We present a detailed analysis and implementation of a splitting strategy to identify simultaneously the local volatility surface and the jump-size distribution from quoted European prices. The underlying model consists of a jump-diffusion driven asset with time- and price-dependent volatility. Our approach uses a forward Dupire-type partial integro-differential equation for the option prices to produce a parameter-to-solution map. The ill-posed inverse problem for this map is then solved by means of a Tikhonov-type convex regularisation. The proofs of convergence and stability of the algorithm are provided together with numerical examples that illustrate the robustness of the method both for synthetic and real data.

中文翻译：

---

跳跃扩散模型标定的拆分策略

我们提供了一种拆分策略的详细分析和实施，以同时从欧洲报价中识别出当地的波动率表面和跳跃规模分布。基本模型由具有时间和价格相关波动性的跳跃扩散驱动资产组成。我们的方法对期权价格使用正向Dupire型偏积分-微分方程，以生成参数-解图。然后通过Tikhonov型凸正则化方法解决该图的不适定逆问题。提供了算法的收敛性和稳定性证明，并提供了数值示例，这些示例说明了该方法对合成数据和实际数据的鲁棒性。