Модель процентных ставок для неопределенно-стохастических финансовых рынков

За последние десятилетия финансовые рынки все чаще демонстрируют черты как случайности, так и неопределенности, что создает трудности для моделей процентных ставок, основанных исключительно на стохастических или неопределенных процессах. Эти модели часто неадекватно отражают двойственную природу неопределенности, что ограничивает их применимость в волатильных и непредсказуемых рыночных условиях. Целью данного исследования является разработка и оценка модели процентной ставки для неопределенно-стохастических финансовых рынков и разработка модели ценообразования облигаций с нулевым купоном в этих условиях. Методология использует неопределенные стохастические дифференциальные уравнения, которые объединяют элементы как теории вероятностей, так и теории неопределенности, тем самым учитывая алеаторные и эпистемические формы неопределенности. Предлагаемая модель расширяет классические модели краткосрочных ставок, вводя два источника неопределенности и предоставляя теоретические выводы для определения цены облигаций. Приведены числовые иллюстрации для демонстрации применения модели к оценке облигаций с нулевым купоном и для выявления отличий от традиционных подходов. Результаты исследования показывают, что процентные ставки и цены облигаций с нулевым купоном на неопределенных стохастических финансовых рынках могут быть эффективно смоделированы с помощью неопределенных случайных процессов, что приводит к повышению точности ценообразования и управлению рисками в условиях неполной информации и непредсказуемых шоков. Ключевой вывод заключается в том, что включение неопределенных стохастических дифференциальных уравнений в моделирование процентных ставок и цен облигаций с нулевым купоном обеспечивает более надежную и гибкую структуру для неопределенных стохастических рынков. Данное исследование вносит вклад в растущий объем знаний неопределенных стохастических финансов, подчеркивая необходимость гибридных моделей, способных помочь политикам, инвесторам и финансовым учреждениям обеспечить стабильность и устойчивость в условиях будущей рыночной неопределенности. 

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