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

 آمار

تعداد نشریات44
تعداد شماره‌ها1,340
تعداد مقالات16,468
تعداد مشاهده مقاله53,445,145
تعداد دریافت فایل اصل مقاله16,005,164
Aalaei, Mahboubeh, Manteqipour, Mahnaz. (1401). An adaptive Monte Carlo algorithm for European and American options. سامانه مدیریت نشریات علمی, 10(2), 489-501. doi: 10.22034/cmde.2021.37369.1654
Mahboubeh Aalaei; Mahnaz Manteqipour. "An adaptive Monte Carlo algorithm for European and American options". سامانه مدیریت نشریات علمی, 10, 2, 1401, 489-501. doi: 10.22034/cmde.2021.37369.1654
Aalaei, Mahboubeh, Manteqipour, Mahnaz. (1401). 'An adaptive Monte Carlo algorithm for European and American options', سامانه مدیریت نشریات علمی, 10(2), pp. 489-501. doi: 10.22034/cmde.2021.37369.1654
Aalaei, Mahboubeh, Manteqipour, Mahnaz. An adaptive Monte Carlo algorithm for European and American options. سامانه مدیریت نشریات علمی, 1401; 10(2): 489-501. doi: 10.22034/cmde.2021.37369.1654

An adaptive Monte Carlo algorithm for European and American options

Computational Methods for Differential Equations
مقاله 15، دوره 10، شماره 2، تیر 2022، صفحه 489-501    اصل مقاله (495.34 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2021.37369.1654
نویسندگان
Mahboubeh Aalaei* ؛ Mahnaz Manteqipour
Insurance Research Center, Saadat Abad, Tehran, Iran.
چکیده
In this paper, a new adaptive Monte Carlo algorithm is proposed to solve systems of linear algebraic equations (SLAEs). The corresponding properties of the algorithm and its advantages over the conventional and previous adaptive Monte Carlo algorithms are discussed and theoretical results are established to justify the convergence of the algorithm. Furthermore, the algorithm is used to solve the SLAEs obtained from finite difference method for the problem of European and American options pricing. Numerical tests are performed on examples with matrices of different sizes and on SLAEs coming from option pricing problems. Comparisons with standard numerical and stochastic algorithms are also done which demonstrate the computational efficiency of the proposed algorithm. 
کلیدواژه‌ها
Adaptive Monte Carlo algorithm؛ Finite difference method؛ Black Scholes model؛ European and American put option
مراجع
  • [1]          V. N. Alexandrov, C. G. Martel, and J. Straßburg, Monte Carlo scalable algorithms for computational finance, Procedia Computer Science, 4 (2011), 1708–1715.
  • [2]          A. R. Bacinello, Regression-based algorithms for life insurance contracts with surrender guarantees, Quantitative Finance, 10(9) (2010), 1077–1090.
  • [3]          D. Bauer, A. Kling, and J. Rub, A universal pricing framework for guaranteed minimum benefits in variable annuities, ASTIN Bulletin, 38 (2008), 621–651.
  • [4]          M. H. Chiang, H. H. Fu, Y. T. Huang, C. L. Lo, and P. T. Shih, Analytical Approximations for American Options: The Binary Power Option Approach, Journal of Financial Studies, 26(3) (2018).
  • [5]          M. Dehghan and M. Hajarian, SSHI methods for solving general linear matrix equations, Engineering Computations, 2012.
  • [6]          I. Dimov, S. Maire, and J. M. Sellier, A new walk on equations Monte Carlo method for solving systems of linear algebraic equations, Appl. Math. Model, 39 (2015), 4494–4510
  • [7]          R. Farnoosh and M. Aalaei, New adaptive Monte Carlo algorithm for parallel solution of large linear systems with applications, Proceedings of the Romanian Academy Series A, 16(1) (2015), 11–19.
  • [8]          R. Farnoosh, M. Aalaei, and M. Ebrahimi, Combined probabilistic algorithm for solving high dimensional problems, Stochastics An International Journal of Probability and Stochastic Processes, 87(1) (2015), 30–47.
  • [9]          W. Hackbusch, Iterative Solution of Large Sparse Systems of Equations, Applied Mathematical Sciences, 95 (2016).
  • [10]        J. Halton, Sequential Monte Carlo, Proceedings of the Cambridge Philosophical Society, 58 (1962), 57–78.
  • [11]        C. H. Han and Y. Lai, A smooth estimator for MC/QMC methods in finance, Mathematics and Computers in simulation, 81(3) (2010), 536–550.
  • [12]        A. Jasra and P. D. Moral, Sequential Monte Carlo methods for option pricing, Stochastic analysis and applications, 29 (2011), 292–316.
  • [13]        F. Kiyoumarsi, European and American put valuation via a high-order semi-discretization scheme, Computational Methods for Differential Equations, 6(1) (2018), 63–79.
  • [14]        Y. Lai, Adaptive Monte Carlo methods for matrix equations with applications, Journal of Computational  and  Applied Mathematics, 231 (2009), 705–714.
  • [15]        R. Y. Rubinstein, Simulation and the Monte Carlo method, Wiley, New York, 1981.
  • [16]        D.Y. Tangman, A. Gopaul, and M. Bhuruth, A fast high-order finite difference algorithm for pricing American options, J. Comput. Appl. Math., 222 (2008), 17–29.
  • [17]        I. Vidid, Numerical methods for option pricing, Master Thesis, Master in Advanced Computing for Science and Engineering, Politecnica University, 2012.
آمار
تعداد مشاهده مقاله: 655
تعداد دریافت فایل اصل مقاله: 699


سامانه مدیریت نشریات علمی. قدرت گرفته از سیناوب