Higher-order small time asymptotic expansion of Itô semimartingale characteristic function with application to estimation of leverage from options

Abstract

In this paper, we derive a higher-order asymptotic expansion of characteristic functions of an Itô semimartingale over asymptotically shrinking time intervals. The leading term in the expansion is determined by the value of the diffusive coefficient at the beginning of the interval. The higher-order terms are determined by the jump compensator as well as the coefficients appearing in the diffusion dynamics. The result is applied to develop a nearly rate-efficient estimator of the leverage coefficient of an asset price, i.e., the coefficient in its volatility dynamics that appears in front of the Brownian motion that drives also the asset price.