Empirical evidences witness that the jumps appear to be very frequent in the financial markets. In this paper, we consider the statistical inference of spot correlation and spot market Beta between two different assets by using high frequency data, under the setting that both the co-jumps and the individual jumps contained in the underlying driven processes could be of infinite variation. Starting from the estimation of spot covariance, we propose consistent estimators of spot correlation and spot market Beta when the jump processes involved are general semi-martingales. The second order approximation for the estimators, namely the central limit theorems are established under the assumption that the jumps around zero are of stable L evy type. Our estimation procedure is based on the empirical characteristic function of the increments of the processes and the application of the polarization identity, and the bias terms stem from the jumps are removed in an iterative way. The finite sample performance of the proposed estimators and other existing estimators are assessed and compared by using simulated data-sets from various models, and our estimators are also applied to some real high frequency financial data-sets.