bond.cir: Simulates the values and yields of zero-coupon bonds when the...

Description Usage Arguments Value Note Author(s) References Examples

Description

Simulates the values and yields of zero-coupon bonds when the (annualized ) spot rate (in percent) is modeled by a Feller process satisfying

dr = alpha(beta-r)dt + sigma sqrt(r) dW,

with market price of risk q = q1/sqrt(r) +q2 sqrt(r). The maturities are 1,3,6 and 12 months.

Usage

1
bond.cir(alpha, beta, sigma, q1, q2, r0, n, maturities, days = 360)

Arguments

alpha

Mean-reversion parameter.

beta

Long term mean.

sigma

Volatility parameter.

q1

Market prime of risk parameter.

q2

Market prime of risk parameter.

r0

Initial rate value.

n

Number of periods.

maturities

Maturities in years (row vector).

days

Days in a year convention (360 default).

Value

P

Bond values.

R

Annual rate for the bond.

tau

Maturities in years.

Note

Translated from Matlab by David-Shaun Guay (HEC Montreal grant).

Author(s)

Bruno Remillard

References

Chapter 5 of 'Statistical Methods for Financial Engineering, B. Remillard, CRC Press, (2013).

Examples

1
out = bond.cir(0.5,2.55,0.365,0.3,0,3.55,1080,c(1/12, 3/12, 6/12, 1),365)

Example output

Loading required package: ggplot2
Loading required package: reshape
Loading required package: corpcor
[1] 30.12314
[1] 48.48102
[1] 32.98553
[1] 35.41636
[1] 25.96343
[1] 51.78656
[1] 34.82703
[1] 36.35213
[1] 34.82777
[1] 26.44669
[1] 39.04664
[1] 31.39807
[1] 30.63557
[1] 32.51419
[1] 36.22576
[1] 33.0517
[1] 52.40529
[1] 29.48238
[1] 45.61717
[1] 37.1412
[1] 27.53733
[1] 55.72955
[1] 43.97201
[1] 39.07869
[1] 29.59749
[1] 37.81171
[1] 33.50894
[1] 35.40406
[1] 51.66497
[1] 40.37302
[1] 43.44668
[1] 35.83414
[1] 33.31331
[1] 37.99299
[1] 34.30542
[1] 56.15551
[1] 45.50388
[1] 63.79374
[1] 49.08206
[1] 27.57982
[1] 34.08568
[1] 27.70287
[1] 39.31921
[1] 32.81123
[1] 31.39528
[1] 31.67779
[1] 42.12539
[1] 25.96879
[1] 34.46317
[1] 33.12497
[1] 42.04635
[1] 30.16559
[1] 37.32172
[1] 37.65069
[1] 45.24339
[1] 45.07828
[1] 38.37924
[1] 41.79789
[1] 28.06909
[1] 20.35057
[1] 35.87857
[1] 49.5109
[1] 36.70626
[1] 27.5837
[1] 25.25087
[1] 31.35015
[1] 26.1296
[1] 31.54258
[1] 50.36392
[1] 30.42636
[1] 33.1844
[1] 31.19268
[1] 42.94887
[1] 30.29513
[1] 46.12018
[1] 44.85953
[1] 37.98122
[1] 39.89815
[1] 35.80832
[1] 36.78991
[1] 50.36913
[1] 41.76405
[1] 49.63332
[1] 38.61705
[1] 37.21963
[1] 30.6982
[1] 33.98368
[1] 36.33669
[1] 29.50976
[1] 33.7444
[1] 38.81484
[1] 44.48161
[1] 50.58939
[1] 30.68842
[1] 28.39656
[1] 32.13533
[1] 25.10631
[1] 37.45983
[1] 32.1697
[1] 44.75663
[1] 23.32385
[1] 44.86214
[1] 29.2302
[1] 40.73408
[1] 49.28504
[1] 27.36074
[1] 24.64509
[1] 38.10809
[1] 31.8996
[1] 37.61719
[1] 38.0716
[1] 37.80761
[1] 46.05055
[1] 41.13237
[1] 27.12315
[1] 50.33026
[1] 40.71317
[1] 28.45529
[1] 29.94647
[1] 40.66095
[1] 36.33654
[1] 30.56981
[1] 48.22717
[1] 34.30118
[1] 24.9897
[1] 20.51928
[1] 26.35961
[1] 30.88024
[1] 39.24648
[1] 40.69854
[1] 36.42196
[1] 25.20521
[1] 46.72554
[1] 41.16047
[1] 27.98428
[1] 49.99502
[1] 53.39261
[1] 38.32277
[1] 33.83264
[1] 32.54342
[1] 36.51241
[1] 53.47317
[1] 51.84023
[1] 29.20682
[1] 33.81192
[1] 40.84844
[1] 28.10905
[1] 37.44324
[1] 24.06816
[1] 30.94702
[1] 46.67106
[1] 31.39709
[1] 34.8592
[1] 22.82621
[1] 35.29195
[1] 54.3244
[1] 42.52846
[1] 32.22477
[1] 29.64109
[1] 42.9666
[1] 27.13768
[1] 24.93557
[1] 23.80606
[1] 26.68488
[1] 39.44206
[1] 43.2495
[1] 32.29905
[1] 28.13518
[1] 24.27226
[1] 49.62645
[1] 32.52333
[1] 27.4684
[1] 31.72381
[1] 37.29203
[1] 43.74482
[1] 30.80569
[1] 33.0922
[1] 53.08098
[1] 37.23347
[1] 40.49391
[1] 39.68629
[1] 32.77557
[1] 41.36412
[1] 40.62058
[1] 44.1289
[1] 18.87503
[1] 31.88709
[1] 35.57117
[1] 30.49348
[1] 36.33502
[1] 27.43552
[1] 44.05055
[1] 33.27019
[1] 35.44431
[1] 28.09648
[1] 31.2978
[1] 32.71596
[1] 39.78801
[1] 40.73674
[1] 39.76822
[1] 39.52434
[1] 46.52088
[1] 26.30097
[1] 34.93386
[1] 32.30207
[1] 53.1787
[1] 44.45009
[1] 40.09302
[1] 43.53328
[1] 33.80099
[1] 30.08226
[1] 34.96918
[1] 27.01768
[1] 18.73172
[1] 32.15811
[1] 45.81781
[1] 37.57069
[1] 22.62801
[1] 44.72829
[1] 33.37182
[1] 36.94091
[1] 24.40743
[1] 38.88244
[1] 38.17406
[1] 28.79377
[1] 38.14988
[1] 36.71607
[1] 55.19847
[1] 30.67868
[1] 50.08698
[1] 34.17468
[1] 27.12835
[1] 37.17921
[1] 59.10413
[1] 36.9746
[1] 43.88238
[1] 48.862
[1] 51.62331
[1] 35.96445
[1] 30.93029
[1] 27.0473
[1] 31.16753
[1] 38.58303
[1] 46.92001
[1] 28.34483
[1] 34.61226
[1] 37.58729
[1] 53.92882
[1] 44.33621
[1] 31.22661
[1] 35.20003
[1] 55.13138
[1] 44.09544
[1] 37.75057
[1] 37.78357
[1] 30.09853
[1] 30.63265
[1] 64.915
[1] 55.84579
[1] 16.69019
[1] 26.59293
[1] 35.75304
[1] 30.83041
[1] 39.26844
[1] 43.48713
[1] 29.03518
[1] 36.40562
[1] 35.70397
[1] 27.73955
[1] 56.64475
[1] 56.26779
[1] 43.23374
[1] 29.93153
[1] 28.24299
[1] 48.18274
[1] 44.03729
[1] 39.22368
[1] 47.27925
[1] 44.87906
[1] 45.21963
[1] 32.8471
[1] 23.06787
[1] 32.75418
[1] 33.01404
[1] 34.84224
[1] 34.6371
[1] 31.2981
[1] 40.97159
[1] 30.83715
[1] 44.38357
[1] 21.92397
[1] 51.52754
[1] 36.65094
[1] 40.06006
[1] 36.67703
[1] 42.90905
[1] 34.65798
[1] 47.26493
[1] 36.6953
[1] 29.36493
[1] 42.60454
[1] 27.39254
[1] 34.89509
[1] 32.5983
[1] 40.32044
[1] 37.53318
[1] 25.90502
[1] 31.41167
[1] 33.40122
[1] 24.67572
[1] 27.9794
[1] 24.24406
[1] 39.64661
[1] 45.38787
[1] 30.02103
[1] 35.269
[1] 39.35513
[1] 39.50301
[1] 41.14722
[1] 44.57321
[1] 30.79151
[1] 52.96992
[1] 33.76783
[1] 27.13786
[1] 46.2558
[1] 33.94221
[1] 38.80191
[1] 47.07141
[1] 32.95811
[1] 32.04196
[1] 38.73687
[1] 41.02811
[1] 45.90539
[1] 37.41779
[1] 35.56686
[1] 35.2128
[1] 26.89042
[1] 38.93336
[1] 43.4212
[1] 33.72261
[1] 50.40302
[1] 43.88484
[1] 38.43634
[1] 30.87447
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[1] 47.59137
[1] 25.08298
[1] 36.24387
[1] 36.88655
[1] 34.3405
[1] 23.48369
[1] 27.22967
[1] 37.76276
[1] 38.60515
[1] 54.98102
[1] 27.58246
[1] 39.05455
[1] 49.18665
[1] 38.28952
[1] 30.31162
[1] 56.37265
[1] 38.92605
[1] 28.95101
[1] 37.88661
[1] 62.10115
[1] 39.42699
[1] 55.48212
[1] 32.12911
[1] 30.56362
[1] 38.21883
[1] 36.00815
[1] 29.53829
[1] 29.11828
[1] 34.69598
[1] 28.75299
[1] 32.21696
[1] 32.10246
[1] 30.12335
[1] 49.99092
[1] 41.7242
[1] 38.34171
[1] 31.38871
[1] 43.57331
[1] 30.03476
[1] 35.68209
[1] 44.24188
[1] 45.6449
[1] 25.0811
[1] 46.39668
[1] 26.8597
[1] 35.61821
[1] 46.96797
[1] 68.53849
[1] 38.92435
[1] 30.58878
[1] 35.4752
[1] 26.20585
[1] 37.89979
[1] 34.05867
[1] 62.10226
[1] 30.08588
[1] 29.52639
[1] 55.11542
[1] 44.20373
[1] 33.34066
[1] 41.80545
[1] 33.05001
[1] 55.0079
[1] 26.55062
[1] 36.07087
[1] 32.64627
[1] 37.54903
[1] 39.94913
[1] 40.66378
[1] 61.6195
[1] 31.02898
[1] 35.3938
[1] 41.57636
[1] 39.09707
[1] 41.13745
[1] 40.3991
[1] 54.83296
[1] 31.21981
[1] 37.57643
[1] 40.73325
[1] 41.18775
[1] 32.09264
[1] 30.40437
[1] 37.94311
[1] 27.69371
[1] 29.93609
[1] 19.90826
[1] 38.17709
[1] 39.82776
[1] 24.29239
[1] 42.30506
[1] 31.71623
[1] 32.43482
[1] 48.33768
[1] 33.80715
[1] 39.09769
[1] 35.85553
[1] 36.84674
[1] 41.78862
[1] 45.31095
[1] 43.81214
[1] 40.58682
[1] 24.91793
[1] 20.11559
[1] 32.3137
[1] 32.18014
[1] 36.69938
[1] 37.53345
[1] 42.0727
[1] 18.64279
[1] 31.91132
[1] 29.54339
[1] 20.29006
[1] 47.55138
[1] 58.82736
[1] 36.86683
[1] 32.7129
[1] 51.10835
[1] 66.80719
[1] 27.88307
[1] 39.90961
[1] 33.49959
[1] 31.87694
[1] 42.26957
[1] 41.03379
[1] 33.8576
[1] 31.6221
[1] 32.28134
[1] 44.04494
[1] 38.34329
[1] 41.56755
[1] 39.13246
[1] 45.64682
[1] 52.85198
[1] 43.72252
[1] 45.16151
[1] 33.58478
[1] 41.16782
[1] 26.90288
[1] 34.34716
[1] 36.71035
[1] 43.36019
[1] 58.68117
[1] 69.49682
[1] 41.21229
[1] 35.45775
[1] 34.49264
[1] 24.33397
[1] 20.36439
[1] 32.83696
[1] 36.24136
[1] 37.60363
[1] 24.68132
[1] 40.09941
[1] 47.89412
[1] 37.77065
[1] 29.7424
[1] 43.97063
[1] 41.82447
[1] 33.41347
[1] 38.3729
[1] 35.24997
[1] 45.79265
[1] 32.4056
[1] 39.57015
[1] 32.51704
[1] 27.68127
[1] 42.45385
[1] 33.48863
[1] 37.1469
[1] 35.32741
[1] 26.11765
[1] 36.6324
[1] 25.75717
[1] 35.07402
[1] 33.0943
[1] 49.344
[1] 29.92674
[1] 33.54529
[1] 43.15767
[1] 50.22389
[1] 27.72143
[1] 31.15555
[1] 54.20839
[1] 33.65614
[1] 39.51616
[1] 25.8231
[1] 37.70712
[1] 34.96732
[1] 27.58901
[1] 33.23093
[1] 43.01191
[1] 41.57814
[1] 43.38186
[1] 41.39563
[1] 25.26203
[1] 44.37839
[1] 51.24585
[1] 42.86233
[1] 43.63608
[1] 51.5776
[1] 18.6883
[1] 39.64474
[1] 32.18439
[1] 26.13325
[1] 46.46692
[1] 34.95713
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[1] 39.35209
[1] 33.71467
[1] 38.91935
[1] 51.26146
[1] 18.27418
[1] 66.41498
[1] 38.50605
[1] 32.68463
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[1] 27.62825
[1] 33.54979
[1] 60.02142
[1] 17.71183
[1] 32.6153
[1] 37.48766
[1] 31.75085
[1] 52.78063
[1] 32.70437
[1] 43.18142
[1] 18.77458
[1] 26.9894
[1] 35.33798
[1] 30.47414
[1] 43.79962
[1] 42.9525
[1] 35.7855
[1] 45.34698
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[1] 32.79698
[1] 48.16197
[1] 34.67957
[1] 40.80878
[1] 45.17544
[1] 38.77547
[1] 33.05253
[1] 51.89964
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[1] 39.20915
[1] 50.35115
[1] 37.90674
[1] 55.75273
[1] 26.04652
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[1] 31.76023
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[1] 59.88125
[1] 40.03987
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[1] 48.04228
[1] 38.4634
[1] 43.14407
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[1] 55.27894
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[1] 39.69707
[1] 40.9926
[1] 36.7838
[1] 32.2614
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[1] 49.6702
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[1] 34.86016
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[1] 53.26089
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[1] 49.69867
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[1] 45.65215
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[1] 36.56019
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[1] 58.43637
[1] 36.72514
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[1] 33.69489
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[1] 49.80464
[1] 28.6888
[1] 45.49871
[1] 25.26303
[1] 35.31102
[1] 38.12384
[1] 31.55337
[1] 40.64413
[1] 77.03901
[1] 39.73047
[1] 40.42259
[1] 59.87776
[1] 24.66105
[1] 36.22797
[1] 41.09026
[1] 32.05313
[1] 31.61
[1] 50.09587
[1] 33.92299
[1] 30.61021
[1] 63.85845
[1] 39.52916
[1] 25.08842
[1] 34.84235
[1] 40.13307
[1] 40.18545
[1] 27.6048
[1] 35.85832
[1] 38.30445
[1] 37.59044
[1] 34.33299
[1] 45.00231
[1] 35.68199
[1] 30.4718
[1] 42.48724
[1] 23.20108
[1] 20.89622
[1] 55.38993
[1] 30.15286
[1] 43.08617
[1] 37.35465
[1] 32.12689
[1] 53.32472
[1] 39.27198
[1] 33.13502
[1] 33.37785
[1] 37.65495
[1] 37.98707
[1] 29.36256
[1] 33.10138
[1] 45.7158
[1] 40.78512
[1] 42.15331
[1] 39.58987
[1] 37.70409
[1] 40.12005
[1] 34.00655
[1] 39.69036
[1] 34.43149
[1] 42.5554
[1] 43.33667
[1] 40.52849
[1] 23.41892
[1] 37.60957
[1] 39.86259
[1] 37.22817
[1] 30.34918
[1] 36.33683
[1] 36.43603
[1] 36.76487
[1] 36.17706
[1] 46.68365
[1] 43.65019
[1] 29.12467
[1] 26.78387
[1] 37.71159
[1] 28.13387
[1] 52.85106
[1] 35.02459
[1] 38.99707
[1] 39.75537
[1] 35.86104
[1] 38.40729
[1] 48.53471
[1] 36.84904
[1] 44.11756
[1] 41.66807
[1] 28.34708
[1] 39.1841
[1] 34.19937
[1] 30.9973
[1] 40.57681
[1] 41.46828
[1] 31.72425
[1] 26.29391
[1] 49.72706
[1] 34.72996
[1] 48.73647
[1] 38.20264
[1] 34.44347
[1] 31.59864
[1] 41.54795
[1] 33.31137
[1] 40.98113
[1] 34.64073
[1] 27.56192
[1] 27.04954
[1] 44.72
[1] 35.64761
[1] 38.01087
[1] 46.52477
[1] 36.31422
[1] 41.07894
[1] 36.42118
[1] 29.11752
[1] 25.92138
[1] 37.97018
[1] 29.29072
[1] 38.52507
[1] 36.10657
[1] 31.12793
[1] 28.40158
[1] 25.35098
[1] 49.26762
[1] 51.08119
[1] 37.68489
[1] 33.17734
[1] 52.61732
[1] 39.02655
[1] 36.45557
[1] 37.21335
[1] 33.62695
[1] 37.39917
[1] 15.30613
[1] 31.51765
[1] 50.88631
[1] 26.34187
[1] 34.4108
[1] 30.9762
[1] 32.59175
[1] 43.46184
[1] 45.17919
[1] 64.62102
[1] 34.22303
[1] 54.93573
[1] 29.91738
[1] 24.45546
[1] 48.09678
[1] 37.97369
[1] 36.35998
[1] 57.6099
[1] 36.95976
[1] 43.56874
[1] 48.08585
[1] 29.16239
[1] 37.66166
[1] 35.34712
[1] 42.67999
[1] 40.92838
[1] 15.85893
[1] 40.29474
[1] 32.46345
[1] 29.55166
[1] 33.88438
[1] 36.56891
[1] 46.56972
[1] 52.72271
[1] 32.04688
[1] 57.20739
[1] 44.74426
[1] 45.16404
[1] 28.22732
[1] 20.68555
[1] 30.522
[1] 32.33275
[1] 26.0816
[1] 19.09827
[1] 35.99611
[1] 26.713
[1] 34.12221
[1] 23.61896
[1] 22.10157
[1] 50.54869
[1] 38.58915
[1] 33.83468
[1] 48.09891
[1] 58.15456
[1] 51.34422
[1] 45.36348
[1] 28.38476
[1] 30.91507
[1] 45.16062
[1] 23.37506
[1] 33.30344
[1] 44.23197
[1] 34.92138
[1] 35.14542
[1] 23.39897
[1] 42.63267
[1] 47.46488
[1] 47.67284
[1] 36.12404
[1] 35.63165
[1] 27.46479
[1] 41.00197
[1] 41.86757
[1] 39.82999
[1] 30.61726
[1] 34.72688
[1] 24.54371
[1] 29.70401
[1] 34.882
[1] 36.77052
[1] 60.47502
[1] 36.42747
[1] 47.31384
[1] 48.93276
[1] 37.32833
[1] 34.07097
[1] 30.61807
[1] 29.4441
[1] 41.0316
[1] 23.76486
[1] 33.38029
[1] 43.64716
[1] 30.94445
[1] 29.52155
[1] 59.17457
[1] 30.55208

SMFI5 documentation built on May 2, 2019, 10:25 a.m.

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