Метод оценки риск-нейтральной плотности вероятности по котировкам опционов

Тарас Громницкий, Виктор Лапшин

Abstract


В данной работе разработан метод построения риск-нейтральной плотности вероятности по котировкам опционов, позволяющий дать оценку точности искомой плотности. Риск-нейтральная плотность представляется сплайном, который
1) минимизирует расстояние Кульбака-Лейблера до логнормальной плотности (что обеспечивает связь с моделью Блека-Шоулза),
2) минимизирует отклонение цен, восстановленных по полученной плотности, от действительных цен опционов.

Неопределенность, возникающая из-за Bid-Ask спреда не позволяет однозначно  построить кривую плотности, поэтому методом Монте Карло строится оценка точности. При построении оценки используется факторный анализ приращений «улыбок» волатильности, меняющихся с течением времени. Результаты факторного анализа позволяют генерировать свойственные рынку кривые, которые и составляют оценку точности.


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