In this paper, we consider the design of optimal transceiver and relay processing algorithms for a full-duplex (FD) two-way amplify-and-forward (AF) multiple-input multiple-output (MIMO) relaying system. We assume the channel state information of loopback self-interference (SI) channels to be imperfect. The nodes employ precoders and receive filters for suppressing the residual SI. The optimal precoders at transceivers are designed by equalising the signal-to-interference-plus-noise ratio at the relay and transceiver. Using the transceiver precoders thus designed, we then design the optimal relay precoder and transceiver receive filters by minimizing the sum of mean square error (SMSE) at the transceivers. The optimal precoders and receive filters are continuously updated to account for the cumulative interference effect caused by AF operation of the FD relay. The secrecy performance of this system in the presence of a passive eavesdropper is analyzed by considering the relay signal to be artificial noise (AN) for the eavesdropper. The effectiveness of the proposed design is demonstrated in our simulation results.