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.
Figueroa-L´ opez, Ruoting Gong, and Yuzhao Han,Estimation of tempered stable L´ evy models of infinite variation, Methodology and Computing in Applied Probability24(2022), 713–747
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First-order ATM call-price and IV asymptotics for exponential Lévy models under α-stable domain-of-attraction assumptions (α∈(1,2)), with new convergence rates t^{1/α}ℓ(t) when no Brownian component and universality of √t when Brownian component is present.
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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.
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At-the-money short-time call-price asymptotics for new classes of exponential L\'evy models
First-order ATM call-price and IV asymptotics for exponential Lévy models under α-stable domain-of-attraction assumptions (α∈(1,2)), with new convergence rates t^{1/α}ℓ(t) when no Brownian component and universality of √t when Brownian component is present.