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!
Add a comment
|
2 Answers
$\begingroup$
$\endgroup$
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)
$\begingroup$
$\endgroup$
You should try to start with implied volatilities as long as you have other financial instruments on similar underlyings that have good liquidity and can be priced using Black 76.
In this case, let's say you want to price treasury bond options. These are most likely OTC traded. Assume there are abundant trades on treasury futures options(related to bonds) traded on exchanges. Then it is a good idea to get a volatility surface from treasury futures options of different maturities and use these vols as input parameters.
Historical vols are backward-looking and your options are forward-looking, so it would be more natural to use implied vols in general. However in markets where products are thinly traded and implied vols are not stable or even available, you can use historical vols as long as it justifies your goals.
