can someone plz help me with this: annual volatility of rate within 1 year term = 22.5% the forward rates are calculated from each month until the end of the year (i.e. the 11-month forward rate 1 month from now, the 10-month forward rate 2 months from now, … the 1-month forward rate 11 months from now) Age (in months) Forward rate to rest of term 0 2.770 1 2.787 2 2.803 3 2.821 4 2.833 5 2.841 6 2.842 7 2.853 8 2.865 9 2.876 10 2.889 11 2.900 now we calculate the volatility (stdev) of each of these forward rates, starting with age 1 so for age 1, rate = 2.787, the volatility = .225 * SQRT(1/12) for age 2, rate = 2.803, the volatility = .225 * SQRT (2/12) and so on i dont understand how they come up with this formula for the standard deviation of each forward rate, any ideas? thx.
The basic calculation is: I tell you a stock has 10% annual vol, what is it’s semi-annual vol? You say, 10%*Sqrt(0.5) (Am I being asked to prove that?) So here there is the issue of what is the vol of a rate 7 months from now if the annual vol is 22.5% and we use the same formula 22.5%*Sqrt(7/12). But that vol is like the vol of the exchange rate fixed on a particular date (i.e., the 12/5/2009 exchange rate) not the 11 month forward rate. The 11 month forward rate has vol something like spot vol * interest rate vol or something.
thx joey. but i dont understand how the formula for standard deviation works. i thought stdev (1/12X) = stdev (x) * 1/12 if the annual standard deviation is .225, doesnt the semi annual standard deviation just become .225 * 1/2.
I’m not really sure what youre trying to get at here but the semi annual std is not .225 * 1/2. You can’t manipulate std devs like that. You can manipulate variances like that though, so what you would need to do to find the semi annual std dev is sqrt(.225^2*1/2) = sqrt(.225^2)*sqrt(1/2)=.225*sqrt(1/2) Thats why if you want convert your annual std dev to a monthly figure you would use .225*sqrt(1/12) or more generally, stdev*sqrt(time).