P1.T4 "Valuation & Risk Model" EOC 13.14

[AUola2165]

question:
Suppose that the 12-month and 30-month spot rates are chosen as key rates. Plot the key rate 01 shifts.

why is the 12-month shift plotted so that the shift starts from maturity 0 and then starts the decline from maturity 1 (12 months) onwards whereas the plotting the 30.month spot rate shift starts increasing at 1 (12-month maturity) and doesn't decline after 2,5 maturity (30 months)?

How would 24 month spot rate be 01 shifted?

Answer:

 

[David Harper CFA FRM]

Hi @AUola2165 It's on the next page. I think it would be better if the solution showed a single graph with two lines, where the span from 1.0 year to 2.5 years ( = 30 months) showed the overlapping lines. But those lines do look correct to me. A way to "check" the solution is to verify that any maturity sums to 1.0 basis point, which is the case here; e.g., at 2.0 years, the height of each line is 0.5 basis point. I hope that helps! Thanks,

 

[David Harper CFA FRM]

Hi @AUola2165 I must have replied (effectively) prior to your edit. To respond to

why is the 12-month shift plotted so that the shift starts from maturity 0 and then starts the decline from maturity 1 (12 months) onwards whereas the plotting the 30.month spot rate shift starts increasing at 1 (12-month maturity) and doesn't decline after 2,5 maturity (30 months)?

The question only specifies to key rates:

• For the 1.0 year KR: shift from 0 to 1.0 year; then interpolate down to 2.5 because it is the nearest neighbor
• For the 2.5 year KR: interpolate up from 1.0 because it is nearest neighbor; then flat to 30 year
  (no decline from zero to first key rate, and no decline from last key rate to final maturity)

From 1.0 to 2.5, each maturity sums to 1.0 because the two neighbors contribute to the shift

How would 24 month spot rate be 01 shifted?

• +0.333 For the 1.0 year KR because = 12/(30-12); i.e., two-third down the 1.0's interpolated slope
• +0.667 For the 2.5 year KR because = 6/(30-12); i.e., two-thirds up 2.5's the interpolated slope
• These sum to 1.0. Thanks,