A Stochastic Volatility Model with Mean-reverting Volatility Risk Premium

Abstract

The volatility risk premium (VRP) has long been the core issue in option pricing and risk management. The VRP is usually defined as a linear function of volatility which ignores the time-varying property of VRP and limits the degree of freedom of the model. In this paper, we adopt a CIR process in the stochastic volatility model (VRP-CIR-SV) to incorporate the mean-reverting and time-varying properties of VRP. We show that the decomposition of VRP is consistent to investor’s behaviour. Our Monte Carlo simulation results show that, compared with the traditional linear VRP model, the VRP-CIR-SV model can better depict the rich shapes of implied volatility curve. Our paper innovatively models the time-varying VRP with mean-reverting property, which may provide new thoughts for VRP estimation.