TY - JOUR
T1 - Analysis of Markov chain approximation for Asian options and occupation-time derivatives
T2 - Greeks and convergence rates
AU - Yang, Wensheng
AU - Ma, Jingtang
AU - Cui, Zhenyu
N1 - Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH, DE part of Springer Nature.
PY - 2021/4
Y1 - 2021/4
N2 - 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.
AB - 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.
KW - Continuous-time Markov chains
KW - Convergence rates
KW - Greeks
KW - Laplace inversion
KW - Non-uniform grids
KW - Option pricing
KW - Path-dependent options
KW - Sensitivity analysis
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U2 - 10.1007/s00186-020-00735-5
DO - 10.1007/s00186-020-00735-5
M3 - Article
AN - SCOPUS:85100184068
SN - 1432-2994
VL - 93
SP - 359
EP - 412
JO - Mathematical Methods of Operations Research
JF - Mathematical Methods of Operations Research
IS - 2
ER -