412
Views
14
CrossRef citations to date
0
Altmetric
Original Articles

Parameter identification for the discretely observed geometric fractional Brownian motion

, &
Pages 269-283 | Received 12 Mar 2013, Accepted 07 Jun 2013, Published online: 29 Jul 2013

References

  • Black F, Scholes M The pricing of options and corporate liabilities. J Political Econ., 1973;81(3):637–654. (doi: 10.1086/260062)
  • Henry ÓT. Long memory in stock returns: some international evidence. Appl Financial Econ., 2002;12(10):725–729. (doi: 10.1080/09603100010025733)
  • Los CA, Yu B Persistence characteristics of the chinese stock markets. Int Rev Financial Anal., 2008;17(1):64–82. (doi: 10.1016/j.irfa.2006.04.001)
  • Mantegna RN, Stanley HE. An introduction to Econophysics: correlations and complexity in finance. Cambridge: Cambridge University Press; 2000.
  • Sadique S, Silvapulle P Long-term memory in stock market returns: international evidence. Int J Finance Econ., 2001;6(1):59–67. (doi: 10.1002/ijfe.143)
  • Duncan TE, Hu Y, Pasik-Duncan B Stochastic calculus for fractional Brownian motion. I. Theory. SIAM J Control Optim., 2000;38(2):582–612. (doi: 10.1137/S036301299834171X)
  • Elliott RJ, Chan L Perpetual American options with fractional Brownian motion. Quant Finance., 2004;4(2):123–128. (doi: 10.1080/14697680400000016)
  • Elliott RJ, Van Der Hoek J A general fractional white noise theory and applications to finance. Math Finance., 2003;13(2):301–330. (doi: 10.1111/1467-9965.00018)
  • Hu Y, Øksendal B Fractional white noise calculus and applications to finance. Infin Dimens Anal Quantum Probab Relat Top., 2003;6(1):1–32. (doi: 10.1142/S0219025703001110)
  • Mishura Y. Stochastic calculus for fractional Brownian motion and related processes, Berlin: Springer Verlag; 2008.
  • Rostek S. Option pricing in fractional Brownian markets, Berlin: Springer Verlag; 2009.
  • Rao BLSP. Statistical inference for fractional diffusion processes, Chichester: Wiley; 2010.
  • Decreusefond L, Üstünel AS. Stochastic analysis of the fractional Brownian motion. Potential Anal. 1999;10(2):177–214.
  • Hu Y, Nualart D Parameter estimation for fractional Ornstein–Uhlenbeck processes. jStatist Probab Lett., 2010;80(11):1030–1038. (doi: 10.1016/j.spl.2010.02.018)
  • Brouste A Asymptotic properties of MLE for partially observed fractional diffusion system with dependent noises. J Statist Plann Inference., 2010;140(2):551–558. (doi: 10.1016/j.jspi.2009.08.001)
  • Cialenco I Parameter estimations for SPDEs with multiplicative fractional noise. Stoch Dyn., 2010;10(4):561–576. (doi: 10.1142/S0219493710003091)
  • Kleptsyna ML, Le Breton A Statistical analysis of the fractional Ornstein-Uuhlenbeck type process. Stat Inference Stoch Process., 2002;5(3):229–248. (doi: 10.1023/A:1021220818545)
  • Tudor CA, Viens FG Statistical aspects of the fractional stochastic calculus. Ann Statist., 2007;35(3):1183–1212. (doi: 10.1214/009053606000001541)
  • Bertin K, Torres S, Tudor CA Maximum-likelihood estimators and random walks in long memory models. Statistics., 2011;45(4):361–374. (doi: 10.1080/02331881003768750)
  • Hu Y, Nualart D, Xiao W, Zhang W Exact maximum likelihood estimator for drift fractional Brownian motion at discrete observation. Acta Math Sci., 2011;31(5):1851–1859.
  • Xiao WL, Zhang WG, Zhang XL Maximum-likelihood estimators in the mixed fractional Brownian motion. Statistics., 2011;45(1):73–85. (doi: 10.1080/02331888.2010.541254)
  • Xiao W, Zhang W, Xu W Parameter estimation for fractional Ornstein-Uhlenbeck processes at discrete observation. Appl Math Model., 2011;35(9):4196–4207. (doi: 10.1016/j.apm.2011.02.047)
  • Kubilius K, Melichov D Quadratic variations and estimation of the hurst index of the solution of SDE driven by a fractional Brownian motion. Lithuanian Math J., 2010;50(4):401–417. (doi: 10.1007/s10986-010-9095-z)
  • Robbertse W, Lombard FOn maximum likelihood estimation of the long-memory parameter in fractional Gaussian noise. J Stat Comput Simul., 2012, 1–14. In press. doi: 10.1080/00949655.2012.732076
  • Golub GH, Van Loan CF. Matrix computations. Vol. 3. Baltimore and London: Johns Hopkins University Press; 1996.
  • Nualart D, Ortiz-Latorre S. Central limit theorems for multiple stochastic integrals and Malliavin calculus. Stoch Process Appl. 2008;118(4):614–628.
  • Misiran M, Lu Z, Teo KL. Fractional Black-Scholes models: complete MLE with application to fractional option pricing. In International conference on optimization and control; Guiyang, China; 2010 p. 573–586.
  • Coeurjolly JF Simulation and identification of the fractional Brownian motion: a bibliographical and comparative study. J Stat Softw., 2000;5(7):1–53.
  • Paxson V Fast, approximate synthesis of fractional gaussian noise for enerating self-similar network traffic. ACM SIGCOMM Comp Commun Rev., 1997;27(5):5–18. (doi: 10.1145/269790.269792)

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.