Perhaps there are many separate parts to your question:
1) Government controlled stability
2) Bank & insurance controlled stability
3) Multinational influenced stability
4) Speculator controlled stability
5) Payroll confidence
6) Purchaser confidence
7) Resource price uniformity
8) Other
The Wikipedia article on hyperinflation describes 39 separate incidents of hyperinflation, starting with “Angola experienced high inflation from 1991 to 1995. It was a result of exchange restrictions following the introduction of the novo kwanza (AON) to replace the original kwanza (AOK) in 1990.”, “Argentina went through steady inflation from 1975 to 1991. Democratically elected on December 10, 1983, President Alfonsin inherited a foreign debt crisis and record budget deficits, resulting in US$43 billion foreign debt, with Argentina’s entire trade surplus going to debt service.”, “Armenia experienced high inflation and hyperinflation from January 1992-December 1994. Its first episode of hyperinflation was due to the use of the Russian ruble after the dissolution of the Soviet Union.”
1) I vividly remember an incident when the the shadow treasurer John Howard deliberately tried to destroy the stability of the Australian dollar by telling everyone to take their money out of the bank. Only the rapid response by Bob Hawke saved Australia from total disaster.
The greatest cause of financial instability is war. Writing in 2011, “Every major war in the past century brought inflation to some degree”. So you can see that diplomatic efforts to keep the peace count as work in keeping currencies stable.
Loans between difference countries act to stabilise the economies of those countries. During the American Revolution the fledgling county of America defaulted on government loans from Europe.
2) It is in the interests of banks, insurance companies and other financial institutions to foster financial stability. In Australia, the legislated need for banks to keep a certain fraction of their money in liquid form aids stability.
3) Ditto
4) The Black–Scholes model is a mathematical model of a financial market containing certain derivative investment instruments. If speculators agree on the same pricing structure then even speculators help to even out price fluctuations.
The commodities market was originally intended as a way of stabilising prices that would otherwise be influenced by vagaries such as unseasonal weather and plagues.
Another stabilising influence against natural disasters is insurance.
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7) It is even possible to see “refrigeration”, other methods of “food preservation” and the “development of crop strains with extended shelf life” as stabilising influences on currency. They help to ensure close-to-uniform prices for resources throughout the year. Similar resource price stabilisation is seen in the global agreements on oil pricing.
8) Does bankruptcy law help to ensure national financial stability?