American option evaluations using higher moments
Studies in Economics and Finance
ISSN: 1086-7376
Article publication date: 21 November 2023
Issue publication date: 14 November 2024
Abstract
Purpose
By using higher moments, this paper extends the quadratic local risk-minimizing approach in a general discrete incomplete financial market. The local optimization subproblems are convex or nonconvex, depending on the moment variants used in the modeling. Inspired by Lai et al. (2006), the authors propose a new multiobjective approach for the combination of moments that is transformed into a multigoal programming problem.
Design/methodology/approach
The authors evaluate financial derivatives with American features using local risk-minimizing strategies. The financial structure is in line with Schweizer (1988): the market is discrete, self-financing is not guaranteed, but deviations are controlled and reduced by minimizing the second moment. As for the quadratic approach, the algorithm proceeds backwardly.
Findings
In the context of evaluating American option, a transposition of this multigoal programming leads not only to nonconvex optimization subproblems but also to the undesirable fact that local zero deviations from self-financing are penalized. The analysis shows that issuers should consider some higher moments when evaluating contingent claims because they help reshape the distribution of global cumulative deviations from self-financing.
Practical implications
A detailed numerical analysis that compares all the moments or some combinations of them is performed.
Originality/value
The quadratic approach is extended by exploring other higher moments, positive combinations of moments and variants to enforce asymmetry. This study also investigates the impact of two types of exercise decisions and multiple assets.
Keywords
Acknowledgements
The authors are very grateful to the referees for their valuable comments and suggestions. This research was supported by the Natural Sciences and Engineering Research Council of Canada.
Citation
Gaillardetz, P. and Hachem, S. (2024), "American option evaluations using higher moments", Studies in Economics and Finance, Vol. 41 No. 5, pp. 981-997. https://doi.org/10.1108/SEF-08-2023-0458
Publisher
:Emerald Publishing Limited
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