Volatility function technique by using interpolation approach plays an important role in extracting the risk-neutral density (RND) of options. The aim of this study is to compare the performances of two interpolation approaches namely smoothing spline and fourth order polynomial in extracting the RND. The implied volatility of options with respect to strike prices/delta are interpolated to obtain a well behaved density. The statistical analysis and forecast accuracy are tested using moments of distribution. The difference between the first moment of distribution and the price of underlying asset at maturity is used as an input to analyze forecast accuracy. RNDs are extracted from the Dow Jones Industrial Average (DJIA) index options with a one month constant maturity for the period from January 2011 until December 2015. The empirical results suggest that the estimation of RND using a fourth order polynomial is more appropriate to be used compared to a smoothing spline in which the fourth order polynomial gives the lowest mean square error (MSE). The results can be used to help market participants capture market expectations of the future developments of the underlying asset.
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7 August 2017
PROCEEDINGS OF THE 24TH NATIONAL SYMPOSIUM ON MATHEMATICAL SCIENCES: Mathematical Sciences Exploration for the Universal Preservation
27–29 September 2016
Kuala Terengganu, Malaysia
Research Article|
August 07 2017
Comparison of volatility function technique for risk-neutral densities estimation
Hafizah Bahaludin;
Hafizah Bahaludin
a)
Department of Computational and Theoretical Sciences,
Kulliyyah of Science International Islamic University Malaysia
, Bandar Indera Mahkota Campus, Jalan Sultan Ahmad Shah, 25200 Kuantan, Pahang, Malaysia
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Mimi Hafizah Abdullah
Mimi Hafizah Abdullah
b)
Department of Computational and Theoretical Sciences,
Kulliyyah of Science International Islamic University Malaysia
, Bandar Indera Mahkota Campus, Jalan Sultan Ahmad Shah, 25200 Kuantan, Pahang, Malaysia
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a)
Corresponding author: [email protected]
AIP Conf. Proc. 1870, 040073 (2017)
Citation
Hafizah Bahaludin, Mimi Hafizah Abdullah; Comparison of volatility function technique for risk-neutral densities estimation. AIP Conf. Proc. 7 August 2017; 1870 (1): 040073. https://doi.org/10.1063/1.4995905
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