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A General Fractional White Noise Theory And Applications To Finance

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Cited by:

  1. Taghipour, M. & Aminikhah, H., 2022. "A spectral collocation method based on fractional Pell functions for solving time–fractional Black–Scholes option pricing model," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).
  2. Nikolai Leonenko & EStuart Petherick & Emanuele Taufer, 2012. "Multifractal Scaling for Risky Asset Modelling," DISA Working Papers 2012/07, Department of Computer and Management Sciences, University of Trento, Italy, revised Jul 2012.
  3. Grecksch Wilfried & Roth Christian, 2008. "A quasilinear stochastic partial differential equation driven by fractional white noise," Monte Carlo Methods and Applications, De Gruyter, vol. 13(5-6), pages 353-367, January.
  4. Kedia, Nikki & Alikhanov, Anatoly A. & Singh, Vineet Kumar, 2024. "Robust finite difference scheme for the non-linear generalized time-fractional diffusion equation with non-smooth solution," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 219(C), pages 337-354.
  5. Didier Alain Njamen Njomen & Eric Djeutcha, 2019. "Solving Black-Schole Equation Using Standard Fractional Brownian Motion," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 11(2), pages 142-157, April.
  6. Bender, Christian, 2014. "Backward SDEs driven by Gaussian processes," Stochastic Processes and their Applications, Elsevier, vol. 124(9), pages 2892-2916.
  7. Wang, Xiao-Tian, 2011. "Scaling and long-range dependence in option pricing V: Multiscaling hedging and implied volatility smiles under the fractional Black–Scholes model with transaction costs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(9), pages 1623-1634.
  8. Lahiri, Ananya & Sen, Rituparna, 2020. "Fractional Brownian markets with time-varying volatility and high-frequency data," Econometrics and Statistics, Elsevier, vol. 16(C), pages 91-107.
  9. Zunino, L. & Pérez, D.G. & Garavaglia, M. & Rosso, O.A., 2007. "Wavelet entropy of stochastic processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 379(2), pages 503-512.
  10. Los, Cornelis A. & Yu, Bing, 2008. "Persistence characteristics of the Chinese stock markets," International Review of Financial Analysis, Elsevier, vol. 17(1), pages 64-82.
  11. Xiao, Weilin & Zhang, Weiguo & Xu, Weijun & Zhang, Xili, 2012. "The valuation of equity warrants in a fractional Brownian environment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(4), pages 1742-1752.
  12. R. Vilela Mendes & M. J. Oliveira & A. M. Rodrigues, 2012. "The fractional volatility model: No-arbitrage, leverage and completeness," Papers 1205.2866, arXiv.org.
  13. Zhaoqiang Yang, 2017. "Efficient valuation and exercise boundary of American fractional lookback option in a mixed jump-diffusion model," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 4(02n03), pages 1-29, June.
  14. Pérez, D.G. & Zunino, L. & Garavaglia, M. & Rosso, O.A., 2006. "Wavelet entropy and fractional Brownian motion time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 365(2), pages 282-288.
  15. Akinlar, M.A. & Inc, Mustafa & Gómez-Aguilar, J.F. & Boutarfa, B., 2020. "Solutions of a disease model with fractional white noise," Chaos, Solitons & Fractals, Elsevier, vol. 137(C).
  16. Changhong Guo & Shaomei Fang & Yong He, 2023. "Derivation and Application of Some Fractional Black–Scholes Equations Driven by Fractional G-Brownian Motion," Computational Economics, Springer;Society for Computational Economics, vol. 61(4), pages 1681-1705, April.
  17. Cornelis A. Los & Rossitsa M. Yalamova, 2004. "Multi-Fractal Spectral Analysis of the 1987 Stock Market Crash," Finance 0409050, University Library of Munich, Germany.
  18. Stoyan V. Stoyanov & Svetlozar T. Rachev & Stefan Mittnik & Frank J. Fabozzi, 2019. "Pricing Derivatives In Hermite Markets," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(06), pages 1-27, September.
  19. Erhan Bayraktar & H. Vincent Poor & K. Ronnie Sircar, 2004. "Estimating The Fractal Dimension Of The S&P 500 Index Using Wavelet Analysis," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 7(05), pages 615-643.
  20. Ngai Hang Chan & Chi Tim Ng, 2007. "Fractional constant elasticity of variance model," Papers math/0702810, arXiv.org.
  21. Long Bai & Peng Liu, 2019. "Drawdown and Drawup for Fractional Brownian Motion with Trend," Journal of Theoretical Probability, Springer, vol. 32(3), pages 1581-1612, September.
  22. Yan, Litan, 2004. "Maximal inequalities for the iterated fractional integrals," Statistics & Probability Letters, Elsevier, vol. 69(1), pages 69-79, August.
  23. Kim, Hyun-Gyoon & Kim, See-Woo & Kim, Jeong-Hoon, 2024. "Variance and volatility swaps and options under the exponential fractional Ornstein–Uhlenbeck model," The North American Journal of Economics and Finance, Elsevier, vol. 72(C).
  24. Kyaw, NyoNyo A. & Los, Cornelis A. & Zong, Sijing, 2006. "Persistence characteristics of Latin American financial markets," Journal of Multinational Financial Management, Elsevier, vol. 16(3), pages 269-290, July.
  25. Karuppiah, Jeyanthi & Los, Cornelis A., 2005. "Wavelet multiresolution analysis of high-frequency Asian FX rates, Summer 1997," International Review of Financial Analysis, Elsevier, vol. 14(2), pages 211-246.
  26. Azmoodeh Ehsan & Mishura Yuliya & Valkeila Esko, 2009. "On hedging European options in geometric fractional Brownian motion market model," Statistics & Risk Modeling, De Gruyter, vol. 27(02), pages 129-144, December.
  27. Changhong Guo & Shaomei Fang & Yong He, 2023. "A Generalized Stochastic Process: Fractional G-Brownian Motion," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-34, March.
  28. Wolfgang Schadner & Sebastian Lang, 2023. "The value of expected return persistence," Annals of Finance, Springer, vol. 19(4), pages 449-476, December.
  29. Leonenko, Nikolai & Petherick, Stuart & Taufer, Emanuele, 2013. "Multifractal models via products of geometric OU-processes: Review and applications," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(1), pages 7-16.
  30. Kim, Seong-Tae & Kim, Hyun-Gyoon & Kim, Jeong-Hoon, 2021. "ELS pricing and hedging in a fractional Brownian motion environment," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
  31. Xu, Xiao & Wang, Li & Du, Zhenbin & Kao, Yonggui, 2023. "H∞ Sampled-Data Control for Uncertain Fuzzy Systems under Markovian Jump and FBm," Applied Mathematics and Computation, Elsevier, vol. 451(C).
  32. Heydari, M.H. & Avazzadeh, Z. & Mahmoudi, M.R., 2019. "Chebyshev cardinal wavelets for nonlinear stochastic differential equations driven with variable-order fractional Brownian motion," Chaos, Solitons & Fractals, Elsevier, vol. 124(C), pages 105-124.
  33. Wolfgang Schadner, 2019. "Risk-Neutral Momentum and Market Fear," Working Papers on Finance 1915, University of St. Gallen, School of Finance.
  34. Alpay, Daniel & Attia, Haim & Levanony, David, 2010. "On the characteristics of a class of Gaussian processes within the white noise space setting," Stochastic Processes and their Applications, Elsevier, vol. 120(7), pages 1074-1104, July.
  35. Xiao, Wei-Lin & Zhang, Wei-Guo & Zhang, Xili & Zhang, Xiaoli, 2012. "Pricing model for equity warrants in a mixed fractional Brownian environment and its algorithm," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(24), pages 6418-6431.
  36. Yuecai Han & Xudong Zheng, 2022. "Approximate Pricing of Derivatives Under Fractional Stochastic Volatility Model," Papers 2210.15453, arXiv.org.
  37. Jamdee, Sutthisit & Los, Cornelis A., 2007. "Long memory options: LM evidence and simulations," Research in International Business and Finance, Elsevier, vol. 21(2), pages 260-280, June.
  38. Rostek, Stefan & Schöbel, Rainer, 2006. "Risk preference based option pricing in a fractional Brownian market," Tübinger Diskussionsbeiträge 299, University of Tübingen, School of Business and Economics.
  39. Jian Pan & Xiangying Zhou, 2017. "Pricing for options in a mixed fractional Hull–White interest rate model," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 4(01), pages 1-15, March.
  40. Nils Chr. Framstad, 2014. "When can the environmental profile and emissions reduction be optimised independently of the pollutant level?," Journal of Environmental Economics and Policy, Taylor & Francis Journals, vol. 3(1), pages 25-45, March.
  41. Los, Cornelis A. & Tungsong, Satjaporn, 2008. "Investment Model Uncertainty and Fair Pricing," MPRA Paper 8859, University Library of Munich, Germany.
  42. Wang, Xiao-Tian & Wu, Min & Zhou, Ze-Min & Jing, Wei-Shu, 2012. "Pricing European option with transaction costs under the fractional long memory stochastic volatility model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(4), pages 1469-1480.
  43. Schadner, Wolfgang, 2020. "An idea of risk-neutral momentum and market fear," Finance Research Letters, Elsevier, vol. 37(C).
  44. Tebaldi, Claudio, 2005. "Hedging using simulation: a least squares approach," Journal of Economic Dynamics and Control, Elsevier, vol. 29(8), pages 1287-1312, August.
  45. Jung, Paul & Markowsky, Greg, 2014. "On the Tanaka formula for the derivative of self-intersection local time of fractional Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 124(11), pages 3846-3868.
  46. Yang, Zhaoqiang, 2020. "Default probability of American lookback option in a mixed jump-diffusion model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
  47. Stoyan V. Stoyanov & Yong Shin Kim & Svetlozar T. Rachev & Frank J. Fabozzi, 2017. "Option pricing for Informed Traders," Papers 1711.09445, arXiv.org.
  48. Biagini, Francesca & Fink, Holger & Klüppelberg, Claudia, 2013. "A fractional credit model with long range dependent default rate," Stochastic Processes and their Applications, Elsevier, vol. 123(4), pages 1319-1347.
  49. Kazmerchuk, Yuriy & Swishchuk, Anatoliy & Wu, Jianhong, 2007. "The pricing of options for securities markets with delayed response," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 75(3), pages 69-79.
  50. Lebovits, Joachim & Lévy Véhel, Jacques & Herbin, Erick, 2014. "Stochastic integration with respect to multifractional Brownian motion via tangent fractional Brownian motions," Stochastic Processes and their Applications, Elsevier, vol. 124(1), pages 678-708.
  51. Dufera, Tamirat Temesgen, 2024. "Fractional Brownian motion in option pricing and dynamic delta hedging: Experimental simulations," The North American Journal of Economics and Finance, Elsevier, vol. 69(PB).
  52. Tapiero, Charles S. & Vallois, Pierre, 2018. "Fractional Randomness and the Brownian Bridge," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 503(C), pages 835-843.
  53. Litan Yan & Yu Sun & Yunsheng Lu, 2008. "On the Linear Fractional Self-attracting Diffusion," Journal of Theoretical Probability, Springer, vol. 21(2), pages 502-516, June.
  54. Jean-Philippe Aguilar & Jan Korbel & Yuri Luchko, 2019. "Applications of the Fractional Diffusion Equation to Option Pricing and Risk Calculations," Mathematics, MDPI, vol. 7(9), pages 1-23, September.
  55. Xiao, Wei-Lin & Zhang, Wei-Guo & Zhang, Xi-Li & Wang, Ying-Luo, 2010. "Pricing currency options in a fractional Brownian motion with jumps," Economic Modelling, Elsevier, vol. 27(5), pages 935-942, September.
  56. Hamza Guennoun & Antoine Jacquier & Patrick Roome & Fangwei Shi, 2014. "Asymptotic behaviour of the fractional Heston model," Papers 1411.7653, arXiv.org, revised Aug 2017.
  57. Rostek, S. & Schöbel, R., 2013. "A note on the use of fractional Brownian motion for financial modeling," Economic Modelling, Elsevier, vol. 30(C), pages 30-35.
  58. Vilela Mendes, R. & Oliveira, M.J. & Rodrigues, A.M., 2015. "No-arbitrage, leverage and completeness in a fractional volatility model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 419(C), pages 470-478.
  59. Christian Bender & Robert J. Elliott, 2004. "Arbitrage in a Discrete Version of the Wick-Fractional Black-Scholes Market," Mathematics of Operations Research, INFORMS, vol. 29(4), pages 935-945, November.
  60. Panhong Cheng & Zhihong Xu & Zexing Dai, 2023. "Valuation of vulnerable options with stochastic corporate liabilities in a mixed fractional Brownian motion environment," Mathematics and Financial Economics, Springer, volume 17, number 3, March.
  61. Sun, Lin, 2013. "Pricing currency options in the mixed fractional Brownian motion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(16), pages 3441-3458.
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