Tempered stable Ornstein– Uhlenbeck processes: A practical view

References

• Abramowitz, M., Stegun, I. A. (1974). Handbook of Mathematical Functions: With Formulas, Graphs, and Mathematical Tables. New York: Dover Publications.
   Google Scholar
• Ballotta, L., Kyriakou, I. (2014). Monte Carlo simulation of the CGMY process and option pricing. Journal of Futures Markets 34:1095–1121.
   Google Scholar
• Barndorff-Nielsen, O. E., Shephard, N. (2001). Non-Gaussian Ornstein-Uhlenbeck-based models and some of their uses in financial economics. Journal of the Royal Statistical Society: Series B 63:167–241.
   Google Scholar
• Barndorff-Nielsen, O. E., Shephard, N. (2003). Integrated OU processes and non-Gaussian OU-based stochastic volatility models. Scandinavian Journal of Statistics 30:277–295.
   Google Scholar
• Bianchi, M. L. (2012). An Empirical Comparison of Alternative Credit Default Swap Pricing Models. Working Paper 882. Bank of Italy: The Bank of Italy.
   Google Scholar
• Bianchi, M. L. (2015). Are the Log-Returns of Italian Open-End Funds Normally Distributed?A Risk Assessment Perspective. Journal of Asset Management. 16:437–449.
   Google Scholar
• Bianchi, M. L., Fabozzi, F. J. (2015). Investigating the performance of non-Gaussian stochastic intensity models in the calibration of credit default swap spreads. Computational Economics 46:243–273.
   Google Scholar
• Bianchi, M. L., Fabozzi, F. J., Rachev, S. T. (2016). Calibrating the Italian smile with time-varying volatility and heavy-tailed models. Computational Economics, forthcoming.
   Google Scholar
• Bianchi, M. L., Rachev, S. T., Kim, Y. S., Fabozzi, F. J. (2010a). Tempered stable distributions and processes in finance: Numerical analysis. In: Corazza, M., Pizzi, C., eds. Mathematical and Statistical Methods for Actuarial Sciences and Finance. Berlin, Heidelberg; New York: Springer, pp. 33–42.
   Google Scholar
• Bianchi, M. L., Rachev, S. T., Kim, Y. S., Fabozzi, F. J. (2010b). Tempered infinitely divisible distributions and processes. Theory of Probability and Its Applications 55:59–86.
   Google Scholar
• Cariboni, J., Schoutens, W. (2009). Jumps in intensity models: Investigating the performance of Ornstein-Uhlenbeck processes in credit risk modeling. Metrika 69:173–198.
   Google Scholar
• Chambers, J. M., Mallows, C. L., Stuck, B. W. (1976). A method for simulating stable random variables. Journal of the American Statistical Association 71:340–344.
   Google Scholar
• Cont, R., Tankov, P. (2004). Financial Modelling with Jump Processes. Boca Raton, FL: Chapman & Hall.
   Google Scholar
• Devroye, L. (2009). Random variate generation for exponentially and polynomially tilted stable distributions. ACM Transactions on Modeling and Computer Simulation 19(article 18).
   Google Scholar
• Eberlein, E., Raible, S. (1999). Term structure models driven by general Lévy processes. Mathematical Finance 9:31–53.
   Google Scholar
• Gentle, J. E. (2003). Random Number Generation and Monte Carlo Methods. New York: Springer.
   Google Scholar
• Gil, A., Segura, J., Temme, N. M. (2007). Numerical Methods for Special Functions. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM).
   Google Scholar
• Grabchak, M. (2012). On a new class of tempered stable distributions: Moments and regular variation. Journal of Applied Probability 49:1015–1035.
   Google Scholar
• Gradshteĭn, I. S., Ryzhik, I. M. (2007). Table of Integrals, Series, and Products. 7th ed. San Diego, CA: Academic Press.
   Google Scholar
• Imai, J., Kawai, R. (2011). On finite truncation of infinite shot noise series representation of tempered stable laws. Physics A 390:4411–4425.
   Google Scholar
• Jelonek, P. (2012). Generating Tempered Stable Random Variates from Mixture Representation. Working Paper 14. University of Leicester, Department of Economics Leicester, UK: University of Leicester.
   Google Scholar
• Johnson, N. L., Kotz, S., Balakrishnan, N. (1994). Continuous Univariate Distributions. Vol. 1. 2nd ed. New York: John Wiley & Sons.
   Google Scholar
• Kawai, R., Masuda, H. (2011a). Exact discrete sampling of finite variation tempered stable Ornstein-Uhlenbeck processes. Monte Carlo Methods and Applications 17:279–300.
   Google Scholar
• Kawai, R., Masuda, H. (2001b). On simulation of tempered stable random variates. Journal of Computational and Applied Mathematics 235:2873–2887.
   Google Scholar
• Kawai, R., Masuda, H. (2012). Infinite variation tempered stable Ornstein-Uhlenbeck processes with discrete observations. Communications in Statistics - Simulation and Computation 41:125–139.
   Google Scholar
• Keller-Ressel, M., Papapantoleon, A., Teichmann, J. (2013). The affine LIBOR models. Mathematical Finance 23:627–658.
   Google Scholar
• Kim, Y. S., Rachev, S. T., Bianchi, M. L., Fabozzi, F. J. (2010b). Tempered stable and tempered infinitely divisible GARCH models. Journal of Banking and Finance 34:2096–2109.
   Google Scholar
• Kokholm, T., Nicolato, E. (2010). Sato processes in default modelling. Applied Mathematical Finance 17:377–397.
   Google Scholar
• Nicolato, E., Venardos, E. (2003). Option pricing in stochastic volatility models of the Ornstein-Uhlenbeck type. Mathematical Finance 13:445–466.
   Google Scholar
• Rachev, S. T., Kim, Y. S., Bianchi, M. L., Fabozzi, F. J. (2011). Financial Models with Lévy Processes and Volatility Clustering. Hoboken, NJ: Wiley.
   Google Scholar
• Ridout, M. S. (2009). Generating random numbers from a distribution specified by its Laplace transform. Statistics and Computing 19:439–450.
   Google Scholar
• Rosiński, J. (2001). Series representations of Lévy processes from the perspective of point processes. In: Barndorff-Nielsen, O. E., Mikosch, T., Resnick, S. I., eds. Lévy Processes: Theory and Applications. Boston; Basel; Berlin: Birkhäuser, pp. 401–415.
   Google Scholar
• Rosiński, J. (2007). Tempering stable processes. Stochastic Processes and their Applications 117:677–707.
   Google Scholar
• Rosiński, J., Sinclair, J. L. (2010). Generalized tempered stable processes. In: Misiewicz, J. K., ed. Stability in Probability. Warsaw: Banach Center Publication 90, pp. 153–170.
   Google Scholar
• Scherer, M., Rachev, S. T., Kim, Y. S., Fabozzi, F. J. (2012). Approximation of skewed and leptokurtic return distributions. Applied Financial Economics 22:1305–1316.
   Google Scholar
• Schoenberg, I. J. (1938). Metric spaces and completely monotone functions. Annals of Mathematics 39:811–841.
   Google Scholar
• Schoutens, W. (2003). Lévy processes in Finance: Pricing Financial Derivatives. New York: Wiley.
   Google Scholar
• Stoyanov, S., Racheva-Iotova, B. (2004). Numerical methods for stable modeling in financial risk management. In: Rachev, S. T., ed. Handbook of Computational and Numerical Methods in Finance. Boston; Basel; Berlin: Birkhäuser, pp. 299–329.
   Google Scholar
• Terdik, G., Woyczyński, W. A. (2006). Rosiński measures for tempered stable and related Ornstein-Uhlenbeck processes. Probability and Mathematical Statistics 26:213–243.
   Google Scholar
• Tricomi, F. G. (1954). Funzioni Ipergeometriche Confluenti. Roma: Edizioni Cremonese.
   Google Scholar
• Wyłomańska, A. (2011). Measures of dependence for Ornstein-Uhlenbeck processes with tempered stable distribution. Acta Physica Polonica B 42:2049–2062.
   Google Scholar
• Zhang, S. (2011). Exact simulation of tempered stable Ornstein-Uhlenbeck processes. Journal of Statistical Computation and Simulation 81(11):1533–1544.
   Google Scholar
• Zhang, S., Zhang, X. (2008). Exact simulation of IG-OU processes. Methodology and Computing in Applied Probability 10:337–355.
   Google Scholar
• Zhang, S., Zhang, X. (2009). On the transition law of tempered stable Ornstein-Uhlenbeck processes. Journal of Applied Probability 46:721–731.
   Google Scholar