Motivated by model risk considerations, we develop a statistical procedure that determines whether the inclusion of a jump component in a simpler, diffusion-based price model significantly influences the prices of specific options on this underlying. The basis of our statistical testing procedure is simulating the sensitivity of the option price in the framework of jump-diffusion Markov Chains. The jumps are assumed to follow a compound Poisson process. The stochastic gradient representation of the resulting model risk is general: it can be applied to quantify the difference between performance functions of two Markov Chains at multiple future times. The sensitivity estimator samples the jump-diffusion within the base diffusion process. We show that our statistical test is vastly superior to the two-sample t-test. We also demonstrate that the test is particularly powerful in situations where either the volatility or the jump component is dominant.

受模型风险考虑的推动，我们开发了一个统计程序，以确定在更简单的、基于扩散的价格模型中包含跳跃组件是否会显着影响该标的特定期权的价格。我们统计测试程序的基础是在跳跃扩散马尔可夫链的框架内模拟期权价格的敏感性。假设跳跃遵循复合泊松过程。结果模型风险的随机梯度表示是通用的：它可以用于量化两个马尔可夫链在多个未来时间的性能函数之间的差异。灵敏度估计器对基础扩散过程中的跳跃扩散进行采样。我们表明我们的统计检验大大优于双样本 t 检验。