I am interested to model the impact of recently negative interest bonds on the portfolio. The literature on modelling negative interest rates is limited, and the only theory I could find was the "liquiduity gap" one and the plasma currency (electronic money having to take over regular cash). Here there are some points (some might be contradictory) about which I am asking for some actual formulae/algorithms, if it happens you to know any: The value of higher presently outgoing cash flows is les important than the value of future incoming cash flows. To me this sounds to be the case for intertemporal rate marginal substitution (pensions, etc), where this is a model to model a margin and not the whole rate. From the computational point of view I see it as marking to the future market rather than marking to the presently observed market prices, in order to do (spreads/model) calibration. Since the real cash presence in the transactions is the main issue, in addition to the present netting system, consider an additional netting, the one of all the electronic /credit cards/checks based (plasma currency of Keynes's liquidity trap) cash flows and derive different formulae for electronic and non-electronic settlement. With this additional netting in place, from the portfolio's owner point of view the negative non-plasma flows should be discounted at the funding rate (the by-principal-weighted average of all the incoming/positive cash flows) and the positive non-plasma flows (deposited) should be discounted at the average investing rate (the weighted-by-principal return rate of all the non-plasma future flows). In spite of EBA's accounting principles. The discounting curves are generally inferred from zero coupon bonds, especially for short rates, where such coupons exist. Given the recent gouvernamental interest rate bonds, this implies that the discounting curve has to be negative, at least for short rates. But the negative interest rates to be modelled with a Japanese style inverted yield curve might not be optimal, given that the historically known inverse curves. They were due to short rates becoming larger than the longs ones and short positive rates stopped to increase by the government stepping in and lowering the them. Such a move cannot revert the actual curve to a normal one, and also, the considered credit quality might not be the same at the terms considered when comparing short-term to long-term interest rates. The presently observed negative interest rates seem to increase in magnitude with the term. Could their modeling follow the one for positive rates, having all the signs reversed, without taking care of the sign? A sort of imaginary rates, that become negative only when one takes their Since the increase in magnitude of the negative interest rate can be modeled by an increase in the perceived credit risk, might momentum profitability drive future investments? As, for the high risk, momentum profitability decreases with size, will be the volume be practically capped by its averaged credit rating? Because the amount which can be borrowed by an entity is limited and depositing now might be treated as collateral to borrowing in the future, could be that the maximum depositing amount is limited? In this case the magnitude of negative interest rates should increment depending on the left size of the depositable amount. Should then portfolio-specific negative interest rates be modeled, taking into account not only the time, but also the frequency and the magnitude of the cash flows? Will negative interest rates evolution continue to be smooth, with rating states neglected in practice and only reflected in continuous spreads, or jumps need consideration due to discrete credit rating system? Should the magnitude of the negative interested rate be modeled into a correlated fashion with the increase in fixed assets prices and the cross-currency basis spreads would need to be simulated correlated with the associated negative interest rates? And how should be their volatility / correlation coefficients determined? Should the credit risk be considered completed integrated in the actually observed market prices, and the change in the credit rate to trigger the change in the interest rate/market value? Hoping that you could give your opinion and come with an actual mathematical formula/algorithm on how to model the influence of future negative rates on risk at the portfolio level, or links to such a documentation