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Выпуклость Множества Цен Опционов Как Необходимое И Достаточное Условие Отсутствия Арбитража

Author

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  • Курочкин С.В.

Abstract

Для того чтобы совокупность опционов с различными ценами исполнения на один базовый актив не содержала арбитражных возможностей (т.е. извлечения положительной прибыли при нулевых вложениях капитала и отсутствии риска потерь), их рыночные цены в каждый момент времени должны удовлетворять определенным соотношениям. Известны некоторые соотношения такого типа – монотонность, липшицевость, выпуклость, – являющиеся следствием требования безарбитражности. В работе получен полный и независимый набор конструктивно проверяемых соотношений типа выпуклости для цен опционов, представляющий необходимое и достаточное условие отсутствия арбитража. Для доказательства основного результата потребовалось сформулировать и доказать специальный вариант леммы Фаркаша. Конструкция допускает обобщение на деривативы, зависящие от нескольких базовых активов и/или имеющие произвольные кусочно-линейные профили выплат. Для этого случая доказано, что всегда имеется возможность выбрать конечное число характеристик портфеля опционов, по которым можно было бы судить о том, является ли он арбитражным.

Suggested Citation

  • Курочкин С.В., 2016. "Выпуклость Множества Цен Опционов Как Необходимое И Достаточное Условие Отсутствия Арбитража," Журнал Экономика и математические методы (ЭММ), Центральный Экономико-Математический Институт (ЦЭМИ), vol. 52(2), pages 103-111, апрель.
    • Handle: RePEc:scn:cememm:v:52:y:2016:i:2:p:103-111
    Note: Москва
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    References listed on IDEAS

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