Risk Measures

Modified duration, D_Mod, for a single-tranche MBS maturing at M can be calculated using the formula:

[18]

Similarly, convexity, C_x, can be calculated using the formula:

VAL01, the dollar value of a 100 basis point change in yield, can be calculated as follows:

[20]

where

FP(Y_s)=price plus accrued calculated at a semi-annual yield of Y_s;

Duration and convexity can also be calculated using shocks to the yield curve:;

[21]

[22]

Note that, in the numerators of equations 20 through 22, accrued interest cancels out; thus, market prices could be used. However, in the denominators of 21 and 22, the full price including accrued interest must be used.