‎A GENERALIZED ADAPTIVE MONTE CARLO ALGORITHM BASED ‎ON A ‎‎‎‎TWO-STEP ‎ITERATIVE ‎METHOD‎ FOR ‎LINEAR ‎SYSTEMS AND ITS APPLICATION TO OPTION PRICING

Document Type : Research Paper

Author

Insurance Research Center, Saadat Abad, Tehran, Iran.

Abstract

In this paper‎, ‎we present a ‎‎‎‎generalized‎ adaptive Monte Carlo algorithm ‎using‎ Diagonal and Off-Diagonal Splitting (DOS) iteration method to ‎solve‎ system of linear algebraic equations ‎(SLAE)‎‎.‎ I‎n ‎fact, ‎t‎he DOS method is a generalized iterative method ‎which has some known iterative methods such as Jacobi‎, ‎Gauss-Seidel and Successive Overrelaxation methods‎ as its special cases‎. ‎Monte Carlo algorithms ‎usually‎ use the Jacobi method ‎to ‎solve‎ ‎SLAE‎‎. ‎In this paper‎, the DOS ‎method ‎is ‎used‎ instead of the Jacobi method ‎w‎hich transforms the Monte Carlo ‎algorithm‎ into the generalized Monte Carlo ‎algorithm‎. ‎we ‎establish‎ t‎heoretical ‎results‎ to justify the convergence of the algorithm‎.‎‎ ‎‎Finally‎, ‎numerical experiments are discussed to illustrate the accuracy and ‎eff‎i‎ciency of the theoretical results‎. Furthermore, ‎‎‎the ‎generalized‎ algorithm is ‎implemented‎ to ‎price ‎options‎ ‎using‎ ‎fi‎nite ‎diff‎erence ‎method‎. ‎We compare the generalized algorithm with ‎standard numerical and stochastic algorithms ‎to ‎show ‎its‎ ‎eff‎i‎ciency.‎‎‎

Keywords

Main Subjects

Computational Methods for Differential Equations

Articles in Press, Accepted Manuscript
Available Online from 30 March 2024

Files

History

  • Receive Date: 24 May 2022
  • Revise Date: 06 January 2024
  • Accept Date: 09 February 2024

Share

How to cite

Statistics