Meixner Process

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 special type of L´vy process which origie nates from the scheme of immaterial 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 statistical distribution is a very poor model to ?t log-returns of ?nancial assets like stockpiles or indices. In cabaret to achieve a better ?t we replace the Normal distribution by the more advance(a) 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 proce ss in order 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 apparent motion by the more ?exible Meixner process. However, there let off is a discrepancy between market and theoretical prices.

The of import make which these L´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 estimate which was developed in [9], one can moderate these stochastic volatility e?ects. The resulting op tion prices can be fine-tune almost perfect! ly to empirical prices. 2 1 initiation Financial math has youthfully enjoyed considerable prestige on account of its bear upon on the ?nance industry. In parallel, the theory of L´vy processes e has also seen exciting developments in recent years [2] [4] [26]. The nuclear fusion of these two ?elds of mathematics has provided advanced applied modeling perspectives inside the context of ?nance and further...If you sine qua non to get a expert essay, order it on our website: OrderCustomPaper.com

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