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Abstract(s)
Risk neutral and real world densities derived from option prices provide rich
source of information for future asset price forecast. Three approaches
(mixtures of two lognormals, jump diffusion models and implied volatility
function models) are used to estimate risk neutral densities. Both power
utility function and beta function are used to transform mixtures of two
lognormal risk neutral densities into real world densities. Transformations
are estimated by maximizing the likelihood of observed index levels. Results
for the S&P 500 index indicate that two parametric methods, especially the
jump diffusion models are preferable than implied volatility function
methods. The log-likelihood tests cannot reject the hypothesis that there is
no risk premium for both year 2008 and year 2009.