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American option evaluations using higher moments

American option evaluations using higher moments 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/approachThe 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.FindingsIn 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 implicationsA detailed numerical analysis that compares all the moments or some combinations of them is performed.Originality/valueThe 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Studies in Economics and Finance Emerald Publishing

American option evaluations using higher moments

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References (20)

Publisher
Emerald Publishing
Copyright
© Emerald Publishing Limited
ISSN
1086-7376
eISSN
1755-6791
DOI
10.1108/sef-08-2023-0458
Publisher site
See Article on Publisher Site

Abstract

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/approachThe 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.FindingsIn 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 implicationsA detailed numerical analysis that compares all the moments or some combinations of them is performed.Originality/valueThe 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.

Journal

Studies in Economics and Finance – Emerald Publishing

Published: Nov 14, 2024

Keywords: Higher moments; American options; Hedging errors; Local risk-minimizing strategies; Polynomial goal programming

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