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<p>Vulnerable options of European and American style with a possible occurrence of an exogenous termination are studied under market incompleteness in a hazard-process setup. It is proved that the reduced upper price of a <i>vulnerable European option</i> coincides with the unique price of an American option with a properly defined payoff and holder’s exercise times constrained to the random set given by the right support of the hazard process. For a <i>vulnerable American option</i>, it is shown that the reduced upper price equals the price of a specific American option with unrestricted exercise times, whereas the reduced lower price coincides with the price of a particular game option in which the issuer’s exercise times are constrained to the above-mentioned random set.</p>

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Vulnerable European and American options in a hazard-process model

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年3月5日

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  • Libo Li,
  • Ruyi Liu,
  • Marek Rutkowski

摘要

Vulnerable options of European and American style with a possible occurrence of an exogenous termination are studied under market incompleteness in a hazard-process setup. It is proved that the reduced upper price of a vulnerable European option coincides with the unique price of an American option with a properly defined payoff and holder’s exercise times constrained to the random set given by the right support of the hazard process. For a vulnerable American option, it is shown that the reduced upper price equals the price of a specific American option with unrestricted exercise times, whereas the reduced lower price coincides with the price of a particular game option in which the issuer’s exercise times are constrained to the above-mentioned random set.