This paper shows that Edgeworth expansions for option valuation are equivalent to approximating option payoffs using Hermite polynomials. Consequently, the value of an option is the value of an infinite series of replicating polynomials. The resultant formulas express option values in terms of skewness, kurtosis, and higher moments. Unfortunately, the Hermite series diverges for fat-tailed models, so we provide alternative moment-based formulas. These formulas are a computationally efficient alternative to Fourier transform valuation and can value options even when the characteristic function is unknown. Applications include the first convergent solution for Hull and White’s stochastic volatility model.

Motivated by the literature on investment flows and optimal trading, we examine intraday predictability in the cross‐section of stock returns. We find a striking pattern of return continuation at half‐hour intervals that are exact multiples of a trading day, and this effect lasts for at least 40 trading days. Volume, order imbalance, volatility, and bid‐ask spreads exhibit similar patterns, but do not explain the return patterns. We also show that short‐term return reversal is driven by temporary liquidity imbalances lasting less than an hour and bid‐ask bounce. Timing trades can reduce execution costs by the equivalent of the effective spread.