The Valuation on Compound Options under the Diffusion-CGMY Model

[[abstract]]本文證明了在一些特殊的情況下minimal martingale measure與Esscher transform的測度是相同的。利用平賭方法，首先我們在擴散-CGMY模型下推導標準複合選擇權價格的封閉解公式。在沒有跳躍過程的情況下，也就是在單純的擴散過程，我們的公式會完全等於Geske所推導的複合選擇權評價公式。以同樣的方法，我們將複合選擇權從2階擴展到N階，並求得它的價格公式。最後數值結果以擴散-CGMY模型為例子來探討標準複合選擇權價格公式的精確度。[[abstract]]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.[[note]]博