I am not seeing a lot of research popping up where the numeraire is changed from the "LIBOR bank account" to the "OIS collateral account". Everyone seems to be frantically busy trying to decide if OIS applies to collateralised and un-collateralised trades but no one seems to talk about the impact of changing the numeraire. Has anyone else thought about this or is the reason for it non-existence a matter of non-relevance? If I am right then this will have a significant effect on modelling XVA.My understanding is as follows:Let's assume that we are using OIS discount curves (be it because of Hull-White arguments or be it because of funding arguments). Then, to fair-value a vanilla Interest Rate Swap, you need at least two curves:- The first is the x-month LIBOR used to project cash flows- The second is the OIS discount curve to discount floating/fixed paymentsIn a world where LIBOR is risk-free, we could resort to simulating one curve, the LIBOR curve and use this for both steps mentioned above. But, if we assume a different risk-free rate, equal to the OIS rate, then we need to simulate the OIS rate (in order to discount cash flows) under the "OIS measure", but also simulate the LIBOR curve under the same OIS measure. I did however find this one lonely paper which implements this idea but I am curious to here what wilmotters are thinking?cheersg

When it comes to simulation, we talk about forward Libor rate, and this value depends on the measure we choose. Under the single curve assumption, textbooks usually use the fact that there is a non-arbitrage relation between forward libor and bonds to conclude that it is a martingale under the T-forward measure( we can conclude the same result differently).Usually our references to build the libor curve are swap quotes collateralized ( OIS discounted) , and the most convenient way to extract information from a standard swap is to define the T-Forward measure( OIS), so we keep the classic (model-independent) pricing formula DF*delta*FW. This forward libor is by construction a martingale under the t-forward(OIS) measure. So everything remains the same as before, except that the measure as moved from T-forward LIBOR measure to t-forward OIS measure.