Comment on 'The Large-Maturity Smile for the Heston Model'

Reformulating the results of del Baño Rollin, Ferreiro-Castilla, and Utzet (2010), we are able to give necessary and sufficient conditions for the moments of the stock price to exist and extend Theorem 2.1 of Forde and Jacquier (2011). Precisely Forde and Jacquier (2011) provide necessary conditions for the moments to exist when κ > ρσ. Although this assumption is satisfied on Equity markets (because the correlation is generally negative), it does not hold for FX-related derivatives. Furthermore we give a detailed classification of the cases when the rate function is essentially smooth under both the original and the share measures. This classification complements the correction note of Forde, Jacquier and Mijatovic (2011). It shows that the application of Gärtner-Ellis theorem as in Forde and Jacquier (2011) can not be directly used to obtain the asymptotic behavior of calls or puts with large maturity when κ > ρσ. However it can be used for put options when κ <=ρσ