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We characterize the asymptotic smile and term structure of implied volatility in the Heston model at small maturities. Using saddlepoint methods we derive a small-maturity expansion formula for call option prices, which we then transform into a closed-form expansion (including the leading-order and correction terms) for implied volatility. This refined expansion reveals the relationship between the small-expiry smile and all Heston parameters (including the pair in the volatility drift coefficient), sharpening the leading-order result of Forde and Jacquier [Int. J. Theor. Appl. Finance, 12 (2009), pp. 861--876], which found the relationship between the zero-expiry smile and the diffusion coefficients.

The Small-Time Smile and Term Structure of Implied Volatility under the Heston Model