Assessing the impact of jumps in an option pricing model: A gradient estimation approach

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.