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

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 gazump The Meixner mental summons is a special type of L´vy process which origie nates from the theory of orthogonal polynomials. It is related to the Meixner-Pollaczek polynomials by a martingale relation. We discuss several properties of the Meixner process. We apply the Meixner process to ?nancial data. First, we battle arrays that the ruler distribution is a very poor model to ?t log-returns of ?nancial assets like stocks or indices. In order to achieve a better ?t we replace the Normal distribution by the more sophisticated 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 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 motion by the more ?exible Meixner process. However, there let off is a discrepancy between market and theoretical prices.



The of import feature 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 idea which was developed in [9], one can moderate these stochastic volatility e?ects. The resulting option prices can be calibrated almost perfectly to empirical prices.

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Introduction

Financial math has recently 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 new applied modeling perspectives inside the context of ?nance and further...If you want to get a expert essay, order it on our website: Orderessay



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