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Original Articles

Market calibration under a long memory stochastic volatility model

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Pages 323-343 | Received 08 Jan 2015, Accepted 15 Dec 2016, Published online: 25 Jan 2017

References

  • Asai, M., M. McAleer, and M. C. Medeiros. 2012. “Modelling and Forecasting Noisy Realized Volatility.” Computation Statist Data Analysis 56 (1): 217–230. doi:10.1016/j.csda.2011.06.024.
  • Bates, D. S. 1996. “Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options.” Review of Financial Studies 9 (1): 69–107. doi:10.1093/rfs/9.1.69.
  • Beran, J., Y. Feng, S. Ghosh, and R. Kulik. 2013. Long-Memory Processes. Heidelberg: Springer,Probabilistic properties and statistical methods.
  • Bollerslev, T., and O. H. Mikkelsen. 1996. “Modeling and Pricing Long Memory in Stock Market Volatility.” Journal of Econometrics 73 (1): 151–184. doi:10.1016/0304-4076(95)01736-4.
  • Breidt, F. J., N. Crato, and P. De Lima. 1998. “The Detection and Estimation of Long Memory in Stochastic Volatility.” Journal of Econometrics 83 (1–2): 325–348. doi:10.1016/S0304-4076(97)00072-9.
  • Čekal, M., 2012 The Effect of Long Memory Volatility on Option Pricing. Master’s thesis, University of Amsterdam.
  • Comte, F., L. Coutin, and E. M. ´ Renault. 2012. “Affine Fractional Stochastic Volatility Models.” Annals of Finance 8 (2–3): 337–378. doi:10.1007/s10436-010-0165-3.
  • Comte, F., and E. ´M. Renault. 1998. “Long Memory in Continuous-Time Stochastic Volatility Models.” Mathematical Finance 8 (4): 291–323. doi:10.1111/mafi.1998.8.issue-4.
  • Cont, R. 2001. “Empirical Properties of Asset Returns: Stylized Facts and Statistical Issues.” Quantitative Finance 1 (2): 223–236. doi:10.1080/713665670.
  • Ding, Z., C. W. J. Granger, and R. F. Engle. 1993. “A Long Memory Property of Stock Market Returns and A New Model.” Journal of Empirical Finance 1 (1): 83–106. doi:10.1016/0927-5398(93)90006-D.
  • Duffie, D., J. Pan, and K. Singleton. 2000. “Transform Analysis and Asset Pricing for Affine Jump-Diffusions.” Econometrica 68: 1343–1376. doi:10.1111/ecta.2000.68.issue-6.
  • Gatheral, J. 2006. The Volatility Surface: A Practitioner’s Guide. Hoboken, NJ: Wiley Finance (John Wiley & Sons).
  • Granger, C. W. J., and R. Joyeux. 1980. “An Introduction to Long-Memory Time Series Models and Fractional Differencing.” Journal of Time Series Analysis 1 (1): 15–29. doi:10.1111/j.1467-9892.1980.tb00297.x.
  • Heston, S. L. 1993. “A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options.” Review of Financial Studies 6: 327–343. doi:10.1093/rfs/6.2.327.
  • Intarasit, A., and P. Sattayatham. 2011. “An Approximate Formula of European Option for Fractional Stochastic Volatility Jump-Diffusion Model.” Journal of Mathematics and Statistics 7 (3): 230–238. doi:10.3844/jmssp.2011.230.238.
  • Koopman, S. J., B. Jungbacker, and E. Hol. 2005. “Forecasting Daily Variability of the S&P 100 Stock Index Using Historical, Realised and Implied Volatility Measurements.” Journal of Empirical Finance 12 (3): 445–475. doi:10.1016/j.jempfin.2004.04.009.
  • Lewis, A. L. 2000. Option Valuation under Stochastic Volatility, with Mathematica Code. Newport Beach, CA: Finance Press.
  • Mandelbrot, B., and J. Van Ness. 1968. “Fractional Brownian Motions, Fractional Noises and Applications.” SIAM Review 10: 422–437. doi:10.1137/1010093.
  • Martens, M., D. Van Dijk, and M. De Pooter, Modeling and Forecasting S&P 500 Volatility: Long Memory, Structural Breaks and Nonlinearity. (2004), Technical report TI 04–067/4, Tinbergen Institute.
  • Mikhailov, S., and U. Nögel (2003) Heston’s Stochastic Volatility Model-Implementation, Calibration and Some Extensions., Wilmott magazine, pp. 74–79.
  • Øksendal, B. (2003) Stochastic Differential Equations. An Introduction With Applications. Sixth edition. Universitext. Springer-Verlag, Berlin. ISBN: 3-540-04758-1
  • Osajima, Y., The Asymptotic Expansion Formula of Implied Volatility for Dynamic SABR Model and FX Hybrid Model. (2007), Technical report, BNP Paribas Available from SSRN: http://ssrn.com/abstract=965265.
  • Shreve, S. E. 2004. Stochastic Calculus for Finance. II. New York: Springer Finance Springer-Verlag.
  • Sircar, K. R., and G. C. Papanicolaou. 1999. “Stochastic Volatility, Smile & Asymptotics.” Applied Mathematical Finance 6 (2): 107–145. doi:10.1080/135048699334573.
  • Sobotka, T., 2014 Stochastic and fractional stochastic volatility models. Master’s thesis, University of West Bohemia.
  • Taylor, S. 1986. Modelling Financial Time Series. Chichester: John Wiley & Sons.
  • Thao, T. H. 2006. “An Approximate Approach to Fractional Analysis for Finance.” Nonlinear Analysis: Real World Applications 7: 124–132. doi:10.1016/j.nonrwa.2004.08.012.
  • Thao, T. H., and T. T. Nguyen. 2003. “Fractal Langevin Equation.” Vietnam Journal Mathematics 30 (1): 89–96.
  • Zähle, M. (1998). Integration With Respect To Fractal Functions And Stochastic Calculus. I. Probability Theory Related Fields 111 (3): 333–374. doi:10.1007/s004400050171
  • Zumbach, G. 2013. Discrete Time Series, Processes, and Applications in Finance. Heidelberg: Springer Finance (Springer.
  • Zumbach, G., and L. Fern´Andez. 2013. “Fast and Realistic European ARCH Option Pricing and Hedging.” Quantitative Finance 13 (5): 713–728. doi:10.1080/14697688.2012.750009.
  • Zumbach, G., and L. Fern´Andez. 2014. “Option Pricing with Realistic ARCH Processes.” Quantitative Finance 14 (1): 143–170. doi:10.1080/14697688.2013.816437.

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