In the CGMY model with Y in (1,2), the normalized ATM call price admits the expansion c(t,0) = d1 t^{1/Y} + d2 t + o(t) as t approaches 0, where d1 is the known stable limit and d2 is an explicit integral from the characteristic exponent.
Madan, and Marc Yor,The fine structure of asset returns: an empirical investigation, The Journal of Business75(2002), no
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Higher-order ATM asymptotics for the CGMY model via the characteristic function
In the CGMY model with Y in (1,2), the normalized ATM call price admits the expansion c(t,0) = d1 t^{1/Y} + d2 t + o(t) as t approaches 0, where d1 is the known stable limit and d2 is an explicit integral from the characteristic exponent.