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Parameter Estimation And Application Of The Pareto-Beta Jump-Diffusion Model

Posted on:2013-07-02Degree:MasterType:Thesis
Country:ChinaCandidate:L YangFull Text:PDF
GTID:2249330371491738Subject:Applied Mathematics
Abstract/Summary:PDF Full Text Request
In1973, Fischer Black and Myron Scholes prove the famous Black-Scholes model, which made the biggest affect in the pricing of financial derivatives. The model was a landmark achievement of a financial market containing certain derivative investment instruments. And it created a new field for the development of some related disciplines. However, with the development of finance, especially, from the serious impact concerning recent rare financial events and many questions of financial reform, the Black-Scholes model was found to be not appropriate for changes of the modern financial market. So, some improvements and generalizations began to make by the researchers, basing on the Black-Scholes model.In1976, Merton established a jump diffusion model, considering the option pricing with the assume that the price of stock was not a continuous function of time. After Merton’s work, Kou proposed double exponential jump diffusion model and Ramezani and Zeng proposed Pareto-Bate jump diffusion model, basing on different supposes and different parameters. These models can properly reflect the highly of skewed and leptokurtic distribution of the asset returns. And they also reflect the feature of volatility smile smirk.Basing on understanding the models, which are used to description the fluctuation of the stock price, I choose the empirical assessment of the PBJD model. In the paper, I use the basic statistics and the estimation values of six parameters to explain that the PBJD model can reflect the jump in the market, when some important news and financial events occurred.In the empirical assessment of the PBJD model, I choose the data of the shanghai composite index, coming from the time period of the financial crisis and before it. The data, from2003s to2005s, represent the time before the financial crisis, and the data, from2007s to2008s, represent the time period of the financial crisis. The method of calculation in the paper, I choose MLE and the Bound optimization by quadratic approximation (BOBYQA) to obtain the estimation values of the six parameters. By comparison, we find that the China stock market become unstable and the reaction become sensitive to some important news, when the financial crisis happens. Also the jump intensity and the jump magnitudes of stock price become larger.
Keywords/Search Tags:leptokurtic, Pareto-Beta jump diffusion, maximum likelihood estimation, shanghai composite index, financial crisis
PDF Full Text Request
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