Is there a calculation for exchange rate stability?
This site can help you calculate the beta of Bitcoin:

https://btcvol.info/

"What definition of volatility does btcvol.info use?

The standard deviation of daily returns for the preceding 30- and 60-day windows. These are measures of historical volatility based on past Bitcoin prices. When the Bitcoin options market matures, it will be possible to calculate Bitcoin's implied volatility, which is in many ways a better measure."

https://en.wikipedia.org/wiki/Beta_(finance)

In finance, the beta (β or beta coefficient) of an investment indicates whether the investment is more or less volatile than the market. In general, a beta less than 1 indicates that the investment is less volatile than the market, while a beta more than 1 indicates that the investment is more volatile than the market. Volatility is measured as the fluctuation of the price around the mean: the standard deviation.