A Simple Robust Test for the Presence of Jumps in Asset Prices

We develop a simple robust test for the presence of jumps in the price of an asset underlying an option. Our test examines the prices of at and out-of-the-money options as the time to maturity of the option approaches zero. We show that these prices converge to zero at speeds which depend on whether the price process is pure diffusion, pure jump, or a mixture of both. By applying our test to S&P 500 options data, we conclude that this index contains a jump component. Furthermore, there are strong indications of both a diffusion component and stochastic volatility.