Abstract

In this paper, we price the vulnerable option under the assumption that both underlying and counterparty asset price follow correlated jump diffusion processes. By the two-dimensional Itô-Doeblin formula, we initially derive a partial integro-differential equation (PIDE) satisfied by the price of the vulnerable option with flexible jumps. Then, the double Mellin transform converts the PIDE into an ordinary differential equation (ODE), which possesses an explicit solution. Further, the inverse Mellin transform of the explicit solution to the ODE turns out to be a rigorous solution to the PIDE for vulnerable option. Finally, by carrying out some numerical experiments, we demonstrate that the PIDE’s solution produces price with a convincing degree of precision.

摘要

在本文中，我们假设基础资产和交易对手资产价格都遵循相关的跳跃扩散过程，从而为易受攻击的期权定价。通过二维 Itô-Doeblin 公式，我们初步推导了一个偏积分微分方程（PIDE），该方程满足具有灵活跳跃的易受攻击期权的价格。然后，双梅林变换将 PIDE 转换为具有显式解的常微分方程(ODE)。此外，ODE 显式解的 Mellin 逆变换证明是 PIDE 易受攻击选项的严格解。最后，通过进行一些数值实验，我们证明了 PIDE 的解决方案以令人信服的精度生成价格。