Computable Error Bounds of Laplace Inversion for Pricing Asian Options

The prices of Asian options, which are among the most important options in financial engineering, can often be written in terms of Laplace transforms. However, computable error bounds of the Laplace inversions are rarely available to guarantee their accuracy. We conduct a thorough analysis of the in...

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Bibliographic Details
Published in:INFORMS journal on computing 2018-09, Vol.30 (4), p.634-645
Main Authors: Song, Yingda, Cai, Ning, Kou, Steven
Format: Article
Language:English
Subjects:
Approximation
continuous-time Markov chains
continuously monitored Asian options
discretely monitored Asian options
Errors
Inverse problems
Inversions
Laplace inversion
Laplace transformation
Laplace transforms
Markov chains
Markov processes
Prices and rates
Securities prices
Stock options
Stocks
Truncation errors
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Summary:The prices of Asian options, which are among the most important options in financial engineering, can often be written in terms of Laplace transforms. However, computable error bounds of the Laplace inversions are rarely available to guarantee their accuracy. We conduct a thorough analysis of the inversion of the Laplace transforms for continuously and discretely monitored Asian option prices under general continuous-time Markov chains (CTMCs), which can be used to approximate any one-dimensional Markov process. More precisely, we derive computable bounds for the discretization and truncation errors involved in the inversion of Laplace transforms. Numerical results indicate that the algorithm is fast and easy to implement, and the computable error bounds are especially suitable to provide benchmark prices under CTMCs. The online supplement is available at https://doi.org/10.1287/ijoc.2017.0805 .
ISSN:1091-9856
1526-5528
1091-9856
DOI:10.1287/ijoc.2017.0805