We develop a joint model for the S&P500 and VIX indices to extract forward-looking; market-consistent information on their correlation. The model is based on time changed Lévy processes; deriving analytical expressions from the joint characteristic function; and utilizing market quotes of options on both indices. A piece-wise joint calibration to option prices ensures precision; considering data availability and liquidity. Calibrated parameters quantify the 'leverage/volatility feedback' effect along the VIX options' term structure and corresponding futures. The model is illustrated using market data on SPX options and VIX futures and options. This work is in collaboration with Ernst Eberlein and Gregory Rayée.