Session 3 by kramkov

OPTIONS ON A SINGLE STOCK IN BLACK MODEL

PARAMETERS OF BLACK MODEL:

interest rate = 0.07
spot price = 100
convenience yield = 0.02
sigma = 0.2
lambda = 0.05
initial time = 0

quality = 200

AMERICAN BUTTERFLY OPTION IN ASSET MODEL

strike for put = 90
strike for call = 110

exercise times:
[0] = 0.0416667
[1] = 0.0833333
[2] = 0.125
[3] = 0.166667
[4] = 0.208333
[5] = 0.25
[6] = 0.291667
[7] = 0.333333
[8] = 0.375
[9] = 0.416667
[10] = 0.458333
[11] = 0.5

RISK REPORT: 

price = 4.08812
delta = 15.9525
one percent gamma = 4.37145

OPTION VALUES VERSUS SPOT:

    spot            option
 90.4837           4.60764
 92.3116           4.17745
 94.1765           3.90516
 96.0789           3.79648
 98.0199           3.85621
     100           4.08812
  102.02            4.4948
 104.081           5.07758
 106.184           5.83636
 108.329           6.76959
 110.517           7.87422

CALL ON FORWARD PRICE IN ASSET MODEL

strike = 100
maturity of call = 0.5
maturity of forward = 1

RISK REPORT: 

price = 8.21058
delta = 64.5263
one percent gamma = 3.06006

OPTION VALUES VERSUS SPOT:

    spot            option
 90.4837           3.27568
 92.3116           4.02644
 94.1765           4.89139
 96.0789           5.87537
 98.0199           6.98141
     100           8.21058
  102.02           9.56203
 104.081           11.0332
 106.184           12.6199
 108.329            14.317
 110.517           16.1181

CORRIDOR OPTION IN ASSET MODEL

notional = 100
lower barrier = 95
upper barrier = 110

barrier times:
[0] = 0.0416667
[1] = 0.0833333
[2] = 0.125
[3] = 0.166667
[4] = 0.208333
[5] = 0.25
[6] = 0.291667
[7] = 0.333333
[8] = 0.375
[9] = 0.416667
[10] = 0.458333
[11] = 0.5

RISK REPORT: 

price = 54.3701
delta = 97.8176
one percent gamma = -56.506

OPTION VALUES VERSUS SPOT:

    spot            option
 90.4837           27.3615
 92.3116           33.5957
 94.1765           40.1726
 96.0789           46.3612
 98.0199           51.3156
     100           54.3701
  102.02           55.1814
 104.081           53.6778
 106.184           49.9946
 108.329           44.5193
 110.517           37.9394

DOWN-AND-OUT CALL OPTION IN ASSET MODEL

strike = 100
maturity = 0.5
lower barrier = 90

barrier times:
[0] = 0.04
[1] = 0.08
[2] = 0.12
[3] = 0.16
[4] = 0.2
[5] = 0.24
[6] = 0.28
[7] = 0.32
[8] = 0.36
[9] = 0.4

RISK REPORT: 

price = 6.5385
delta = 61.83
one percent gamma = 2.48014

OPTION VALUES VERSUS SPOT:

    spot            option
 90.4837           1.49277
 92.3116            2.3008
 94.1765           3.23146
 96.0789            4.2505
 98.0199           5.35023
     100            6.5385
  102.02           7.82575
 104.081           9.21928
 106.184           10.7227
 108.329           12.3365
 110.517           14.0589

