We introduce a tractable multivariate pure jump process in which the trading time is described by an additive subordinator. The multivariate process retains the additivity property, and therefore is time inhomogeneous, i.e., its increments are independent but non stationary. We provide the theoretical framework of our process, perform a sensitivity analysis with respect to the time inhomogeneity parameters, and design a Monte Carlo scheme to simulate the trajectories of the process. We then employ the model in the context of option pricing in the FX market. We take advantage of the specific features of currency triangles to extract the joint dynamics of FX log-rates. Extensive tests based on observed market data show that our model outperforms well established pure jump benchmarks.

中文翻译：

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多元加法从属关系及其在金融领域的应用


我们引入了一个可处理的多变量纯跳跃过程，其中交易时间由加法从属器描述。多元过程保留了加性特性，因此是时间不均匀的，即它的增量是独立的但非平稳的。我们提供过程的理论框架，对时间不均匀性参数进行敏感性分析，并设计蒙特卡洛方案来模拟过程的轨迹。然后，我们在外汇市场的期权定价环境中使用该模型。我们利用货币三角形的特定特征来提取外汇对数率的联合动态。基于观察到的市场数据的广泛测试表明，我们的模型优于成熟的纯跳跃基准。