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Parameter Estimation using Empirical Likelihood combined with Market Information

During the last decade Levy processes with jumps have received increasing popularity for modelling market behaviour for both derviative pricing and risk management purposes. Chan et al. (2009) introduced the use of empirical likelihood methods to estimate the parameters of various diffusion processes via their characteristic functions which are readily avaiable in most cases. Return series from the market are used for estimation. In addition to the return series, there are many derivatives actively traded in the market whose prices also contain information about parameters of the underlying process. This observation motivates us, in this paper, to combine the return series and the associated derivative prices observed at the market so as to provide a more reflective estimation with respect to the market movement and achieve a gain of effciency. The usual asymptotic properties, including consistency and asymptotic normality, are established under suitable regularity conditions. Simulation and case studies are performed to demonstrate the feasibility and effectiveness of the proposed method.