The objective of this study is to upgrade the lossy financial transmission right (FTR) mechanism through the introduction of lossy option FTRs. The lossy FTR mechanism retains the potential to deliver superior risk hedging performance compared with the traditionally deployed lossless FTR mechanism since the locational marginal price decomposition is unnecessary for the settlement of lossy FTRs. The existing lossy FTR theory is, however, based on only obligation FTRs. Although obligation FTRs are the primary risk hedging instruments under any FTR mechanism, option FTRs can improve market competition by allowing flexible hedge positions. Therefore, an investigation is carried out to explore a lossy version of option FTRs. The configuration template and the settlement rule for lossy option FTRs are established. A suitable auction model is prepared for the issuance of lossy option FTRs. The lossy FTR auction formulation is carried out based on a novel representation of power flow equations. Detailed case studies are presented to show the practical utility of the proposed lossy FTR instrument.