We study a hedging problem in a market where traders have various levels of information. The exclusive information available only to informed traders is modelled by a diffusion process rather than discrete arrivals of new information. The asset price follows a jump-diffusion process and an information process affects jump sizes of the asset price. We find the local risk minimization hedging strategy of informed traders. Numerical examples as well as their comparison with the Black-Scholes strategy are provided via Monte Carlo.