Mellin transform of call prices
= Mellin transform of call prices
{c}
For $C(k)=\mathbb E(e^\xi-e^k)^+$ and $\operatorname{Re}z>1$ in the <exponential moment> domain, the <moment-generating function> satisfies $\mathbb Ee^{z\xi}=\int_{\mathbb R}C(k)z(z-1)e^{(z-1)k}dk$.