Modeling the dynamics of equity index option implied volatilities in a real world scenario set

This article proposes a method of analyzing and modeling the real world dynamics of equity put/call option implied volatilities using the risk neutral Heston model with specific parameter restrictions.

In our modeling approach, we construct a stable and accurate method for calibrating the Heston model to historic market data. In this way, the risk neutral Heston model is embedded in a real world scenario generator and can be used to generate implied volatility structures, evaluate option investment strategies or to construct hedging strategies. The proposed methodology results in a stable valu-ation of embedded options, which is in practice preferred by, among others, insurance companies and pension funds.