In this paper, we propose a new theory for the formation of volatility which takes into account the influence of option hedging on the assets price dynamics. By analogy with statistical mechanics, we build a self-consistent equation for the volatility, we show it is well-posed and we explain how it can be solved. © 2006.
Lions, P. L., & Lasry, J. M. (2006). Towards a self-consistent theory of volatility. Journal Des Mathematiques Pures et Appliquees, 86(6), 541–551. https://doi.org/10.1016/j.matpur.2006.04.006