DSAS - MSc Public Lecture - Lin Fang

Title:  Stochastic modelling of implied correlation index and herd behavior index. Evidence, properties and pricing.

Abstract:
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 choices of 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. For each digital CIX option, we observe that a 40% increase in the speed of reversion of the SV parameter causes the option price to increase by 6% in the first CSV model as well as 3% in the second CSV model. However, when the volatility of SV parameter grows significantly (i.e. sixfold), the option price falls 60% in the first CSV model and drops 22% in the second CSV model.

Supervisor: Marcos Escobar-Anel