. Based on the empirical results, it is suggested that the multiparameter exponential distribution be used in the jump diffusion model instead of the power law distribution or exponential distribution as the probability distribution of the jump interval.
【學(xué)位授予單位】：云南財(cái)經(jīng)大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：F224;F830.9

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本文編號(hào)：1619522