We recommend the addition of a deterministic displacement to multi-factor affine models to calibrate and hedge SPX and VIX derivatives jointly. The proposed model, labeled Heston calibrates both markets with an average relative error (on quoted implied volatilities over two years of data) of 2%,...

The market for ultra short-term (zero days-to-expiry or 0DTE) options has grown exponentially over the last few years. In 2023, daily volume in 0DTEs reached over 45% of overall daily options volume. After briefly describing this exploding new market, we present a novel pricing formula designed...