Maximum Likelihood Estimation of Asymmetric Jump-Diffusion Processes : Application to Security Prices

An asymmetric jump-diffusion model of stock price behavior is proposed. In an extension of Merton's (1976), we posit that returns dynamics are determined by a drift component, a Wiener process and two jump processes representing the arrival of quot;goodquot; or quot;badquot; news that lead to jumps in security prices. We assume that good and bad news may arrive with different intensities and the distribution of jump magnitudes representing each type is different. To admit and test these distinctions, we assume that news arrives according to two Poisson processes and jump magnitudes representing good and bad news are Pareto and Beta distributed. We develop cumulant and maximum likelihood estimators and use daily stock prices data to estimate the proposed model. Empirical results strongly support the posited model. Likelihood based test provides support to the hypothesis that stock prices respond differently to the arrival of good and bad news