TY - GEN A1 - Jacquier, Antoine T1 - The small-time smile and term structure of implied volatility under the Heston model N2 - We characterise the asymptotic smile and term structure of implied volatility in the Heston model at small maturities and all strikes. 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~\cite{FJ09I} which found the relationship between the zero-expiry smile and the diffusion coefficients. We solve for in/out-of-the-money and at-the-money cases; in the latter case our proof involves subleading-order saddlepoint approximation along a suitable path of integration. KW - implied volatility KW - Heston KW - stochastic volatility KW - asymptotics KW - saddlepoint method Y1 - 2011 UR - https://opus4.kobv.de/opus4-matheon/frontdoor/index/index/docId/855 UR - https://nbn-resolving.org/urn:nbn:de:0296-matheon-8555 ER -