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

Wensheng Yang (), Jingtang Ma () and Zhenyu Cui ()
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Wensheng Yang: Southwestern University of Finance and Economics
Jingtang Ma: Southwestern University of Finance and Economics
Zhenyu Cui: Stevens Institute of Technology

Mathematical Methods of Operations Research, 2021, vol. 93, issue 2, No 6, 359-412

Abstract: 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.

Keywords: Option pricing; Sensitivity analysis; Continuous-time Markov chains; Non-uniform grids; Convergence rates; Path-dependent options; Greeks; Laplace inversion (search for similar items in EconPapers)
JEL-codes: C63 G13 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s00186-020-00735-5

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