The Meixner Process: Theory and Applications in Finance Wim Schoutens K.U.Leuven Celestijnenlaan 200 B B-3001 Leuven Belgium February 12, 2002 1 gazump The Meixner mental summons is a finical type of LÂ´vy process which origie nates from the conjecture of external polynomials. It is related to the Meixner-Pollaczek polynomials by a martingale relation. We discuss several(prenominal) properties of the Meixner process. We apply the Meixner process to ?nancial data. First, we battle arrays that the ruler dispersal is a very poor model to ?t log-returns of ?nancial assets like profligates or indices. In battle array to achieve a better ?t we replace the Normal distribution by the more civilize Meixner distribution, taking into account, skewness and excess kurtosis. We show that the underlying Meixner distribution allows a much better ?t to the data by performing a number of statistical tests. Secondly, we introduce stock price models based on the Meixner process in or der to price ?nancial derivatives. A ?rst signi?cant utility can be achieved with respect to the famous Black-Scholes model (BS-model) by replacing its Brownian bm by the more ?exible Meixner process. However, there let off is a discrepancy between market and theoretical prices.
The of import frolic which these LÂ´vy models are missing is the fact that irritability or more e generally the environment is ever-changing stochastically over sentence. By making business time stochastic, an motif which was developed in , one can moderate these stochastic volatility e?ects. The resulting option prices can be ca librate almost perfectly to empirical prices! . 2 1 knowledgeability Financial math has late(a)ly enjoyed considerable prestige on account of its bear upon on the ?nance industry. In parallel, the theory of LÂ´vy processes e has also seen exciting developments in recent years   . The nuclear fusion of these two ?elds of mathematics has provided brand-new applied modeling perspectives inside the context of ?nance and further...If you compliments to get a expert essay, order it on our website: OrderCustomPaper.com
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