In this study, a market framework is proposed for the practical implementation of lossy financial transmission rights (FTRs). The advantage of lossy FTRs over conventional FTRs is that the lossy FTRs can be settled directly according to locational marginal prices (LMPs) without requiring any LMP decomposition. Therefore, the price risk for a forward contract can be perfectly hedged if the power transaction involved perfectly matches the corresponding FTR. Although proposed long back, lossy FTRs still did not find an entry to the market because of the prejudice of market complexity and inefficiency. The principal aim of this study is, thus, to create the necessary environment so as to make those fine risk-hedging tools available in the market. First of all, a suitable format for forward contracts is prescribed to enable proper utilisation of lossy FTRs. The detailed lossy FTR auction model is prepared based upon a suitable optimal power flow (OPF) formulation. In addition, the implementation of lossy FTRs is shown for an AC-DC system by appropriately modelling the DC-line power flow behaviour according to the chosen OPF framework. The lossy FTR auction model prepared is thoroughly verified for the FTR issuance as per the market expectations.