# Calculating the volatility of an interest rate swap

At its most basic the volatility of an instrument is the standard deviation of its return series over time calculated as percentage change of the price series.

How would this work for interest rate swaps where the "price" is a rate and is expressed as a percentage? I would be inclined to proceed using the percentage change in the swap rate to calculate the volatility. Is this the correct approach?

• Commented Jun 5, 2023 at 10:56

Volatility is a measure of the deviation from expected value over a given time horizon. The expected value of an IRS is the forward rate of the IRS to that time horizon. Let's assume this forward rate is normally distributed. Standard volatility quote convention for vols in IRS vol markets is basis points/day $$\sigma_d$$ (this is an absolute change in bps of the swap rate) and is related to the annualized bp volatility $$\sigma$$ via $$\sigma=\sigma_d\sqrt{252}$$ (for 252 business days in a year). So if the $$n$$-year vol of an $$N$$-year swap is $$\sigma_d$$ bps/day and the $$n$$-year forward rate is $$F$$, then this means that there is a 68% probability that the $$N$$-year swap rate in $$n$$-years time will be in the range $$F\pm\sigma\sqrt{n}$$.