Abstract
In this study we deal with aspects of the modeling of the asset prices by means Ornstein-Uhlenbech process driven by Lévy process. Barndorff-Nielsen and Shephard stochastic volatility model allows the volatility parameter to be a self-decomposable distribution. BNS models allow flexible modeling. For this reason we use as a model the IG-Ornstein-Uhlenbeck process. We calibrate moments of Lévy process and OU process. Finally we fit the model some real data series. We present a simulation study.
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References
Barndorff-Nielsen, O.E., Shephard, N.: Non-Gaussian Ornstein-Uhlenbeck-based models and some of their uses in financial economics (with discussion). J. Roy. Stat. Soc. Series B 63, 167–241 (2001).
Barndorff-Nielsen, O.E., Shephard, N.: Financial volatility, Lévy processes and pover variation (2000). www.levyprocess.org.
Schoutens, W.: Lévy Processes in Finance: Pricing Financial Derivatives. Wiley, England (2003)
Papapantoleon, A.: An introduction to Lévy proceses with application to finance (2008). http://arxiv.org/PS_cache/arxiv/pdf/0804/0804.0482v2.pdf
Graf, F.: Exotic option pricing in stochastic volatility Lévy models and with fractional Brownian motion. Thesis, Universitat Konstanz (2007)
Protter, P.: Stochastic Integration and Differential Equations. Springer, Berlin (1990)
Sato, K.I.: Levy Processes and Infinitely Divisible Distributions. Cambridge University Press, Cambridge (1991)
Spiliopoulos, K.: Method of moments of Ornstein-Uhlenbeck processes driven by general Lévy processes (2008). http://www.math.umd.edu/~kspiliop/
Valdivieso, L.: Parameter estimation for an IG_OU stochastic volatility model (2005). http://lstat.kuleuven.be/research/seminars_events/files/3afmd/valdivieso.PDF
Lindberg, C.: The estimation of the Barndorff-Nielsen and Shephard model from daily data based on measures of trading intensity. Appl. Stochast. Model. Business Indus. 24, 277–289 (2008)
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Önalan, Ö. (2010). The Ornstein–Uhlenbeck Processes Driven by Lévy Process and Application to Finance. In: Ao, SI., Gelman, L. (eds) Electronic Engineering and Computing Technology. Lecture Notes in Electrical Engineering, vol 60. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-8776-8_38
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DOI: https://doi.org/10.1007/978-90-481-8776-8_38
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