All Title Author
Keywords Abstract


Underlying Assets Distribution in Derivatives: The BRIC Case

DOI: 10.4236/tel.2018.83035, PP. 502-513

Keywords: Derivatives, Normal Inverse Gaussian, Valuation, Returns, BRIC

Full-Text   Cite this paper   Add to My Lib

Abstract:

This paper addresses one of the main issues regarding numerical derivatives valuation, particularly the search for an alternative to the normality assumption of underlying asset returns, to obtain the price by using numerical techniques. There might be difficulties in making normality assumptions, which could produce over-valuated or sub-valuated prices of derivatives. Under this consideration, the Generalized Hyperbolic family has been proven to be a proper selection to model heavy tailed distribution behavior. The Normal Inverse Gaussian (NIG) distribution is a member flexible enough to model financial returns. NIG distribution can be used to model distribution returns under different states of nature. The indexes of the Brazil, Russia, India and China (BRIC) economies were studied at different time-periods using return data series from 2002 to 2005, 2006 to 2010 and 2011 to 2015, in such a manner to demonstrate with statistical criteria that NIG fits the empirical distribution in the three periods; even throughout economic downturn. This result may be used as an improvement in derivatives valuation with indexes as underlying assets.

References

[1]  Bachélier, L. (1900) Théorie de la speculation. [The Theory of Speculation.] Annales scientifiques de l’école Normale Supérieure, 3, 21-86.
https://doi.org/10.24033/asens.476
[2]  Bank for International Settlements (2017) Statistical Release: OTC Derivatives Statistics at End June 2017. BIS Semiannual OTC Derivatives Statistics.
https://www.bis.org/publ/otc_hy1711.pdf
[3]  Eberlein, E. and Keller, U. (1995) Hyperbolic Distributions in Finance. Bernoulli, 1, 281-299.
https://doi.org/10.2307/3318481
[4]  Eberlein, E. and Prause, K. (2002) The Generalized Hyperbolic Model: Financial Derivatives and Risk Measures. In: Geman, H., Madan, D., Pliska, S.R. and Vorst, T., Eds., Mathematical Finance—Bachelier Congress 2000, Springer, Berlin, Heidelberg, 245-267.
https://doi.org/10.1007/978-3-662-12429-1_12
[5]  Cont, R. (2001) Empirical Properties of Asset Returns: Stylized Facts and Statistical Issues. Quantitative Finance, 1, 223-236.
https://doi.org/10.1080/713665670
[6]  Barndorff-Nielsen, O.E. (1997) Normal Inverse Gaussian Distributions and Stochastic Volatility Modelling. Scandinavian Journal of Statistics, 24, 1-13.
https://doi.org/10.1111/1467-9469.t01-1-00045
[7]  Barndorff-Nielsen, O.E. and Shephard, N. (2001) Modelling by Lévy Processes for Financial Econometrics. In: Ole, E., Barndorff-Nielsen, T.M. and Sidney, I.R., Eds., Lévy Processes: Theory and Applications, Birkhauser, Boston, 283-318.
https://doi.org/10.1007/978-1-4612-0197-7_13
[8]  Barndorff-Nielsen, O.E. (1977) Exponentially Decreasing Distributions for the Logarithm of Particle Size. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 353, 401-419.
https://doi.org/10.1098/rspa.1977.0041
[9]  Barndorff-Nielsen, O. E. (1995), Normal Inverse Gaussian processes and the Modelling of Stock Returns. Research Report 300, Department of Theoretical Statistics, Institute of Mathematics, University of Aarhus, Aarhus.
[10]  Rydberg, T.H. (1999) Generalized Hyperbolic Diffusion Processes with Applications in Finance. Mathematical Finance, 9, 183-201.
https://doi.org/10.1111/1467-9965.00067
[11]  Trejo, B.R., Núnez, J.A. and Lorenzo, A. (2006) Distribución de los rendimientos del mercado mexicano accionario. Estudios Económicos, 21, 85-118.
[12]  Mota, M. and Mata, L. (2016) Caracterización paramétrica de los rendimientos de los precios del petróleo 2010-2015. Panorama Económico, 11, 63-74.
[13]  Shen, H., et al. (2017) Heavy-Tailed Distribution and Risk Management of Gold Returns. International Journal of Academic Research in Economics and Management Sciences, 3, 15-24.
[14]  Shen, H., Meng, X. and Meng, X. (2017) How to Manage the Risk in the Precious Metals Market? The Case of Gold.
https://doi.org/10.2139/ssrn.3016829
[15]  Neely, C.J. (2004) The Federal Reserve Responds to Crises: September 11th Was Not the First. ICPSR Data Holdings.
[16]  Clark, J. (2016) Emerging Market Capital Flows and U.S. Monetary Policy. Board of Governors of the Federal Reserve System. International Finance Discussion Paper Note.
[17]  Shapiro, S.S. and Francia, R.S. (1972) An Approximate Analysis of Variance Test for Normality. Journal of the American Statistical Association, 67, 215-216.
https://doi.org/10.1080/01621459.1972.10481232
[18]  Anderson, T.W. and Darling, D.A. (1954) A Test of Goodness of Fit. Journal of the American Statistical Association, 49, 765-769.
https://doi.org/10.1080/01621459.1954.10501232

Full-Text

comments powered by Disqus

Contact Us

service@oalib.com

QQ:3279437679

微信:OALib Journal