What is the logic of Bagehot's policy of high interest rate? I have a doubt about monetary policy, as suggested by Walter Bagehot. He wrote a book "Lombard Street" in 1873, to comment on a recent banking crisis. There he recommends these measures to stop a banking panic:


That the central bank lend freely.
At a high rate of interest.
On good banking securities.


The second point is particularly puzzling. In his own words:


  First. That these loans should only be made at a very high rate of interest. This will operate as a heavy fine on unreasonable timidity, and will prevent the greatest number of applications by persons who do not require it. The rate should be raised early in the panic, so that the fine may be paid early; that no one may borrow out of idle precaution without paying well for it; that the Banking reserve may be protected as far as possible.


(From Wikipedia: https://en.wikipedia.org/wiki/Lombard_Street:_A_Description_of_the_Money_Market)

This goes counter the main narrative in the press today, which is that central banks have to lower the interest rate in order to increase lending and economic activity, not to increase it. Bagehot's policies could actually exacerbate the crisis! A high interest rate might produce deflation, which exacerbates debts, like in the Great Depression. What is going on here?
We need to distinguish between a crisis and a normally functioning financial system. During a crisis, there is an unwillingness to lend  against collateral at any price (interest rate). Financial firms are liquidity constrained, and they assume that the entities that want to borrow are similarly constrained. Being able to fund positions in securities at any price is a huge relief, since that means you are not forced to sell (at a distressed price).

As an example, imagine that a financial firm needs to borrow at 12% interest to finance a position in corporate bonds. If that borrowing is done for a month at that rate, the total interest cost would be 1%. This is probably going to be much less costly than being forced to sell the position; a loss of 20% would not be unusual in such a situation.

Furthermore, the crisis lending is done by the central bank to financial firms facing financing issues; it is not aimed at the broad public. During the Financial Crisis, lending programs were aimed at banks and security markets, not non-financial entities.

The level of short-term rates does not really matter that much; once the markets return to normal, you will be able to fund your positions at a much better rate. Having to pay a high rate of overnight interest for a week on a long-term security is not a big deal.

The argument for lender-of-last-resort operations at a high level of interest is that you do not want this facility to be a regular source of financing for the financial system.