I am trying to use the Black 76 model to calculate the price of a bond option. Is it possible to use the historical volatility of the bond prices (say standard deviation of the log returns over the last 30 days) as the volatility input into the Black 76 formula? If not, then what should I be using as the volatility input? Any help would be greatly appreciated. Thanks!
Ideally, you should use the implied volatility: this is the volatility that, when input into the Black formula, returns the price that the option has right now in the market. But if you don't have this data (sometimes, depending on purpose, even if you had this data), you have to get an estimation of the volatility.
In this case, using the historical volatility is a good choice. Keep in mind that using 30 days is just a choice, and that you may get different results (so different option prices) if you use shorter or longer periods (I tend to use as a period the time to maturity: for an option with a 6 month maturity I would use 6 months of data, but, again, this is a disputable choice)