QuantLib - Re: Hull White Accuracy Question...

Re: Hull White Accuracy Question...

Posted by quanta veloce on Sep 03, 2005; 2:18pm
URL: http://quantlib.414.s1.nabble.com/Hull-White-Accuracy-Question-tp4022p4023.html

Sorry, these are the results with constant 20% vol...still don't know why the large diffs...any hints to increase accuracy?

BTW, Quantlib rocks!!

Thanks,

Today: Friday, August 19th, 2005
Settlement date: Tuesday, August 23rd, 2005
Created Swap with following details:
Fixed Rate: 0.05
Start Date: August 23rd, 2006
End Date: August 25th, 2008
Fixed Schedule: semiannual
Float Schedule: semiannual
Pay or Receive: Pay
Swap rate: 0.0494313

swaption maturity: 1 year
swap maturity : 3
Volatility: 0.2
Rate: 4.996649 % act/365 (fixed) simple compounding

swaption maturity: 2 years
swap maturity : 2
Volatility: 0.2
Rate: 5.121482 % act/365 (fixed) simple compounding

swaption maturity: 3 years
swap maturity : 1
Volatility: 0.2
Rate: 5.250472 % act/365 (fixed) simple compounding

Hull-White (analytic formulae) calibration
1x3 details:
Model NPV: 0.0103639, Market NPV: 0.0103422
Vols:: model: 20.04217 %, market: 20.00000 % (+0.04217 %)
Calibration error: 0.0021016
2x2 details:
Model NPV: 0.0094123, Market NPV: 0.0094758
Vols:: model: 19.86501 %, market: 20.00000 % (-0.13499 %)
Calibration error: 0.006705
3x1 details:
Model NPV: 0.0056849, Market NPV: 0.0056588
Vols:: model: 20.09332 %, market: 20.00000 % (+0.09332 %)
Calibration error: 0.004619
calibrated to:
a = 0.0079661, sigma = 0.0097843

Hull-White (numerical) calibration
1x3 details:
Model NPV: 0.0086674, Market NPV: 0.010342
Vols:: model: 16.75290 %, market: 20.00000 % (-3.24710 %)
Calibration error: 0.16194
2x2 details:
Model NPV: 0.0097676, Market NPV: 0.0094758
Vols:: model: 20.62008 %, market: 20.00000 % (+0.62008 %)
Calibration error: 0.030788
3x1 details:
Model NPV: 0.0061994, Market NPV: 0.0056588
Vols:: model: 21.93271 %, market: 20.00000 % (+1.93271 %)
Calibration error: 0.095527
calibrated to:
a = 0.2813, sigma = 0.017122

Black-Karasinski (numerical) calibration
1x3 details:
Model NPV: 0.0090424, Market NPV: 0.010342
Vols:: model: 17.47958 %, market: 20.00000 % (-2.52042 %)
Calibration error: 0.12568
2x2 details:
Model NPV: 0.0097029, Market NPV: 0.0094758
Vols:: model: 20.48256 %, market: 20.00000 % (+0.48256 %)
Calibration error: 0.023962
3x1 details:
Model NPV: 0.0061299, Market NPV: 0.0056588
Vols:: model: 21.68415 %, market: 20.00000 % (+1.68415 %)
Calibration error: 0.083258
calibrated to:
a = 0.26883, sigma = 0.3317

Vanilla swaption struck at 4.94313 % (ATM)
Black Price: 44.953
HW:       44.83
HW (num): 48.879
BK:       47.017
Payer Vanilla swaption struck at 5.93175 % (OTM)
Black Price: 4.1715
HW:       2.8563
HW (num): 4.0987
BK:       5.0303
Payer Vanilla swaption struck at 3.95450 % (ITM)
Black Price: 179.27
HW:       180.44
HW (num): 181.64
BK:       179.69

quanta veloce <[hidden email]> wrote:

Hi,

I'm trying to find out if the following plain vanilla swaption results obtained using Quantlib are ok? The OTM results seem off by quite a bit.

Any suggestions on increasing the accuracy? I used 200 timesteps in the tree swaption pricing and accuracy set to 1e-9. Number of simulation was set to 100000. Vol is constant at 0.20 and I tried to make the tree flat at approx. 5%. Why such large diffs for plain vanilla swaption?

Any help appreciated.

Thanks,

----

Today: Friday, August 19th, 2005
Settlement date: Tuesday, August 23rd, 2005
Created Swap with following details:
Fixed Rate: 0.05
Start Date: August 23rd, 2006
End Date: August 25th, 2008
Fixed Schedule: semiannual
Float Schedule: semiannual
Pay or Receive: Pay
Swap rate: 0.0494313

swaption maturity: 1 year
swap maturity : 3
Volatility: 0.2257
Rate: 4.996649 % act/365 (fixed) simple compounding

swaption maturity: 2 years
swap maturity : 2
Volatility: 0.23136
Rate: 5.121482 % act/365 (fixed) simple compounding

swaption maturity: 3 years
swap maturity : 1
Volatility: 0.21195
Rate: 5.250472 % act/365 (fixed) simple compounding

Hull-White (analytic formulae) calibration
1x3 details:
Model NPV: 0.0115111, Market NPV: 0.0116658
Vols:: model: 22.26942 %, market: 22.57000 % (-0.30058 %)
Calibration error: 0.013263
2x2 details:
Model NPV: 0.010464, Market NPV: 0.010949
Vols:: model: 22.10125 %, market: 23.13600 % (-1.03475 %)
Calibration error: 0.044353
3x1 details:
Model NPV: 0.0063117, Market NPV: 0.0059932
Vols:: model: 22.33494 %, market: 21.19500 % (+1.13994 %)
Calibration error: 0.053131
calibrated to:
a = 0.030186, sigma = 0.011349

Hull-White (numerical) calibration
1x3 details:
Model NPV: 0.0095604, Market NPV: 0.011666
Vols:: model: 18.48374 %, market: 22.57000 % (-4.08626 %)
Calibration error: 0.18048
2x2 details:
Model NPV: 0.010852, Market NPV: 0.010949
Vols:: model: 22.92806 %, market: 23.13600 % (-0.20794 %)
Calibration error: 0.0089088
3x1 details:
Model NPV: 0.0068261, Market NPV: 0.0059932
Vols:: model: 24.18110 %, market: 21.19500 % (+2.98610 %)
Calibration error: 0.13896
calibrated to:
a = 0.20269, sigma = 0.016749

Black-Karasinski (numerical) calibration
1x3 details:
Model NPV: 0.010014, Market NPV: 0.011666
Vols:: model: 19.36327 %, market: 22.57000 % (-3.20673 %)
Calibration error: 0.1416
2x2 details:
Model NPV: 0.010825, Market NPV: 0.010949
Vols:: model: 22.87041 %, market: 23.13600 % (-0.26559 %)
Calibration error: 0.011379
3x1 details:
Model NPV: 0.0067438, Market NPV: 0.0059932
Vols:: model: 23.88529 %, market: 21.19500 % (+2.69029 %)
Calibration error: 0.12523
calibrated to:
a = 0.15478, sigma = 0.30705

Vanilla swaption struck at 4.94313 % (ATM)
Black Price: 44.953
HW: 49.995
HW (num): 54.647
BK: 52.892
Payer Vanilla swaption struck at 5.93175 % (OTM)
Black Price: 4.1715
HW: 4.4733
HW (num): 6.5393
BK: 7.9469
Payer Vanilla swaption struck at 3.95450 % (ITM)
Black Price: 179.27
HW: 182.11
HW (num): 184.07
BK: 181.11

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