We propose a continuous-time model of price impact from rule-based trading strategies, which illustrates how feedback effects lead to endogenous volatility. In our model we use a fixed-point approach to model the equilibrium at any time t between “noise” traders and “systematic” traders following an exogenously given trading rule. The resulting stochastic differential equation enables to quantify the impact of feedback effects in asset volatility. In particular, we show that in the presence of feedback effects, volatility naturally becomes path-dependent, even starting from a constant fundamental asset volatility. We obtain analytical expressions for the realized and implied volatility which may be decomposed as the sum of a fundamental volatility and a liquidity-dependent “excess” volatility. Our results provide insight into the nature of volatility spikes associated with market liquidity events.

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