This article shows that in particular cases, the minimal martingale measure coincides with the equivalent martingale measure inferred from the Esscher transform. Using the martingale approach, we first derive a closed-form formula for the price of the standard compound option under the diffusion-CGMY model. Our expression reduces exactly to Geske’s formula for compound option when the jump component disappears. We then use these results to evaluate the prices of the compound option of order . Numerical analysis shows how to perform a study of the accuracy of the price formula for the standard compound option.