In this work we propose a simple and efficient algorithm to numerically approximate the time-dependent implied volatility for jump-diffusion models in option pricing that generalize the Black–Scholes equation. Here we use implicit-explicit difference schemes to compute the derivative part with fully implicit method and the integral term – in an explicit way. An average in time linearization of the diffusion term is applied, followed by a special decomposition of the unknown volatility function, which enables us to derive the implied volatility in an explicit form. Furthermore, the correctness of the algorithms is established. The presented numerical simulations demonstrate the capabilities of the current approach and confirm the robustness of the proposed methodology.

在这项工作中，我们提出了一种简单有效的算法，可以对Black-Scholes方程泛化的期权定价中跳-扩散模型的时间相关隐含波动率进行数值近似。在这里，我们使用隐式-显式差分方案以显式方式使用完全隐式方法和积分项来计算导数部分。应用扩散项的时间线性平均，然后对未知波动率函数进行特殊分解，这使我们能够以显式形式导出隐含波动率。此外，确定了算法的正确性。提出的数值模拟证明了当前方法的功能，并证实了所提出方法的鲁棒性。