Hull White Accuracy Question...
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Hull White Accuracy Question...
 
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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 __________________________________________________ |
Re: Hull White Accuracy Question...
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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:
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