# Displaced diffusion LMM

In the standard LMM a rate $$L_i(t)=L(t,T_{i-1},T_i)$$ has under the $$T_n$$-forward measure ($$n>i$$) the dynamics $$$$d{L_i}(t) = - {\sigma _i}(t){L_i}(t)\sum\limits_{j = i + 1}^n {\frac{{{\tau _j}{L_j}(t)}}{{1 + {\tau _j}{L_j}(t)}}{\sigma _j}(t){\rho _{ij}}} dt + {\sigma _i}(t){L_i}(t)d{W_i}(t).$$$$ Now that the rates are negative, it would be desired to model a displaced diffusion, i.e. instead of $$dL_i$$ model $$d(L_i+\gamma)$$.

Is such an adjustment possible without breaching the model arbitrage-free assumptions?

I already checked the literature and nowhere I can find any references.