Herding and Stochastic Volatility

Abstract

In this paper we develop a one-factor non-affine stochastic volatility option pricing model where the dynamics of the underlying is endogenously determined from micro-foundations. The interaction and herding of the agents trading the underlying asset induce an amplification of the volatility of the asset over the volatility of the fundamentals. Although the model is non-affine, a closed form option pricing formula can still be derived by using a Gauss-Hermite series expansion methodology. The model is calibrated using S&P 500 index options for the period 1996-2013. When its results are compared to some benchmark models we find that the new non-affine one-factor model outperforms the affine one-factor Heston model, the non-affine one-factor log-normal model and it is competitive with the affine two-factor double Heston model.

Keywords: herding, non-affine option pricing model, Gauss-Hermite expansion

JEL Classification: G12, C61