American condor contracts with a cash component: A variational inequality approach

Abstract

We study a jointly exercised American condor contract whose payoff is a call condor payoff plus a positive cash amount. Its plateau and positive tails produce two inner exercise boundaries and two outer cash-exercise boundaries. We construct the unique bounded solution of the associated variational inequality, strong on each side of the plateau, and identify it with the optimal stopping value. We prove monotonicity and continuity of the four boundaries and determine their limits at expiry. Following Broadie and Detemple, we express the inner boundaries as cutoffs of the boundaries of uncapped contracts with the same cash components. We also prove call-side convexity and volatility monotonicity under a sufficient condition, solve the stationary problems explicitly and present numerical results.

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BibTeX RIS

BibTeX

@misc{jung2026american,
  title = {{American condor contracts with a cash component: A variational inequality approach}},
  author = {Kiyuob Jung and Jehan Oh and Namgwang Woo},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.25105},
  eprint = {2609.25105},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.25105},
}

RIS

TY  - UNPB
TI  - American condor contracts with a cash component: A variational inequality approach
AU  - Kiyuob Jung
AU  - Jehan Oh
AU  - Namgwang Woo
PY  - 2026
DA  - 2026/09/20
PB  - arXiv
DO  - 10.48550/arxiv.2609.25105
UR  - https://arxiv.org/abs/2609.25105
AB  - We study a jointly exercised American condor contract whose payoff is a call condor payoff plus a positive cash amount. Its plateau and positive tails produce two inner exercise boundaries and two outer cash-exercise boundaries. We construct the unique bounded solution of the associated variational inequality, strong on each side of the plateau, and identify it with the optimal stopping value. We prove monotonicity and continuity of the four boundaries and determine their limits at expiry. Following Broadie and Detemple, we express the inner boundaries as cutoffs of the boundaries of uncapped contracts with the same cash components. We also prove call-side convexity and volatility monotonicity under a sufficient condition, solve the stationary problems explicitly and present numerical results.
ER  -

Abstract

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