Contour inversion for call prices
= Contour inversion for call prices
The <Mellin transform of call prices> can be inverted along a vertical contour with real part $x_0>1$: $C(k)=\frac1{2\pi i}\int_{x_0-i\infty}^{x_0+i\infty}\mathbb Ee^{z\xi}/(z(z-1)e^{(z-1)k})\,dz$. A finite <exponential moment> at $x_0$ and the quadratic denominator give absolute convergence.