Forecasting the implied volatility surface in risk-management applications

Abstract

In risk-management, one typically simulates many states of the market using models that are in line with historical data, also known as real-world models. For example, new regulations require insurance companies to value their position on a 1-year horizon. Insurance companies issue guarantees that need to be valued according to market expectations, instead of historical data. By calibrating option pricing models to market prices or equivalently, the implied volatility surface, one obtains market consistent values for these guarantees. Currently, it is common practice to assume that the parameters of these option pricing models are constant, i.e. the calibrated parameters from time t = 0 are used, as the option prices at t = 1 are unknown. However, empirical data shows that the parameters are not constant and depend on the state of the market. In this research, we propose regression models that predict the calibrated parameters, given a set of market variables such as the VIX index and risk-free interest rates. When these market variables are included in the real-world simulation, one is able to predict the calibrated parameters and consequently the option prices which are in line with the simulated state of the market. By performing a regression we are able to predict the out-of-sample implied volatility surfaces accurately. Moreover, the impact on the Solvency Capital Requirement has been evaluated for different points in time. The impact depends on the initial state of the market and varies from -46% to +52%.