sparse grid method in the libor market model. option valuation and the

Figures (6.14) and (6.15) show the slices of a sparse grid delta and vega profiles, respectively,
plotted against a full grid solution. Basis point (bp) is equal to 0.01%.
1.4
L1=5% L2=1.25%
1.4
L1=5% L2=1.25%
1.2
1.2
1
1
Delta value
0.8
0.6
Delta value
0.8
0.6
0.4
0.4
0.2
0.2
Full Delta L6
Sparse Delta L8. dL3 = 7bp
Sparse Delta L8. dL3 =2bp
0
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16
Forward Rate L3
0
Full Delta L6
Sparse Delta L10. dL = 2bp
-0.2
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16
Forward Rate L3
(a) Full L6 vs. Sparse L8. L 2 = 1.25%
(b) Full L6 vs. Sparse L10. L 2 = 1.25%
1.4
L1=L2=5%
1.4
L1=5% L2=5%
1.2
1.2
1
1
Delta value
0.8
0.6
Delta value
0.8
0.6
0.4
0.4
0.2
Full Delta L6
Sparse Delta L6. dL3 = 30bp
Sparse Delta L6. dL3 = 7bp
0
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16
Forward Rate L3
0.2
Full Delta L6
Sparse Delta L8. dL8 = 7bp
0
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16
Forward Rate L3
(c) Full L6 vs. Sparse L6. L 2 = 5%
(d) Full L6 vs. Sparse L8. L 2 = 5%
1.4
L1=5% L2=5.62%
1.4
L1=5% L2=5.62%
1.2
1.2
1
1
Delta value
0.8
0.6
Delta value
0.8
0.6
0.4
0.4
0.2
Full Delta L6
Sparse Delta L8. dL3 = 7bp
Sparse Delta L8. dL3 = 2bp
0
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16
Forward Rate L3
0.2
Full Delta L6
Sparse Delta L10. dL10 = 2bp
0
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16
Forward Rate L3
(e) Full L6 vs. Sparse L8. L 2 = 5.62%
(f) Full L6 vs. Sparse L10. L 2 = 5.62%
Figure 6.14: 3D Bermudan Swaption. L 3 -Delta. Slices corresponding to a fixing in L 1 = 5%
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