Computable Error Bounds of Laplace Inversion for Pricing Asian Options

• 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
• ISSN: 1091-9856; 1526-5528; 1091-9856
• DOI: 10.1287/ijoc.2017.0805

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 .