<p>In this work, the pricing of European options with liquidity shocks is addressed using the local radial point interpolation method. The implicit-explicit numerical methods are developed to solve the coupled semilinear parabolic system of equations arising in the pricing of options with liquidity shocks. The convergence properties are established, and discrete comparison principles are derived for the proposed methods. The numerical experiments are conducted to validate the theoretical findings and to demonstrate the efficiency and accuracy of the proposed methods. The numerical results are further compared with existing literature, offering additional insights and a comprehensive understanding of the performance of proposed methods.</p>