Analysis of Markov chain approximation for Asian options and occupation-time derivatives: Greeks and convergence rates

Wensheng Yang, Jingtang Ma, Zhenyu Cui

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

The continuous-time Markov chain (CTMC) approximation method is a powerful tool that has recently been utilized in the valuation of derivative securities, and it has the advantage of yielding closed-form matrix expressions suitable for efficient implementation. For two types of popular path-dependent derivatives, the arithmetic Asian option and the occupation-time derivative, this paper obtains explicit closed-form matrix expressions for the Laplace transforms of their prices and the Greeks of Asian options, through the novel use of pathwise method and Malliavin calculus techniques. We for the first time establish the exact second-order convergence rates of the CTMC methods when applied to the prices and Greeks of Asian options. We propose a new set of error analysis methods for the CTMC methods applied to these path-dependent derivatives, whose payoffs depend on the average of asset prices. A detailed error and convergence analysis of the algorithms and numerical experiments substantiate the theoretical findings.

Original languageEnglish
Pages (from-to)359-412
Number of pages54
JournalMathematical Methods of Operations Research
Volume93
Issue number2
DOIs
StatePublished - Apr 2021

Keywords

  • Continuous-time Markov chains
  • Convergence rates
  • Greeks
  • Laplace inversion
  • Non-uniform grids
  • Option pricing
  • Path-dependent options
  • Sensitivity analysis

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