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 and it is competitive, especially out-of-sample, with the affine two-factor double Heston model.

A Generalized Bachelier Formula for Pricing Basket and Spread Options

“…Finally, the Gauss-Hermite coefficients can be computed from equation (2) using the C-GCSE approximation of the probability density function obtained in the previous step. A similar procedure was employed in Farkas, Necula, and Waelchli (2015) to obtain closed-form option prices in the context of a non-affine stochastic volatility model.…”

A micro-foundation of a simple financial model with finite-time singularity bubble and its agent-based simulation

“…In the model of Rheinlaender and Steinkamp (2004), excess demands for fundamentalists and momentum traders in the market are considered, and the phenomenon of endogenous phase transitions in market stability is studied. In Farkas et al (2017), a micro-foundation of a stochastic volatility model is proposed by setting up an excess demand model of rational agents and irrational agents who overreact to price changes assuming a herding effect on the ratio of the number of these agents. Like these, the current paper has also employed an excess demand model for the micro-foundation.…”