I have an elementary bond volatility math question - if 5y black vol is 38 and normal vol is 68, and the yield is 1.85%, how do I calculate 1 stdev in yield terms? As in how many basis points (or percentage) would 1 standard deviation be.
The annualized basis point standard deviation is equal to (a) the normal vol and (b) the lognormal (Black) vol times the forward yield of the instrument. In the above question, (a)=68bp and (b)= 0.38*185bp = 70bp so these are roughly in agreement.
The actual standard deviation is equal to the sqrt(expiration) times the annualized s.d , so for example, a 6 month option, sqrt(1/2) times 68bp = about 48bp. (This assumes the actual distribution of the underlying is a normal distribution).