دانشگاه تبریز
فهرست نشریات دارای اعتبار وزارت علوم، تحقیقات و فناوری
پایگاه استنادی علوم جهان اسلام (ISC)

 آمار

تعداد نشریات45
تعداد شماره‌ها1,416
تعداد مقالات17,490
تعداد مشاهده مقاله56,510,330
تعداد دریافت فایل اصل مقاله18,750,569
Dastranj, Elham, Sahebi Fard, Hossein. (1401). Exact solutions and numerical simulation for Bakstein-Howison model. سامانه مدیریت نشریات علمی, 10(2), 461-474. doi: 10.22034/cmde.2021.42640.1834
Elham Dastranj; Hossein Sahebi Fard. "Exact solutions and numerical simulation for Bakstein-Howison model". سامانه مدیریت نشریات علمی, 10, 2, 1401, 461-474. doi: 10.22034/cmde.2021.42640.1834
Dastranj, Elham, Sahebi Fard, Hossein. (1401). 'Exact solutions and numerical simulation for Bakstein-Howison model', سامانه مدیریت نشریات علمی, 10(2), pp. 461-474. doi: 10.22034/cmde.2021.42640.1834
Dastranj, Elham, Sahebi Fard, Hossein. Exact solutions and numerical simulation for Bakstein-Howison model. سامانه مدیریت نشریات علمی, 1401; 10(2): 461-474. doi: 10.22034/cmde.2021.42640.1834

Exact solutions and numerical simulation for Bakstein-Howison model

Computational Methods for Differential Equations
مقاله 13، دوره 10، شماره 2، تیر 2022، صفحه 461-474    اصل مقاله (691.6 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2021.42640.1834
نویسندگان
Elham Dastranj* 1؛ Hossein Sahebi Fard2
1Faculty of Mathematical Sciences, Shahrood university of technology, Shahrood, Semnan, Iran.
2Faculty of Mathematical Sciences, Shahrood university of technology, Shahrood, Semnan, Iran
چکیده
In this paper, European options with transaction cost under some Black-Scholes markets are priced. In fact, stochastic analysis and Lie group analysis are applied to find exact solutions for European options pricing under considered markets. In the sequel, using the finite difference method, numerical solutions are presented as well. Finally, European options pricing are presented in four maturity times under some Black-Scholes models equipped with the gold asset as underlying asset. For this, the daily gold world price has been followed from Jan 1, 2016 to Jan 1, 2019 and the results of the profit and loss of options under the considered models indicate that call options prices prevent arbitrage opportunity but put options create it. 
کلیدواژه‌ها
Black-Scholes models؛ Transaction cost؛ Lie symmetries؛ Finite difference method
مراجع
  • [1]          M. B. Almatrafi, A. R. Alharbi, and C. Tunç, Constructions of the soliton solutions to the good Boussinesq equation, Advances in Difference Equations 2020, 1 (2020), 1-14.
  • [2]          M. Al-Asad, M. N. Alam, C. Tunç,  and M. M. A. Sarker, Heat  Transport  Exploration of  Free  Convection Flow   inside Enclosure Having Vertical Wavy Walls, Journal of Applied and Computational Mechanics, (2020). DOI: 10.22055/jacm.2020.35381.2646.
  • [3]          M. N. Alam and C. Tunç, New solitary wave structures to the (2+ 1)-dimensional KD and KP equations with spatio-temporal dispersion, Journal of King Saud University-Science, 32(8) (2020), 3400-3409.
  • [4]          D. Bakstein and S. Howison, A non-arbitrage liquidity model with observable parameters for derivatives, working paper, Oxford center for industrial and applied mathematics, Oxford, 1-52 (2003).
  • [5]          U. Cetin, R. Jarrow, and P. Protter, Liquidity risk and arbitrage pricing theory, Finance Stoch., 8 (2004), 311-341.
  • [6]          E. Dastranj and S. R. Hejazi, New Solutions for Fokker-Plank Equation of Special Stochastic Process via Lie Point Symmetries, Computational Methods for Differential Equations, 5(1) (2017), 30-42.
  • [7]          E. Dastranj and R. Latifi, A comparison of option pricing models, international journal of financial engineering, February 21, (2017),4.02n03, 1750024.
  • [8]          E. Dastranj and S. R. Hejazi, Exact solutions for Fokker-Plank equation of geometric Brownian  motion  with  Lie  point symmetries,Computational Methods for Differential Equations, 6(3) (2018), 372-379.
  • [9]          E. Dastranj and et al., Power option pricing under the unstable conditions (Evidence of power option pricing under fractional Heston model in the Iran gold market), Physica A: Statistical Mechanics and its Applications, 537: 122690 (2020).
  • [10]        G. Dura and A. M. Moşneagu, Numerical approximation of Black-Scholes equation, Annals of the AlexandruIoan- Cuza University-Mathematics, 56(1) (2010), 39-64.
  • [11]        J. E. Esekon,  A particular solution of a nonlinear Black-Scholes partial differential equation,  International Journal  of Pure and Applied Mathematics, 81(5) (2012), 715-721.
  • [12]        J. E. Esekon, Analytic solution of a nonlinear Black-Scholes equation, International Journal of Pure and Applied Mathematics, 82(4) (2013), 547-555.
  • [13]        M. J. Fleming and E. M. Remolona, Price formation and liquidity in the U.S. Treasury market: The response to public information, The Journal of Finance, 54(5) (1999), 1901-1915.
  • [14]        S. R. Hejazi, Lie group analysis, Hamiltonian equations and conservation laws of Born–Infeld equation, Asian- European Journal of Mathematics, 7(3) (2014), 1450040.
  • [15]        S. R. Hejazi, Lie point symmetries, Hamiltonian equation and conservation laws of the geodesics on a Schwarzschild Black hole, Kragujevac Journal of Mathematics, 42(3) (2014), 453–475.
  • [16]        E. A. Hussain and Y. M. Alrajhi, Numerical Solution of Nonlinear Black–Scholes Equation by Accelerated Genetic Algorithm, Mathematical Theory and Modeling, 5(4) (2015), 53-66.
  • [17]        E. Lashkarian, S. R. Hejazi, N. Habibi, and A. Motamednezhad, Symmetry properties, conservation laws, reduc- tion and numerical approximations of time-fractional cylindrical-Burgers equation, Communications in Nonlinear Science and Numerical Simulation, 67 (2019), 176-191.
  • [18]        E. Lashkarian, E. Saberi, and S. R. Hejazi, Symmetry reductions and  exact  solutions  for  a  class  of  nonlinear PDEs, Asian-European Journal of Mathematics, 9(2) (2016), 1650061.
  • [19]        S. Mashayekhi and J. Hugger,  Finite difference  schemes for a nonlinear Black-Scholes model with transaction cost   and volatility risk, Acta Mathematica Universitatis Comenianae, 84(2) (2015), 255-266.
  • [20]        P. J. Olver, Applications of Lie groups to differential equations, Springer Science and Business Media, 107 (2000).
  • [21]        C. Tunc, C. Islam, M. Alam, and M. Al-Asad, An analytical technique for  solving  new  computational  of  the  modified Zakharov-Kuznetsov equation arising in electrical engineering, Journal of Applied and Computational Mechanics, (2020). DOI: 10.22055/jacm.2020.35571.2687.
آمار
تعداد مشاهده مقاله: 761
تعداد دریافت فایل اصل مقاله: 919


سامانه مدیریت نشریات علمی. قدرت گرفته از سیناوب