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About one week ago the Danish Nordea Kredit started paying mortgage holders to borrow money by charging a negative interest rate. When doing short-selling of shares in the stock market, you promise to sell somebody shares for a price lower than they are selling for, because when the time comes to deliver the shares you are expecting to pick them up cheap. From financial point of view, the negative interest rates mortgages could be represented as a short sale of currency, in the context of a deflationary economy.

Mathematically, the credit risk spread can be mapped, through averaging, to the probability of default. A negative spread would then translate to negative probabilities. For the very moment, the thing that jumps to my mind is what Paul Dirac used to write more than 70 years ago: « Negative energies and probabilities should not be considered as nonsense. They are well-defined concepts mathematically, like a negative of money. » Negative energies do get employed in particle physics. Dirac associated them to antiparticles/holes, which do conceptually resemble to short selling. Anyway, there is a more terre à terre immediate explanation. For the negative interest mortgages, technically the negativity is covered by the negative yield of the mortgage-backed bonds that then the bank emits. In the very end, it is supported by the final investor, as a plus profit is taken by the bank from the spread between the two.

But what about the negative yield corporate bonds, which start to emerge? Technically again, the risk free interest rate is considered to be the rate offered by the central bank. If this rate is negative, investors loose less by investing into a negative yield bond. But why would somebody want to lose money, by exchanging more money now for less money in the future? It looks like the premium you willingly pay for your own future liquidity or, otherwise, against your own probability of default (debt valuation adjustment). When a house builder takes/validates a credit from a bank, a hole is created, representing the money he owns to the bank. The builder’s hole versus the bank is filled in by the money he receives from a new house owner, who has built his house by borrowing money from the same bank. The bank, via the money, transfers the hole from the house builder to the house owner. Further assuming that everybody has debts, money operates as the visualisation mechanism of the hole, which travels in the opposite direction (when money enters, the hole leaves). When money does not fill in any hole (the money owner had no debt), it is only useful as it represents the fill in for future holes or future debts that the owner will encounter. In Feynman’s terms, who gives a second interpretation to negative energies, money represents a hole/debt in the future that travelled back in time, to the present, and future liquidity can be seen as a reflexion on own credit risk, like when paying for pension/retirement.

There is a lot of debate in particle physics on what antiparticles do represent and how negative energies can be made concordant with positive mass. And this is why maybe one could at least use the available mathematical recipes to deal with current financial events. As in order to produce an item one needs to start from primary ingredients, standardly valuated in money, a functioning, producing economy can be naturally assimilated to a Dirac sea of holes. And one can also seem to be naturally happier to pay for being able to invest the money and eventually be taxed on the gain (which is  none under negative investments), than for keeping the cash at zero rates and being taxed on the whole fortune. This does make the mathematics really less difficult understanding.