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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.

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  • $\begingroup$ Volatility is a measure of standard deviation. I would be weary though of using standard deviations it tends to misstate risks. $\endgroup$ Jul 24, 2019 at 14:05
  • $\begingroup$ Thanks. I am comfortable with this in practice. I was looking for the math to calculate (understanding that the risks may be misstated). $\endgroup$ Jul 24, 2019 at 15:59

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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).

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  • $\begingroup$ Thanks! to be clear, in the above example the term is 5 years - so the actual stdev = sqrt(5)*68bps = 152bps? $\endgroup$ Jul 24, 2019 at 21:57
  • $\begingroup$ Yes! I wasn’t sure if that was the term or the maturity of the underlying bond .. $\endgroup$
    – dm63
    Jul 24, 2019 at 23:19

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