# Pricing an American call under the CGMY model

I am pricing an American call under the CGMY model ($0 < Y < 1$) with strike $K$ at grid point $(x_i,\tau_j)$ where $x_i=x_{min}+i\,\Delta x$ for $i=0,1,...N$ and $\Delta x=\frac{x_{max}-x_{min}}{N}$.Why in the region $y\in(x_N-x_i,\infty)$ we have

\begin{align} \int_{x_N-x_i}^{\infty}(w(x_i+y,\tau_j)-w(x_i,\tau_j))\frac{exp(-\lambda_p) y}{\nu(x_i,\tau_j)\, y^{1+Y}}\,\,dy=0 \end{align}

Where $w(x_i,\tau_j)$ is the premium at $(x_i,\tau_j)$.

• what is the question? – emcor Jul 2 '15 at 19:49
• @ emcor Why $\int_{x_N-x_i}^{\infty}(w(x_i+y,\tau_j)-w(x_i,\tau_j))\frac{exp(-\lambda_p) y}{\nu(x_i,\tau_i)\, y^{1+Y}}\,\,dy=0$? – user16651 Jul 2 '15 at 19:52
• Are you saying there are multiple strikes for each $x_i..._N$? – emcor Jul 2 '15 at 19:56
• I assume $\tau$ is time to maturity? Is $w$ the option price or intrinsic/time value? Can you give the literature source? – emcor Jul 2 '15 at 20:04
• @BehrouzMaleki: Any reference for your question? It is hard to know the background and the notations etc. – Gordon Jul 2 '15 at 20:22