ch 10 sabr model v1

7/25/2019 Ch 10 SABR model v1

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2/9

0.!"


3/9

10.33: Market data - Forward USD volatility surface (

$e%or &$M vols 1.'0 1.)' *.00 *.*'

1.00 1 13.32% 31.59% 29.38% 26.09% 22.19%

1.50 2 16.26% 30.09% 27.08% 22.63% 16.19%2.00 3 14.80% 29.35% 26.57% 22.84% 16.98%

3.00 4 16.90% 26.10% 23.68% 21.05% 20.12%

4.00 5 15.72% 25.56% 23.19% 20.50% 19.39%

5.00 6 16.16% 23.81% 21.82% 20.70% 19.73%

6.00 7 15.28% 23.36% 21.90% 20.10% 18.89%

7.00 8 15.24% 23.08% 21.38% 19.64% 18.80%

8.00 9 14.60% 21.20% 20.21% 19.65% 18.68%

9.00 10 14.23% 22.52% 21.02% 19.34% 18.06%

10.00 11 14.16% 21.27% 20.27% 19.57% 18.52%

12.00 12 12.80% 20.43% 18.88% 17.75% 16.48%15.00 13 12.44% 19.80% 18.81% 17.73% 17.19%

20.00 14 11.60% 18.86% 17.06% 16.04% 14.91%

25.00 15 10.63% 17.34% 16.85% 16.07% 15.18%

30.00 16 10.97% 18.21% 16.04% 14.54% 14.34%


4/9

xtracted from orks!eet 10."#

*.'0 3.00 3.'0 +.00 '.00 ,.00 ).00 .00

20.53% 15.94% 12.96% 13.89% 15.19% 17.15% 19.08% 20.80%

16.54% 15.82% 15.10% 15.82% 16.43% 17.72% 18.99% 20.04%17.36% 16.28% 15.50% 15.05% 16.04% 17.32% 18.60% 19.65%

18.69% 17.18% 16.67% 16.43% 16.45% 16.84% 17.50% 18.34%

18.66% 17.19% 16.18% 15.81% 15.94% 16.84% 17.62% 18.35%

18.60% 17.31% 16.42% 15.94% 15.67% 15.94% 16.84% 17.46%

18.06% 16.65% 15.44% 15.24% 15.08% 15.74% 16.24% 16.87%

18.10% 16.45% 16.01% 15.41% 14.88% 15.10% 15.63% 16.43%

17.59% 16.28% 15.40% 14.52% 14.46% 14.72% 15.20% 15.77%

17.17% 16.09% 14.89% 14.44% 13.88% 14.14% 14.99% 15.34%

17.62% 15.81% 14.80% 13.20% 12.93% 13.69% 14.19% 15.01%

16.08% 14.79% 13.61% 13.92% 13.50% 12.65% 12.51% 12.57%15.87% 14.68% 14.33% 12.28% 11.23% 12.18% 13.31% 13.81%

14.91% 13.15% 11.42% 12.68% 11.96% 11.10% 10.59% 11.08%

13.50% 12.96% 13.30% 10.09% 9.89% 11.04% 12.25% 12.66%

13.33% 11.97% 9.46% 12.67% 11.83% 12.03% 11.42% 11.80%


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10.00

22.97%

22.02%21.49%

19.68%

19.62%

18.75%

18.18%

17.40%

16.88%

16.46%

15.70%

14.19%13.70%

13.02%

12.68%

13.44%


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10.3+: S&/ arameters estimated usi% 2elder-M

Term Forward Atm Vol beta alpha

1 3.907% 13.32% 1 0.1006

1.5 3.887% 16.26% 1 0.1604

2 4.237% 14.80% 1 0.1426

3 3.969% 16.90% 1 0.1673

4 3.962% 15.72% 1 0.1527

5 4.010% 16.16% 1 0.1586

6 4.094% 15.28% 1 0.1487

7 4.144% 15.24% 1 0.1490

8 4.240% 14.60% 1 0.1419

9 4.279% 14.23% 1 0.1380

10 4.342% 14.16% 1 0.1379

12 4.422% 12.80% 1 0.1252

15 4.473% 12.44% 1 0.1194

20 4.462% 11.60% 1 0.1134

25 4.232% 10.63% 1 0.0974

30 4.065% 10.97% 1 0.1028


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ad least suares alorit!m

rho v error

0.4536 -0.9112 0.463%

0.1469 -0.3765 0.652%

0.0640 -0.4930 0.647%

0.2285 -0.2857 0.211%

0.1216 -0.3291 0.221%

0.2225 -0.2862 0.071%

0.2081 -0.2965 0.130%

0.2313 -0.2722 0.155%

0.2075 -0.2672 0.138%

0.2257 -0.2673 0.177%

0.2715 -0.2648 0.186%

0.3001 -0.2382 0.211%

0.2676 -0.2539 0.219%

0.3319 -0.2117 0.317%

0.2208 -0.2561 0.353%

0.2541 -0.2215 0.407%


8/9


9/9

market

/T'e## 8 9(8# term 1 term * term 3 sima volatilities

289.5% -2.041 -1.332 0.138 1.532 1.027 21.70% 21.27%

248.1% -1.745 -1.207 0.138 1.446 1.027 20.48% 20.27%

217.1% -1.489 -1.086 0.138 1.371 1.027 19.42% 19.57%

193.0% -1.262 -0.967 0.138 1.305 1.027 18.49% 18.52%

173.7% -1.060 -0.850 0.138 1.247 1.027 17.67% 17.62%

144.7% -0.710 -0.617 0.138 1.151 1.027 16.30% 15.81%

124.1% -0.414 -0.384 0.138 1.078 1.027 15.26% 14.80%

108.6% -0.158 -0.154 0.138 1.025 1.027 14.52% 13.20%

86.8% 0.271 0.278 0.138 0.975 1.027 13.81% 12.93%72.4% 0.621 0.634 0.138 0.979 1.027 13.87% 13.69%

62.0% 0.917 0.907 0.138 1.011 1.027 14.32% 14.19%

54.3% 1.173 1.115 0.138 1.053 1.027 14.91% 15.01%

43.4% 1.602 1.406 0.138 1.139 1.027 16.13% 15.70%

0.00% 2.00% 4.00% 6.00% 8.00% 10.00% 12.00%

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%

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Comparing the SABR curve with Market data

Example: T = 1 !r"

SABR curve

Market

Volatilities

Strike

ch 10 sabr model v1

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