Session 4 by kramkov

INTEREST RATE OPTIONS IN HULL-WHITE MODEL

PARAMETERS OF HULL-WHITE MODEL:

interest rate = 0.07
sigma = 0.02
lambda = 0.05
initial time = 0

quality = 200

FLOOR IN INTEREST RATE MODEL

floor parameters:
notional = 1000
period between payments = 0.25
number of payments = 6
rate = 0.063

RISK REPORT: 

price = 4.08996
delta = 398.264
one percent gamma = 296.342

OPTION VALUES VERSUS SHORT RATE:

 rate            option
 0.17       4.17648e-07
 0.15       4.74518e-05
 0.13        0.00213964
 0.11         0.0464362
 0.09           0.55477
 0.07           4.08996
 0.05           19.9818
 0.03            46.251
 0.01           75.4518
-0.01           105.822
-0.03           137.098

PUT ON FORWARD RATE AGREEMENT IN INTEREST RATE MODEL

maturity = 1.5
fixed rate = 0.07
period for FRA = 0.25
notional = 1000

RISK REPORT: 

price = 2.18092
delta = -102.188
one percent gamma = 28.6845

OPTION VALUES VERSUS SHORT RATE:

 rate            option
 0.17           17.8694
 0.15           14.7734
 0.13           11.4746
 0.11           8.04109
 0.09            4.7596
 0.07           2.18092
 0.05          0.704831
 0.03          0.147274
 0.01         0.0183603
-0.01        0.00125845
-0.03       4.30704e-05

CAP ON SWAP RATE IN INTEREST RATE MODEL

cap parameters:
notional = 1000
period between payments = 0.25
number of payments = 6
rate = 0.077

swap period = 0.5
number of swap payments = 12

RISK REPORT: 

price = 4.36882
delta = -404.811
one percent gamma = 298.131

OPTION VALUES VERSUS SHORT RATE:

 rate            option
 0.17           111.095
 0.15           88.3099
 0.13           65.0981
 0.11           41.6402
 0.09           19.2871
 0.07           4.36882
 0.05          0.672471
 0.03         0.0646337
 0.01        0.00349514
-0.01       9.36009e-05
-0.03       1.04045e-06

CANCELLABLE SWAP SET IN ARREARS IN INTEREST RATE MODEL

swap parameters:
notional = 1000
period between payments = 0.25
number of payments = 6
rate = 0.07
we pay float and receive fixed

RISK REPORT: 

price = 5.94534
delta = 833.463
one percent gamma = 315.767

OPTION VALUES VERSUS SHORT RATE:

 rate            option
 0.17          -24.3835
 0.15          -19.5869
 0.13          -14.7661
 0.11          -9.92099
 0.09          -4.77608
 0.07           5.94534
 0.05           27.9832
 0.03           55.4146
 0.01           84.6342
-0.01           114.826
-0.03           145.901

CANCELLABLE SWAP SET IN ARREARS IN INTEREST RATE MODEL

swap parameters:
notional = 1000
period between payments = 0.25
number of payments = 6
rate = 0.07
we pay fixed and receive float

RISK REPORT: 

price = 7.14615
delta = -860.464
one percent gamma = 286.232

OPTION VALUES VERSUS SHORT RATE:

 rate            option
 0.17           128.379
 0.15            104.33
 0.13           79.5925
 0.11           54.2357
 0.09           28.9507
 0.07           7.14615
 0.05          -4.35129
 0.03          -9.70442
 0.01          -14.6734
-0.01          -19.6669
-0.03          -24.6857

