• The Korean Journal of Applied Statistics
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• v.24 no.6
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• pp.1007-1020
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• 2011

Since the research of Black and Scholes (1973), modeling methods using diffusion processes have performed principal roles in financial engineering. In modern financial theories, various types of diffusion processes were suggested and applied in real situations. An estimation of the model parameters is an indispensible step to analyze financial data using diffusion process models. Many estimation methods were suggested and their properties were investigated. This paper reviews the statistical properties of the, Euler approximation method, New Local Linearization(NLL) method, and Generalized Methods of Moment(GMM) that are known as the most practical methods. From the simulation study, we found the NLL and Euler methods performed better than GMM. GMM is frequently used to estimate the parameters because of its simplicity; however this paper shows the performance of GMM is poorer than the Euler approximation method or the NLL method that are even simpler than GMM. This paper shows the performance of the GMM is extremely poor especially when the parameters in diffusion coefficient are to be estimated.

• Communications for Statistical Applications and Methods
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• v.17 no.4
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• pp.599-609
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• 2010

Many of financial data are explained via diffusion models in modern financial research. Various types of estimation methods of diffusion processes were suggested by many authors. In this paper, we tested the properties of the NLL estimation method, suggested by Shoji and Ozaki (1998), of diffusion processes in the view of the bias and variance of the estimators and applied the method to estimate the model parameters for the U.S. fedral funds rate data and Korean inter-bank exchange rate data. By simulation study we showed that the NLL method provides relatively good estimators, in the meaning that the estimator has less bias than the Euler method, while keeping the variance similar level. We also provide the NLL estimates of U.S fedral funds rate data and Korean inter-bank exchange rate data.