Master of Science
Statistics and Actuarial Sciences
In this work, we provide the definition, study properties, and craft new stochastic models for two dependence indices: the implied correlation index and the herd behavior index (HIX). In particular, we model and price financial derivatives on the basic implied correlation index (CIX) as reported by CBOE. Our analysis is the first revealing the presence of heteroscedasticity in the time series of CIX leading to two Correlation Stochastic Volatility (CSV) models. We describe properties of CSV models and use discretization methods for their simulation. A partial estimation methodology is implemented on CBOE S& P 500 CIX historical data treating the stochastic volatility (SV) as a hidden, unobservable process. The impact of the SV parameters is studied for two types of digital CIX options, both motivated by the usage of CIX as an indicator of crisis conditions.
Fang, Lin, "Stochastic modelling of implied correlation index and herd behavior index. Evidence, properties and pricing." (2018). Electronic Thesis and Dissertation Repository. 5466.