Augmented Lagrangian method applied to American option pricing

K. Zhang, Xiaoqi Yang, K. L. Teo

Research output: Journal article publicationJournal articleAcademic researchpeer-review

14 Citations (Scopus)

Abstract

The American option pricing problem is originally formulated as a stochastic optimal stopping time problem. It is also equivalent to a variational inequality problem or a complementarity problem involving the Black-Scholes partial differential operator. In this paper, the corresponding variational inequality problem is discretized by using a fitted finite volume method. Based on the discretized form, an algorithm is developed by applying augmented Lagrangian method (ALM) to the valuation of the American option. Convergence properties of ALM are considered. By empirical numerical experiments, we conclude that ALM is more effective than penalty method and Lagrangian method, and comparable with the projected successive overrelaxation method (PSOR). Furthermore, numerical results show that ALM is more robust in terms of computation time under changes in market parameters: interest rate and volatility.
Original languageEnglish
Pages (from-to)1407-1416
Number of pages10
JournalAutomatica
Volume42
Issue number8
DOIs
Publication statusPublished - 1 Aug 2006

Keywords

  • Complementarity problems
  • Computational methods
  • Finance

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Electrical and Electronic Engineering

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