Higher-order ATM asymptotics for the CGMY model via the characteristic function
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866910131393921024 |
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| author | Hoffmeyer, Allen Houdré, Christian |
| author_facet | Hoffmeyer, Allen Houdré, Christian |
| contents | Using only the characteristic function, we derive short-time at-the-money (ATM) call-price asymptotics for the exponential CGMY model with activity parameter $Y\in(1,2)$. The Lipton--Lewis formula expresses the normalized ATM call price, denoted $c(t,0)$, in terms of the characteristic exponent, which, upon rescaling at the rate $t^{-1/Y}$ from the $Y$-stable domain of attraction, yields $c(t,0) = d_{1} t^{1/Y} + d_{2} t + o(t)$ as $t\downarrow 0$. The first-order coefficient $d_{1}$ is the known stable limit from the domain of attraction of a symmetric $Y$-stable law, and $d_{2}$ is given by an explicit integral involving the characteristic exponent and the limiting stable exponent. We then extract closed-form higher-order coefficients by keeping the full Lipton--Lewis integrand intact and introducing a dynamic cutoff that partitions the domain into inner, core, and tail regions, establishing the expansion with controlled remainder. All coefficients are verified numerically against existing closed-form expressions where available. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_13798 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Higher-order ATM asymptotics for the CGMY model via the characteristic function Hoffmeyer, Allen Houdré, Christian Pricing of Securities Probability 60E10, 60F99, 60G51, 91G20, 91G60 Using only the characteristic function, we derive short-time at-the-money (ATM) call-price asymptotics for the exponential CGMY model with activity parameter $Y\in(1,2)$. The Lipton--Lewis formula expresses the normalized ATM call price, denoted $c(t,0)$, in terms of the characteristic exponent, which, upon rescaling at the rate $t^{-1/Y}$ from the $Y$-stable domain of attraction, yields $c(t,0) = d_{1} t^{1/Y} + d_{2} t + o(t)$ as $t\downarrow 0$. The first-order coefficient $d_{1}$ is the known stable limit from the domain of attraction of a symmetric $Y$-stable law, and $d_{2}$ is given by an explicit integral involving the characteristic exponent and the limiting stable exponent. We then extract closed-form higher-order coefficients by keeping the full Lipton--Lewis integrand intact and introducing a dynamic cutoff that partitions the domain into inner, core, and tail regions, establishing the expansion with controlled remainder. All coefficients are verified numerically against existing closed-form expressions where available. |
| title | Higher-order ATM asymptotics for the CGMY model via the characteristic function |
| topic | Pricing of Securities Probability 60E10, 60F99, 60G51, 91G20, 91G60 |
| url | https://arxiv.org/abs/2604.13798 |