Price volatility and yield volatility

In fixed-income option markets, prices are often expressed as yield volatilities
rather than the price volatilities on which we have focused. The choice between yield
volatility and price volatility corresponds to the choice of considering the option as
written on an interest rate or on a bond price.
By assuming that the interest rate the option is written on behaves as a random
walk, the Black–Scholes model assumption, the Black–Scholes formulas can be
applied with interest rates substituted for bond prices. The yield volatility of a fixedincome
option, like the price volatility, is thus a Black–Scholes implied volatility. As
is the case for other options quoted in volatility term, this practice does not imply
that dealers believe in the Black–Scholes model. It means only that they find it
convenient to use the formula to express prices.
There is a useful approximation that relates yield and price volatilities:
Yield volatility
Price volatility
Durationîyield
To use the approximation, the yield must be expressed as a decimal. Note that when
yields are low, yield volatility tends to be higher.