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Theory & Methods: Estimation of the Stochastic Volatility Model by the Empirical Characteristic Function Method
Author(s) -
Knight John L.,
Satchell Stephen E.,
Yu Jun
Publication year - 2002
Publication title -
australian and new zealand journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 1369-1473
DOI - 10.1111/1467-842x.00234
Subject(s) - stochastic volatility , mathematics , econometrics , volatility (finance) , likelihood function , maximum likelihood , characteristic function (probability theory) , function (biology) , estimation , statistics , probability density function , economics , management , evolutionary biology , biology
The stochastic volatility model has no closed form for its likelihood and hence the maximum likelihood estimation method is difficult to implement. However, it can be shown that the model has a known characteristic function. As a consequence, the model is estimable via the empirical characteristic function. In this paper, the characteristic function of the model is derived and the estimation procedure is discussed. An application is considered for daily returns of Australian/New Zealand dollar exchange rate. Model checking suggests that the stochastic volatility model together with the empirical characteristic function estimates fit the data well.