caa a22 4500 445363231 CHVBK 20180317142921.0 cr unu---uuuuu 170323e20111201xx s 000 0 eng 10.1007/s00780-010-0147-3 doi (NATIONALLICENCE)springer-10.1007/s00780-010-0147-3 The large-maturity smile for the Heston model [Elektronische Daten] [Martin Forde, Antoine Jacquier] Using the Gärtner-Ellis theorem from large deviations theory, we characterise the leading-order behaviour of call option prices under the Heston model, in a new regime where the maturity is large and the log-moneyness is also proportional to the maturity. Using this result, we then derive the implied volatility in the large-time limit in the new regime, and we find that the large-time smile mimics the large-time smile for the Barndorff-Nielsen normal inverse Gaussian model. This makes precise the sense in which the Heston model tends to an exponential Lévy process for large times. We find that the implied volatility smile does not flatten out as the maturity increases, but rather it spreads out, and the large-time, large-moneyness regime is needed to capture this effect. As a special case, we provide a rigorous proof of the well-known result by Lewis (Option Valuation Under Stochastic Volatility, Finance Press, Newport Beach, 2000) for the implied volatility in the usual large-time, fixed-strike regime, at leading order. We find that there are two critical strike values where there is a qualitative change of behaviour for the call option price, and we use a limiting argument to compute the asymptotic implied volatility in these two cases. Springer-Verlag, 2010 Implied volatility nationallicence Heston nationallicence Asymptotics nationallicence Large deviations nationallicence Forde Martin Department of Mathematical Sciences, Dublin City University, Glasnevin, Dublin 9, Ireland aut Jacquier Antoine Department of Mathematics, Imperial College London, London, UK aut Finance and Stochastics Springer-Verlag 15/4(2011-12-01), 755-780 0949-2984 15:4<755 2011 15 780 https://doi.org/10.1007/s00780-010-0147-3 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00780-010-0147-3 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Forde Martin Department of Mathematical Sciences, Dublin City University, Glasnevin, Dublin 9, Ireland aut NATIONALLICENCE 700 1- Jacquier Antoine Department of Mathematics, Imperial College London, London, UK aut NATIONALLICENCE 773 0- Finance and Stochastics Springer-Verlag 15/4(2011-12-01), 755-780 0949-2984 15:4<755 2011 15 780 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer