This paper introduces the exponentially weighted moving average (EWMA) Heston model, a Markovian stochastic volatility model able to capture a wide range of empirical features related to volatility dynamics while being more tractable for simulations than rough volatility models based on fractional processes. After presenting the model and its principal characteristics, our analysis focuses on the use of its associated Euler-discretization scheme as a time-series generator for Monte-Carlo simulations. Using this discretization scheme, and on the basis of S&P500 empirical time series, we show that the EWMA Heston model is overall consistent with market data, making it a credible alternative to other existing stochastic volatility models. Keywords: tohsti voltility modelD reston modelD qudrti rough reston modelD umh e'etD timeEreversl symmetryD voltility distriutionD returns distriutionF JEL classication: gISD gQPD qIHD qIRD qIUF